AU2002215340A1 - System and method for cone beam volume computed tomography using circle-plus-multiple-arc orbit - Google Patents

Description

SYS EM AND METHOD FOR CONE BEAM VOLUME COMPUTED TOMOGRAPHY USING CIRCLE-PLUS-MULTIPLE ARC ORBIT Cross-Refcrcncc to Related Patents and Applications

1 he applicant is a named co-inventor in U S Patent No 5,999,587 and the named s inventor m U S Patent No 6 075,836 and co-pending U S Patent Application Nos 09/589,1 15 and 09/640,713, all of which concern subject matter related to the present invention The disclosures of all of those patents and applications are hereby incorporated by reference in their entireties into the present disclosure Field of the Invention

10 T he present invention is directed to a system and method for reconstruction of images from cone beam volume computed tomography (CBVCT) and more particularly to such a system and method in which the data are taken over an orbit having a circle and two or more arcs Description of Related Art

15 Among all possible applications of the Radon transform, computed tomography (CT) applied in 2-D medical and non-destructive test imaging technology may be the one that has achieved the greatest success Recognizing the demand for saving scan time in the currently available 2-D CT and consequently greatly improving its functionality, the implementation of CBVC T has been investigated for the past two decades.

'0 The intermediate function derived by Grangeat (P Grangeat, "Mathematical

Framework of Cone Beam 3D Reconstruction via the first Derivative of the Radon I ransiorm," Mathematical Methods in lomogi aphy Lectui Notes in Mathematic s 1497, G 1 I lei man et al eds , New York Springer Vcrlag, 1991 , pp 66-97) establishes a bridge between the piojection oi a 3-D object and its 3-D Radon transform md is much more

> numu i illy tiattablc than pieviously known mtumediate f unctions With the progress in undcistanding the so-called data suf ficiency condition foi an exact lcconsti uction, a few cone beam non-planai scanning oi bits, such as dual orthogonal cπclcs, helical, orthogonal cuclc- and-hnc non-orthogonal dual ellipse, orthogonal ciiclc-plus-aic, and even general vertex path have been proposed Coi iespondingly, the analytic algonthms to exactly leconsti uct a 3 D object based upon those non-planar scanning oibits have also been presented

Generally, a cone beam filtered back-projection (FBP) algorithm can make cone beam reconstruction much more computationally efficient and moie easily implemented in a multi- piocessor parallel computing structuie Hence, an FBP cone beam reconstruction algorithm is desirable practice, and Feldkamp's algorithm (L A Feldkamp, L C Davis, and J W Kress, "Practical cone-beam algouthm," J Opt Soc Am A Vol 1 , pp 612-619, 1984) for the circular orbit is the eai hest example Obviously, Feldkamp's algorithm violates the data sufficiency condition, and an accurate reconstruction without intrinsic artifacts is available only in the central plane overlapping the circular orbit plane, so that some accuracy on the off-central planes has to be sacrificed Although proposed independently, many algonthms of the pnor art featured a common structure of shift variant filtering (SVF) followed by cone beam back-projection Only 1 -D iamp filtering is employed m Feldkamp's algorithm, but a cascade of 2-D operations, such as w eighting, 2 D projection, differentiation and 2-D back projection, are involved in the shift v ariant filtering The complexity of the SVF (OfN⁴) ) is higher than that of the 1 -D ramp filtei ing of Feldkamp's algorithm (0(N³logN) ) Another important common featur e possessed by many algorithms of the pnor art is a normalized redundancy function ( NRf) adopted to compensate foi the multiple intersections of the projection plane with the source trajector y Recently, that kind of algorithm has been extended to a mor e genei al situation in which ΛΩ ai bitiaiy vertex path is involv ed as long as the data sul fie ieney condition is satisfied Appar ently the NRI is data-acqiiisilion-oi bit- dependent and has discontinuities in data acquisition oi bits which meet the data su l f ieieney condition, but it can be analytically calculated for either a specific data acquisition orbit or even an arbitrary vertex path. On the other hand, the algorithm by Hu (H. Hu, "A new cone beam reconstruction algorithm for the circle-and-linc orbit," Proceedings of International Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine, pp. 303-310, 1995; and H. Hu, "Exact regional reconstruction of longitudinally-unbounded objects using the circle-and-line cone beam tomographic system," Proc. SPIE, Vol. 3032, pp. 441-444, 1997) for an orthogonal circle-plus-line orbit is promising in saving computation resource, since a window function, instead of the NRF, is employed for the cone beam reconstruction from the projection data acquired along the line orbit. Due to mechanical feasibility, a circular x-ray source trajectory is still the dominant data acquisition geometry in all commercial 2-D/3-D CT systems currently available. Based upon a circular source trajectory, a number of data acquisition orbits can be implemented by either moving the table or tilting the CT gantry. An orthogonal circle-plus-arc orbit has been presented. It possesses advantages that can not be superseded by other "circle-plus" geometries, especially in the application of image guided interventional procedures requiring intraoperative imaging, in which the movement of a patient table is to be avoided. Further, it can be easily realized on a C-arm-based imaging system, which is being used more and more for tomography in recent years. The orthogonal circle-plus-arc orbit can be realized by acquiring one set of 2-D cone beam circle projections while rotating an x-ray source and a 2D detector on a circular gantry and then acquiring another set of 2-D cone beam arc projections while tilting the gantry along an arc which is orthogonal to and coincident with the circular orbit at the same radius. The exact CBVCT reconstruction algorithm associated with that circle-plus-arc orbit is not in the FBP form. The rebinning process involved in the algorithm requires storage for all information in the Radon space, and makes the CBVCT reconstruction computationally inefficient. Further, the arc sub-orbit provides information covering its Radon sub-domain only once, but the circular sub-orbit provides information covering its Radon sub-domain twice. That unbalanced coverage in the Radon space may result in non-uniformity of noise characteristic in reconstructed images.

A particular application of the present invention is in the detection of lung cancer and other malignancies. CT scanning plays a central role in much of the thoracic imaging used in detection of lung cancer and other malignancies. CT is non-invasive, easy to perform, and usually straightforward to interpret. It is either the primary modality or the referral modality for the detection of pulmonary masses (primary and metastatic), non-invasive staging of primary bronchogenic carcinoma, and for detection of major complications of malignancies, particularly pulmonary emboli, and infections. However, present helical CT has three major technical shortcomings. First, helical CT scans require a long or multiple breathholds for whole lung imaging, depending on slice thickness. Second, slice thickness vs. coverage vs. scan time tradeoff: programming thinner slices increases scan time or decreases coverage. The spatial resolution is not isotropic; through plane resolution is limited by slice thickness and a few times lower than that of in-plane. Third, the clinically achievable in-plane resolution for a large FOV, such as whole lung imaging, is limited and less than or equal to 1.0 lp/mm.

CT of the chest is a potential screening tool for lung carcinoma. While screening programs based on conventional x-rays had poor sensitivity and diagnosed most carcinomas after the window of surgical cure had passed, CT scans reveal nodules below 1 centimeter with higher potential cure rates. A drawback of screening CT is poor specificity. Benign sub-centimeter nodules are common (non-calcified granulomas, intrapulmonary lymph nodes, focal regions of atelectasis). The best diagnostic algorithm post-discovery of sub-centimeter nodules is unclear. Universal resection seems impractical. Potential diagnostic algorithms include evaluating the nodule enhancement, border characteristics, and growth. In all of these cases, accurate depiction of a small nodule is necessary. Helical CT, while readily delecting these nodules, has partial volume averaging problems in accurate characterization. It would therefore be desirable to provide a scanning system and method with sub-millimeter isotropic resolution, which would potentially better characterize the density and size of these small nodules. Accurate size measurement would allow short-term follow-up to evaluate for growth.

While CT screening for bronchogenic carcinoma in the high-risk population may or may not be clinically beneficial and economically practical, chest CT for the detection of metastases is commonly performed. CT is performed at the time of initial diagnosis, as interval monitoring for detection of disease, and as follow-up of detected nodules which are not initially resected. In all cases, improved detection and characterization, particularly that of interval growth, should be clinically beneficial.

Three image intensifier (IΙ)-based cone beam reconstructions for volume lung imaging have been reported before. However, all Il-based CBVCT for volume lung imaging suffers from inaccurate reconstruction due to the use of a single circle cone beam acquisition geometry and its corresponding approximating algorithm by Feldkamp et al, in addition to a limited perfoπnance of the II-CCD imaging chain. The best low contrast detectability of the Il-based cone beam CT for volume lung imaging is 10 HUs for a 3 mm object.

Summary of (lie Invention

It will be readily apparent from the above that a need exists in the art to overcome the above-noted limitations of the prior art. It is therefore an object of the invention to satisfy the data sufficiency condition while achieving a more balanced coverage. It is another object of the invention to do so in a computationally efficient manner which can be adapted to parallel cone beam reconstruction.

To achieve the above and other objects, the present invention is directed to a system and method for reconstructing images from data taken over a circle and two or more arcs. An FBP reconstruction algorithm is presented for reconstructing the images. The efficiency of reconstruction is critical for the application of CBVCT in the image- guided interventional procedures, and the reconstructed images with uniform noise characteristic are desired in practice. In order to overcome the previously mentioned shortcomings of the circle-plus-arc orbit and its associated Radon Transform-based reconstruction algorithm, a circle-plus-two-arc orbit and an analytic FBP cone bean reconstruction algorithm are used. The result given by Hu for the circular cone beam projections is directly incorporated. For the cone beam projections acquired along the arc orbits (namely, arc cone beam projections), originating from the equation established by Grangeat and the inverse Radon transform, an analytic reconstruction solution is obtained. That solution is different from known solutions because a window function, instead of an NRF, is employed to compensate for the multiple intersections of the projection plane with the x-ray source trajectory. Since its support in the Radon domain is very limited, the window function of the present invention significantly reduces the computational cost of the reconstruction from the arc CB projections.

Most objects to be reconstructed in medical or non-destructive x-ray CT are longitudinal ly unbounded. Hence, a cone beam reconstruction algorithm should address such a tuincdtion pioblem In order to solve the so-called tr uncated cone beam projection, several methods have been proposed It has been demonstiatcd that a finite region of interest (ROI), for which the extended data sufficiency condition is satisfied, can be reconstructed accurately, although that finite ROI is slightly smaller than the ROI which can be scanned by a detector I he circle-plus-two-arc orbit and its associated cone beam FBP reconstruction algorithm in the present invention are intrinsically capable of dealing with the truncation problem, and its thorough evaluation is accomplished herein

The circle-plus-arcs orbit possesses advantages over other "circle-plus" orbits for the application of x-ray CBVCT in image-guided interventional procedures requiring intraoperahve imaging, in which movement of the patient table is to be avoided A cone beam circle-plus-two-arc orbit satisfying the data sufficiency condition and a filtered back- projection (FBP) algorithm to reconstruct longitudinally unbounded objects is presented here In the circle sub-orbit, the algorithm employs Feldkamp's formula and another FBP implementation In the arc sub-orbits, an FBP solution is obtained originating from Grangeat's formula, and the reconstruction computation is significantly reduced using a window function to exclude redundancy in Radon domain The algorithm's merits include the following Only 1-D filtering is implemented even in a 3-D reconstruction, only separable 2 D interpolation is required to accomplish the 3-D back projection, and the algorithm structure is appropriate for parallel computation 1 he present invention has the following characteristics and advantages A flat panel detector (I PD) can be used I he invention can incorporate scattering correction and volume- of -interest (VOI) reconstruction I he present invention can be used for medical imaging, nondestructive testing or any other purpose in which such imaging is desired

In the reconstr uction algorithm of the preierred embodiment, all the components are in a filtered backpiojcction for mat I hat reconstruction algor ithm is moie computationally clllcicnt than those ol the pnoi ai t and is ready for parallel cone beam reconstruction I hat algoi ithm can be used to provide an exact reconstruction of a longitudinally unbounded object I hc CBVCT reconstruction of the preferred embodiment is the 3D matrix of attenuation coef ficient distribution of a 3D object In the present invention, the data arc taken through a scan such as a quasi-spiral scan

T o achieve the fastest scan, a simplified scan, such as only tilt in plus circle scan, can be used to satisfy the data sufficiency condition The second set of arc projection scans (gantry tilt-out scans) is optional to improve image quality The total acquisition time can be reduced by decreasing the sampling rate on the arcs or by using only a gantry-tilt-in plus a circle scan during the quasi-spiral scan

The present invention offers the following particular advantages when used to detect lung cancer First, the present invention requires a much shorter volume scanning time relative to helical CT In a single volume scan, an entire acquisition can be performed The present invention can improve acquisition efficiency by a factor of 25 for 1 mm slice thickness per volume scan vs a single ring helical CT Assuming a 25 cm segment to be scanned for a whole lung imaging and 1 mm/slice, the present invention can be at least 24 times faster than a single ring detector helical CT and 3 (for gantries with 0 5 sec /revolution) to 6 times faster than a multi-ring detector helical CT The fast volume scan eliminates the respiratory misregistration problems, such as those caused by the requirement that the patient hold his or her breath, and is less sensitive to patient motion

Second, the present invention can provide isotropic resolution in the x, y and z directions and provide h ue 3D reconstruction images I he spatial resolution of I PD-based CBVC I is limited by the fineness of our detector array, not by colhmation An I PD-based C BVC I achiev es sjiatial resolution on the ordei ol 1 -2 lp/mm in routine mode 1 he present invention can prov ide higher resolution in all thr ee directions than a helical C I T hird, the embodiment with ultra-high resolution VQ1 reconstruction can provide true 3D tomographic reconstruction with spatial resolution approaching that of screen-film projection imaging, but with 50 -100 times better contrast resolution than projection imaging. This spatial resolution capability cannot be achieved in any current helical CT. In addition, the present invention can more efficiently use x-ray tube output and greatly reduce the tube loading requirement. This will reduce the manufacture cost of CT tubes because a very heavy duty and very costly x-ray CT tube ($60,000 - $ 100,000/tube) may not be needed, and/or the operating cost because the life of a CT tube will be many times longer. The present invention thus improves the sensitivity and specificity of lung cancer detection as well as other types of cancer detection. In addition, it will highly significant to the early detection and management, not only of lung cancer, but also of other malignancies.

There are several radiological or biological characteristics of carcinoma that can be imaged. First, carcinoma has different x-ray linear attenuation coefficients from surrounding tissues. Second, carcinoma has a substantially higher volume growth rate compared to a benign tumor, which laσks growth. Third, carcinoma has border patterns distinguishable from those of a benign tumor. Fourth, benign tumors show different contrast enhancement after intravenous contrast injection. Fifth, the presence of neovascularity can indicate cancer. Conventional cancer detection techniques such as chest projection imaging rely mainly on the first characteristic and partially use the third characteristic for cancer detection. Since mammography is a two-dimensional static imaging technique, it cannot provide any information regarding characteristics 2, 4, or 5. The present invention, by allowing fast scans and permitting the use of contrast injection if desired, can be used to detect cancers in accordance with all five characteristics. CT scanning is a key modality for detecting pulmonary malignancies. It can detect lesions as small 2-mm diameter. It is, however, imperfect for detection of nodules for the following reasons:

Nodules may not be imaged if the lungs cannot be scanned in a single breathhold. Respiratory misregistration occurs when a CT scan of the lungs is acquired in several different breathholds. Because patients do not reliably hold their breath in the same phase of respiration, and because pulmonary lesions move cranially or caudally with respiration, a CT scan composed of slices obtained from different breathholds may fail to detect a lesion because that lesion was never imaged. The present invention permits scanning the entire lungs in a single breathhold and thus can eliminate this source of detection error.

Nodules may be present on the CT images but fail to be recognized by the interpreting radiologist. A retrospective review of nine patients with missed lung cancer on CT found five missed tumors that were peripheral and <3mm in diameter and four central tumors measuring up to 8 mm in diameter. These small peripheral nodules were likely not seen while the larger central nodules were not recognized set against the background of the larger complex branching vessels. Review of a CT dataset electronically, and in planes other than the axial plane might also prove to have further increase in sensitivity for nodule detection. The present invention provides the first system capable of scanning the entire chest with sub- millimeter isotropic resolution. Isotropic resolution with sub-millimeter resolution in all directions would be ideally suited for electronic interpretation in axial, oblique, coronal and sagittal planes.

Partial volume averaging with adjacent lung can make small pulmonary nodules difficult or impossible to detect by helical CT^". Helical CT^" of canine metastatic osteo aroma found 44% of metastases <5 mm vs. 91 % of metastases >5mm. Usually, helical CT reconstructs images at an interval approximately equal to the colliniation, 5-7 mm. Some clinically relevant nodules are smaller than the slice thickness. Reconstructing images at a smaller reconstruction interval increases the sensitivity for lung nodule detection. This is due to the non-linear slice sensitivity profile of helical CT reconstruction. These overlapping reconstructions have a better chance of placing small nodules in the center of the slice where they will be displayed with higher density and be more easily seen. The present invention can overcome this problem because slices at <1 mm thick would essentially eliminate partial volume averaging and also assure that a nodule larger than 3mm would have a slice through its approximate center.

Nodule size is difficult to measure accurately by helical CT. The apparent size of a pulmonary nodule depends on the thickness of the slice and where the slice is reconstructed relative to the nodule. Accurate size measurements of the nodules are necessary to detect small amounts of growth in short-term follow-ups. A 3 mm diameter nodule growing to 4 mm diameter has more than doubled in volume. Because the detection of small nodules is becoming increasingly common due to helical CT, it is likely that imaging algorithms will need to incorporate follow-up of small nodules for growth. Accurate sizing would be essential. CBVCT will provide 0.125 — 0.7 mm voxel size and will allow accurate measurements of nodule size and nodule volume.

Small nodule density (attenuation coefficient) is difficult to measure accurately by helical CT. The apparent density of a pulmonary nodule in helical CT depends on the position of the nodule relative to the position of the reconstructed slice. The relative movement of the slice by one or two mm may make a calcified nodule appear non-calcified. For nodules smaller than the slice thickness (routinely 5- 10 mm in helical CT), there is partial volume averaging of the nodule with adjacent air and an accurate density can not be determined, ^"fhe nodule density is useful for characterization in two major respects. One is the detection of calcification indicating benignity, ^'fhe second is that malignant pulmonary nodules appear to have more rapid contrast enhancement than benign nodules. Sub- millimctcr thick slices, achieved by CBVCT, will allow accurate density measurements of small nodules without partial volume averaging and without necessity for post-processed overlapping reconstructions. This should better detect calcification, and more accurately characterize the amount of enhancement.

Fine spiculations and other nodule border characteristics are best determined with high resolution CT. On helical CT scanners, this requires locating the nodule prospectively, as it is impractical to acquire high-resolution CT 1 -mm thick slices throughout the entire lungs. CBVCT would acquire high-resolution images through every nodule without prior knowledge of its location or the need for technologists or physician localization during the scan. The ultra-high resolution VOI reconstruction mode of CBVCT will provide even higher resolution for target imaging after the survey lung imaging of CBVCT with lower resolution. This mode may be even more useful for characterizing nodule border. The value of universal high resolution CT for characterizing benign vs. malignant nodules may also prove beneficial.

A particular implementation of CBVCT provides high contrast resolution of 0.7 — 4 lp/mm, and low contrast detectability of 3-5 CT number within a short breath hold (2 - 8 seconds). Such an implementation preferably includes an appropriate 2D detector system which has a high detection quantum efficiency (DQE), high dynamic range, high spatial resolution, minimal geometric distortion, and which is capable of high image acquisition rates with little image lag and excellent linearity. It also preferably includes a data acquisition scheme that will result in a complete set of projection data with little additional mechanical complexity. This provides an exact cone beam reconstruction algorithm which is based on the complete set of data, thereby permitting imaging in a large FOV (for example 14" - 16"). A thud aspect which is piefeiably included is x-ray scatter control and collection techniques to furthei improve low contrast dctectability

T he present invention expands the application of CBVC T fiom angiography to volume lung imaging and other applications that require soft tissue differentiation CBVCT can potentially be applied to pulmonary emboli detection, liver cancer detection, volumetric brain perfusion, diagnosis of acute stroke, and colon cancer detection, etc

For lung cancer and other malignancies, the present invention has application to malignancy detection, monitoring, management and treatment and in particular to the development of treatment plans.

I \ Brief Description of the Drawings

A preferred embodiment of the present invention will be set forth in detail with reference to the drawings, in which:

Fig. 1 is a schematic drawing showing a cone-beam projection; Fig. 2 is a schematic drawing showing a Radon plane;

Fig. 3 is a schematic drawing in Radon space showing the inability of the circular orbit alone to satisfy the data sufficiency condition;

Fig. 4A is a schematic diagram showing the ability of the circle-plus-two-arc orbit to satisfy the data sufficiency condition; Fig. 4B is a diagram of a quasi-spiral scan used to implement the circle-plus-two-arc orbit;

Fig. 4C is a diagram of a scan used to implement a circle-plus-two-line orbit; Fig. 4D is a diagram of a scan used to implement a helical orbit;

Fig. 5 is a schematic diagram showing the coordinate system and parameters used in the reconstruction of the circular projection;

Fig. 6 is a schematic diagram showing the coordinate system and parameters used in the reconstruction of the arc projections;

Fig. 7 is a plan diagram of a system on which the preferred embodiment is implemented; Figs. 8-1 1 show stages in the operation of the system of Fig. 7; and

Figs. 12A and 12B show a setup for taking scout images for scatter correction. Detailed Description of the Preferred Embodiment

A preferred embodiment of the present invention will now be set forth in detail with reference to the drawings. First, the reconstruction algorithm will be derived. Second, a device on which the reconstruction algorithm can be implemented will be shown. The cone beam projection of a 3-D object is schematically illustrated in Fig. 1 , where

O is the origin of the coordinate of the real 3-D space IR , upon which the algorithm is

derived. Tand Z are the local axes in the plane of the virtual detector. OS = Φ is the vector which represents the cone beam focal point S, and point A ' is the projection on the detector plane of A, which is a point within the 3-D object to be reconstructed, along the unit directional vector

σ = -=____- . (1)

\ SA \

The vector from O to A is f . The cone beam projection of the 3-D object f(r) is defined as:

The reconstruction algorithm is derived for a longitudinally bounded object first, and its capability of regionally reconstructing a longitudinally unbounded object will be analyzed in detail later. Since most objects to be reconstructed in medical and non-destructive test tomography are cylinder-like, the 3-D object to be reconstructed is assumed to be a cylinder whose half height is represented by h, and radius by R.

The definition of a 3-D Radon plane P(/ , p) is schematically illustrated in Fig. 2, where

n = (sin0 eosφ , sinϋ sinφ ,cosθ ) (3) is the normal vector, and p the distance away from the coordinate origin O. In 3- Cartesian coordinates, any plane can be uniquely identified by a normal vector and a distance away from O and is the set of all points for which

r ^■ - p = 0. (4) Recognizing the existence of several versions of the data sufficiency condition, the preferred embodiment uses the one which can be the most simply expressed: All planes passing through the object to be reconstructed must contain a point in the scanning orbit. Obviously, a circular orbit, which is the simplest in practice for 3-D reconstruction, violates the data sufficiency condition in a way demonstrated in Fig. 3, i.e., the Radon transform of the circular CB projections provide no coverage on the shadowed sub-domain in the Radon space. In the perspective of inverse Radon transform, the sub-domain missed in the Radon space by the circular orbit (namely missed Radon sub-domain) has to be covered by additional non-circular orbits.

The requirement for the circle-plus-one-arc orbit to meet the data sufficiency condition and cover the 3-D cylinder object to be reconstructed completely is known in the art to be (see Fig. 4A):

h ^ λ„ = 2 tan^" (6)

D - R, where R is the radius of the cylinder object to be reconstructed, D is the radius of the arc

orbits, and λ_lπ!lι ^ is the minimum arc spanning angle range of the whole single arc.

Since an uneven sampling is achieved by the circle-plus-arc orbit in the missed Radon sub-domain, some artifacts may occur in reconstructed images. Further, the arc sub-orbit is in odd-symmetry in the- plane determined by itself. Such an odd-symmetry makes the non- uniformity of the sampling in Radon space worse, and may result in more reconstruction artifacts On the othei hand, the redundancy function equals 1 within the missed sub domain in the Radon space, while the redundancy function equals 2 within the sub-domain covered by the cuculai data acquisition oibit In the pcispective of signal piocessing, that kind ol difference in the redundancy function results in an uneven noise characteristic in reconstructed images lo avoid the artifacts caused by the odd-symmctiy and maintain identical Radon information redundancy between the sub-domains covered by the circular and arc orbits respectively, a circle-plus-two-arc orbit is used in the preferred embodiment, although the invention could be adapted for a circle plus more than two arc orbits As schematically shown in Tig 4A, the circle-plus-tvvo-arc orbit consists of a circle and a pair of arcs One is called arc sub-orbit 1 and is represented by the solid curves, the other is called arc sub-orbit 2 and is represented by the dashed curves The arc sub-orbit plane is perpendicular to the circular sub-orbit plane, and they are concentric at point O with the same radius D It is noticed that an even-symmetry is achieved by integrating arc sub-orbit 1 and

arc sub-orbit 2 in the arc sub-orbit plane (x₀,y_o)

In the fixed coordinate system (x₀,y_o,z_t ) illustrated m Tig 4A, the circle-plus-two-

arc orbit can be analytically depicted as

j φ_0ι(λ) = ( cosλ, smλ, 0) jλeΛ,,' =[-λ_mιn__l/, 0]U[π-λ __d, π] ⁽⁸⁾

j φ_βi(λ) = (Z)cosλ Dsmλ 0)

[λeΛ„ =|0 λ_Ml U[π, π +λ, _1M ,\ ⁽⁹⁾

wheie φ,(λ) represents the circle sub-orbit, and φ_t (λ) the aie sub-orbit 1 and ψ. (λ) the

aie sub orbit 2 respectively I heoretieally the minimum cone angle for each are in the circle-plus-two-arc orbit is cut down to half that required by the single arc in the circle-plus- one-arc orbit

Accordingly, the reconstruction algorithm can be most broadly expressed as

where f_c(r) is the component reconstructed from the sub-domain in the Radon domain

support corresponding to the circular cone beam projections, and f„(r) the component of the

arc cone beam projections.

The coordinate system on which the reconstruction algorithm for the circular cone

beam projections is derived is illustrated in Fig.5. (x, ,y, ,z,) is the local coordinate system which rotates rigidly in phase with the detector, r represents a vector that determines a point

A within the 3-D object to be reconstructed, and (Y,Z) is the coordinate of the projection of

A in the detector coordinate system. The circular sub-orbit is within the plane determined by

(z₀,x₀), and P_φ(f,Z) is the cone beam projection with the source focal point at Φ .

It has been shown that f_c(r) can be further split into:

fλ7)-f_Cι{r) + f_Cι{r) (12)

f ( ) corresponds to the FDK algorithm and can be obtained using the following formulae

that are modified to match the coordinate system shown in Fig.5:

> ,'(/,-.\=, --.;,, I⁾ , A .,{tr- )\=, -^■■=,—- v_ (14)

I) - ^■ x, I) -- /^■ • x_t

jμ|Jωcxp(/ωZ) (17)

Where ω₀ is the integial limit, which is determined by the spatial sampling liequency of the

detector, in the Fourier domain

On the other hand, f_c (r) can be obtained using the following formulae that are also

modified to match the coordinate system shown in Fig 5

γ{τ) = r v_{t n} ^D (i9)

D-t x,

P_φ {¥) = j-a _φ (Y) (Y - v _φ (Y)dy (20)

^h _jai})= Jyωcλp ωI^'Vω (23)

where L. is the integral limit along the Z direction, and ω₀ is the same as that in (17)

Both (13) and (18) aic in the FBP form, and reconstruction Irom the circular cone

beam projections is computationally clfieicnt because only 1 D filters b ,_|(~) <»ιd (j>) aie

involved in the filtering process In the digital signal processing point of View and

^Λ» H lc-iyl n ^with „ _{≠ 0} ⁽²⁵⁾

In order to reduce numerical artifact and constrain noise, a Hamming window is implemented while filtering.

It is known that the Radon transform of the circular CB projections fulfills only a torus in the 3-D Radon domain. As argued by Hu, the assumption that the redundancy function equals 2 is valid only for the Radon domain point inside the torus. With respect to the Radon domain point on the boundary of the torus, which corresponds to the tangential intersection of the projection plane with the circular orbit in the spatial domain, the redundancy function equals 1. Hence, the reconstruction implemented using Feldkamp's algorithm takes only the contribution from the Radon domain point inside the torus. In order to take the contribution from the Radon domain point on the boundary of the torus into

account, the complementary term f_c (f) should be incorporated into the algorithm to

implement the reconstruction from circular cone beam projections.

As elucidated above, employing the arc sub-orbits provides information in the Radon domain to cover the missed Radon sub-domain. Considering computational efficiency, a reconstruction algorithm for the arc cone beam projections in the FBP form is desired in practice. Before the transform itself is presented, some variables will be defined with ref ence to Fig. 6, The Radon plane containing S and A intersects the detector to define a line .segment having end points I)\ and >.>.. T he point of closest approach of that line segment to () is at a point C 1 he line segment connecting O to C has a length / and defines an angle O with the

)>ι axis T he origin S of the cone beam is along one ol the aic oibits at an angle β fiom the _Λ„

I he 3-D Radon transform and its mveisc of the object /(/^") are defined respectively as

(26)

Based upon the geometry shown in Fig 6 and originating from the equation established by Grangeat and the inverse Radon transform in Equation (27), the reconstruction algorithm for the arc CB projections can be written as (sec APPENDIX A)

L(r) = 5 /_O|(r) + 05 f_aι(r) (28)

where the factor 05 is to compensate for the data redundancy resulting from the double coverage on the missed sub-domain in the Radon domain by the two arc sub-orbits, and

f_a v*⁷) ( ' ^~ (12} ) can be expressed in the FBP form

/„( > (P, Θ)rfΘrfβ (29)

Λ >

/₍(β,ΛΘ)= J J/jι,(l Z)δ(⁾ smΘ + ZcosΘ-/ /F / rZz (31)

/ /J

>^'( = / V ant Z( )=. (32)

D-Γ χ_t / -/^" wlicic 7 represents a vcetoi that determines a point '1 within the 3-D object to be

reconstructed, (),/) '^ the coordinate' of the projection ol Λ in the detector coordinate system, )',- and Z, are the integral limits along J' and Z xes respectively, P_[K/ ()', Z) ( /= /, 2} )

is the cone beam projection at angle β along the arc orbits, and

1 /sin β > D - (l - cosΘ cos β ) u{β ,/,Θ) = 1 /sin β < - - (l + cosθcos β ) (33) 0 elsewhere

is the window function derived in Appendix B to resolve the data redundancy and constrain the back-projection for the arc cone beam projections. The support of the window function

i β, /,Θ) in the sinogram domain is very limited, and the computational resources for the

reconstruction from the arc cone beam projections can be saved substantially. Both the 1 ^SI and 2^π derivative of the sinogram along the distance direction are obtained using the 1 -D

linear digital operator h_/ω (n) .

Notice that the algorithm structure of Equations (29)-(33) look similar to the algorithm presented by Hu. However, there are important differences between the derivation of Equations (29)-(33) and that in the prior art. First, each source point defines a sphere in the Radon domain (namely the Radon sphere), and the diameter of a Radon sphere is determined by the distance between the source point and the origin of the coordinate system. The diameters of the Radon spheres along the arc sub-orbits in that algorithm are constant, but those along the line sub-orbit are variable. With respect to the FBP CBVCT reconstruction, a series of Radon spheres with identical diameter will sample the missed Radon sub-domain more uniformly than a scries of Radon spheres with varying diameters. It is possible for a more uniform sampling in the missed Radon sub-domain to create less artifacts in the FBP cone beam reconstruction. Second, the window function (33) is distinct from that in the prior art.

^"flic capability of regionally reconstructing a longitudinally unbounded object is essential for the application of CBVCT in medical or non-destructive test imaging, since most

-n ob_jects to be leconstiucted in practice arc longitudinally unbounded (that is also called the li uncation pioblcm) I he circlc-plus-two-arc oibit satisfies the extended data sulfieieney condition pioposed by Kudo and Saito (H Kudo and T Saito, "An extended completeness condition for exact cone-beam reconstruction and its application," Ihllll Conf Rec 1994 Nutleai Science and Medical Ima i g, Symposium Norfolk, Virginia, pp 1710- 1714, 1995) Consequently, its associated cone beam FBP reconstruction algorithm presented above

addresses the truncation problem by employing the window function w(β , /, ©) , even though

the object to be reconstructed is assumed longitudinally bounded in its derivation That means that an ROI within a longitudinally unbounded object can be exactly reconstructed if the ROI is smaller than the region that can be completely covered by the x-ray tube-detector during a scan along the circle-plus-two-arc orbit

On the other hand, both h^( ) and h_ju (n) involved in the reconstruction algorithm

further lessen the ROI that can be exactly reconstructed As shown in (15), the filtering by

l _| («) is implemented latitud ally m obtaining f_t[ (τ) Since the object to be reconstructed

is latitudmally bounded, ^(n) incurs no contamination to f_c (f) However, the filtering by

h (n) is implemented longitudinally in reconstructing _Cj (f) (20), and incurs contamination

to f_c (r) because of the longitudinal truncation Similarly, the filtering by h_Ja (n) incurs

contamination to f_a ( ) ( ι = {I 2} ) Fortunately, both h_M(n) and h ψ) are square

summable and drop dramatically, and make the contamination depth resulting from them to

/;, ( ) f T) /,„ (/-) and A, ( ) v eι> limited

I heoictieally, data redundancy can be used to mipi ov e the signal to noise ratio (SNR) of a leconsti ucted image in CBVC I However, unlike nucleai medicine acquiring l cdundant projection data in an x-ray ( BV( I may result in unnecessary radiation to a patient l heieloi e a candidate scanning or bit loi application in in ( BVt I should keep the

^"> 3 data redundancy as low as reasonably achievable (AFΛRA criterion) while satisfying the data sufficiency condition and maintaining the image quality of a reconstructed image clinically acceptable. ^'Fhe circlc-plus-two-arc orbit with the cone beam FBP reconstruction algorithm presented here is one that meets the ALARA criterion. Hence, the evaluation of its performance, such as the quality of the reconstructed image as a function of arc orbit angle sampling interval, arc orbit spanning range, and x-ray source quantum noise levels, as well as its capability to regionally reconstruct a longitudinally unbounded object, is practically important. In order to avoid the transition between the circular data acquisition and the arc data acquisition, the circle-plus-two-arc orbit can be implemented through a "quasi" spiral scan. In that scan, the x-ray tube- detector mounted on a circular gantry continuously rotate. The circular sub-orbit is realized by acquiring 2-D cone beam projections at evenly distributed angular positions along one circle of the x-ray source trajectory while the tilting

angle of the gantry is 0° (see Fig. 4B). The arc sub-orbits are realized by acquiring 2-D cone beam projections at both the top and bottom arcs . The quality of the reconstructed images is still acceptable while the arc sub-orbit sampling interval is only half the circular sub-orbit sampling interval. That means that the total turns of the "quasi" spiral scan in the circle-plus- two-arc orbit can be decreased significantly. Hence, the data acquisition time along the arc sub-orbits can be reduced remarkably. Such a significant decrease in data acquisition time is practically important in the application of CBVCT in the image-guided interventional procedures.

Th capability of the cone beam FBP algorithm to regionally reconstruct a longitudinally unbounded object has been verified, ^"fhe survival of the algorithm from the truncation problem is essential for its application in CB VCT. On the other hand, in the case of shortened arc sub-orbits that violate the data sufficiency condition, a regional exact

2-1 reconstruction can still be obtained. That means that the spanning range of the arc sub-orbit can be lessened if only an ROI within the object is to be reconstructed.

In implementing the algorithm on a computer system, the reconstruction load is divided into several parts and run in parallel on a RACE parallel computation system which is a scalable multi-processor-based system and is provided by Mercury Computer Systems. Initially, a RACE with 8 upgraded processors will be used, so that the reconstruction time of the algorithm will be 10 - 12 minutes. Further reducing the reconstruction time by parallel computation to 2 minutes for 512³ matrix reconstructions, for 288 projections with 512 x 512 pixels per projection, can be achieved using a RACE having 16-32 processors with 1024 Mbytes RAM at a relatively low cost.

In a standard CT, a 3-D reconstruction is obtained by stacking a series of slices. In an CBVCT, a direct reconstruction of an object can be obtained. Referring now to FIG. 1, it is shown how a CBVCT system 700 of the present invention can be used to obtain a direct 3-D reconstruction of an object. It should be understood that the CBVCT scanning apparatus 700 is illustrated in a simplified block diagram form. The invention may preferably be employed in conjunction with such a CBVCT scanning apparatus to generate a 3-D reconstruction matrix of the object. Based on the 3-D reconstruction matrix, the desired three-dimensional display can be obtained.

A CBV CT scanning apparatus examines a body P using a cone shaped radiation beam 704 which traverses a set of paths across the body. As shown in FIG. 7, an x-ray source 710 and a 2-D detector 71 1 such as a flat-panel detector arc mounted on a gantry frame 702 which rotates around the body P being examined, ^'fhe operating voltage for the x-ray source is obtained from a conventional high-voltage generator 708 in such a manner that the x-ray source 710 produces the desired cone-shaped beam of radiation when the high-voltage is applied to it. Fhe high-voltage generator 708 is energized by means of a pow r source 718, through a switch 716.

A first motor 712 is also powered by the power source 718 such that it drives the gantry frame 702 in its orbit about the body, for example, in a clockwise direction as shown by the arrows adjacent to the frame, ^'fhe power source 718 is turned on by means of switch 720 or other conventional control devices, in order to initiate a measurement sequence. A speed control circuit 714 is used to control the speed of rotation of the gantry frame 702 and to provide an output control signal which indicates when the speed of the motor 712 is at the desired level for taking measurements. The output from the rotational control 714 may also be utilized to operate the switch 716 such that the high-voltage generator 708 is only turned on when the gantry frame 702 is driven at the desired speed for making measurements.

In order to obtain the arc measurements as previously discussed, a tilt control 715 is utilized to cause the gantry frame 702 to tilt by a relatively small angle of ±15° to ±30°, by means of the gantry frame tilt motor 713. That tilting allows the acquisition of arc projection data on the perpendicular arc. Such geometry results in a complete set of data for an object with a 25-40 cm diameter corresponding to a 37-60 cm field at the detector 71 1 with a magnification of 1.5. Although the tilting of the gantry 702 is generally available in a standard CT gantry, to acquire arc projections, the minimal modification of a standard CT gantry has to be made such that the tilting of the gantry, the x-ray exposure timing and the projection acquisition are synchronized by a system control computer 724 having a clock 722.

The gantry can be based on modifications of existing equipment made by such companies as GF, Siemens, T oshiba and Marconi. Such modifications include replacing the one-dimensional detector with an I I-C D defector or a silicon or selenium thin film transistor array FP and the old computer system and its control interface boards with a new host computer and new inter lace boards As explained in the co-pending applications cited above, a slip ring is pieferably used to permit communication between equipment on the gantry and equipment off the gantry Initially, volume scanning speed will be only limited by the maximum fiame rate of the real time FPD Currently available real time I PDs have a frame rate of 15 120 frames/sec I he flat panel iesearchers predict that the future frame rate can be up to 120 frames/sec (I K λ I K pixels/frame) and 480 frames/sec with reduced vertical readout lines (256 x 1 pixels/frame) When the frame rate of the detector is increased to 480 frames/sec for a large size FPD in the future, the volume scanning time of entire lungs will shorten to 1 2 seconds depending on the required resolution and/or the projection number can be increased to improve image quality Compared to Il-based VTDA systems the FPD-based CBVCT system represents a significant technologic advancement due to using flat plane detector, slip ring technology, and cone beam reconstruction algorithms that result in accurate reconstruction In addition, the CBVCT system can incorporate a scaleable multiprocessor- based parallel computing system (8-32 processors) provided by Mercury Computer systems A specific scanning protocol will now be described which implements -15 to +15° tilting to obtain 25 cm coverage in the z direction This protocol consists of four steps 1) Positioning gantry — Before starting the scan, the gantry tilts to -15° to prepare for CPA scan, 2) Arc-Projection Acquisition (Gantry tilt-in) -- While the gantry is tilting from -15° to 0°, the x-ray tube and detector rotate, taking projections only at 0 (on the upper arc) and 180 (on the lower arc) of the rotation angle positions to obtain two arc projections per rotation, 3) Circle Projection Acquisition -- When the gantry tilts to a 0 tilting angle the gantry stops tilting and the x ray tube and detector rotate to acquire multiple circle projections and 4) Arc-Projection Acquisition (Optional Gantry tilt out) I! necessary, after completing circle scan the gantry tilts liom 0 to 1 1 5 while the x-ray tube deteetoi lotates taking aie pι θ|eclιons as in step 3 I iguie 4B shows a eiiele-plus-aie scan with six n c projections taken at the positions labeled 1 through 6 along the upper and lower arcs. Fig. 10 shows exposure with the gantry tilted, while Fig. 1 1 shows exposure with the gantry not tilted.

To reduce circle-plus-arcs CBVCT scan time , the quasi-spiral scan mode of the gantry is used because during the scan, the x-ray tube and detector continue rotating on the gantry while the gantry is tilting and the gantry stops tilting at 0 tilting angle to acquire circle projections. The quasi-spiral scan mode eliminates the need to stop the rotation of the x-ray tube and the detector during the scan and reduces the transition time between arc acquisition and circle acquisition. In addition, a complete set of cone beam projection data can be achieved using two opposite half arcs (1-4 arc projections) and a single circle scan orbit. For example, as shown in Fig. 4B, arc projections can be taken only at locations 1 -4, or only at locations 5 and 6, corresponding to gantry tilt-in without tilt-out. With two complete arcs, e.g., projections at all of locations 1 -6 of Fig. 4B, image quality is better. Therefore, gantry tilt-out is an optional mode which can be eliminated in the interest of time constraints. In other words, if the imaging task requires high temporal resolution to reduce motion artifacts or to obtain dynamic information, only a gantry-tilt-in arc scan and a circle scan are required, which reduce the arc scanning time to half.

In detection of lung cancer, since only 25 cm of the trunk of the body will be viewed per scan in the z direction, the gantry needs to be tilted ±15° at most. The volume scan time should be 4-8 seconds, depending on the achievable tilt speed, how large the segment in the z direction is actually viewed and the acquisition rate of the detector. The system provides computer-controlled gantry tilt and synchronized x-ray exposures with 2 exposures/sec for arc projection acquisition. A bidirectional encoder, which is used on the current gantry to track projection angle in the step mode, will be installed to track the projection angle on the arc. ^'Fhe tilt speed on the arc will be 7.5°/sec and the projection numbers on the are wil l be 4 to 12. Since the CBVCT system is based on an existing helical CT gantry and table, the system should have an existing computer-controlled table movement capability. With little modification, a circlc-plus-line (CPL) scan can be achieved. Two bidirectional encoders are added: one is to track the longitudinal position of the x-ray source and the detector, and another to track the angular position of the source and detector. Then the system will be modified to synchronize x-ray exposure with 2 pulses/sec for line projection acquisition. Since only 25 cm of the trunk of the body in the z direction will be viewed per scan, the patient table is fed for 25 cm with the maximum feeding speed of 12.5 cm/sec, and then the volume scan time should be within 4-8 seconds, depending on the achievable feeding speed, required resolution and the actual size of the coverage in the z direction per scan. For detection of cancers such as lung cancer, circle-plus-lines and helical cone-beam scanning can also work.

In addition to the method above to acquire circle and arc projections, alternatively, the circle-plus-arc geometry can be implemented in one of the following two ways. In the first and preferred of the three methods, the gantry 702 is tilted to a small angle (±15° to ±30°.) and then the x-ray tube 710 and the 2-D detector 71 1 are rotated while the gantry 702 is tilted. A half set of arc projections will be acquired only when the x-ray tube 710 and the 2-D detector 71 1 are at the rotation angles of 0° and 180 . When the tilted angle becomes zero, the circle projections will be acquired at the preset rotation angle positions. When the circle projection acquisition is completed, the gantry 702 will be tilted toward - 1 5° to -30°. Another half set of arc projections will be acquired only when the x-ray tube 710 and the 2-D detector 71 1 are at the rotation angle of 0° and 1 80°.

The second alternative method is to mechanically modify a standard CY gantry such that two short arc orbits are added to the gantry, and the x-ray lube 710 and the 2-D detector 71 1 can be moved on the are to acquire the are projections and on the circle to acquire the

2^l> circle projections. One arc constitutes the orbit of the x-ray lube 710 and the other arc is the orbit of the 2-D detector 71 1. ^'Fhe two arc orbits are mounted 180° apart from each other. 'Fhe x-ray tube 710 and the 2-D detector 71 1 aie synchronously moved on the arc orbits to acquire arc projections. Then, the x-ray tube 710 and the 2-D detector 71 1 are rotated on the gantry to acquire circle projections.

Mounted on the gantry frame 702 opposite the x-ray source 710 is a 2-D detector 71 1 which has a dynamic range equal to or greater than 1000: 1 and an image lag of less than 10%, for example a selenium thin film transistor (STFT) array or a silicon STFT array, in order to provide 2-D projections that correspond to an x-ray attenuation signal pattern. The x- ray source 710 and the 2-D detector 71 1 are mounted on the gantry frame 702 in such a manner that they both move synchronously.

The cone-shaped beam of radiation 704 generated by the x-ray source 710 is projected through the body or object under test. The 2-D detector cone measures the radiation transmitted along the set of beam paths across the cone. Alternatively, a continuous series of two-dimensional detectors (not shown) can be fixedly mounted proximate to the gantry frame 702 and the x-ray source 710 is mounted to the gantry frame such that, upon rotation of the gantry frame, the cone-shaped radiation beam 704 is projected through the body P under test and sequentially received by each of the series of detectors. A 2-D projection acquisition control and A/D conversion unit 726, under control of the scanning pulses sequentially obtained from the system control computer 724, which includes the clock 722, receives a sequence of outputs corresponding to different lines of the 2-D detector 71 1 , Each line of the 2-D detector consists of many detection cells (at least 1 00). ^'Fhe output of each detector cell represents^* a line integral of attenuation alues measurable along one of the respective beam paths. The cone-shaped beam 704 subtends a cone angle-

It) sul ficient to include the entire region ol interest of the body I hus, a complete scan ol the ob|cct can be made by meiely orbiting the gantry frame 702 supporting the x-iay source 71 and the 2-D detector 71 1 around the body to acquire the 2-D projection signals at different angular positions 1 he analog-to-digital conversion unit 726 serves to digiti/c the projection signals and to save them in the 3-D image reconstruction array processor 728 and storage device 730 The method employed by the 3 D image reconstruction array processor 728 is the invented algorithm described herein The 3-D image reconstruction array processor 728 serves to transform the digitized projection signals into x-ray attenuation data vectors The x-ray attenuation data matrix corresponds to x-ray attenuation at spaced grid locations within the body trunk being examined Each data element of the matrix represents an x-ray attenuation value and the location of the element corresponds to a respective 3-D grid location within the body

In accordance with the principles of the invention discussed previously, a display processor 732 obtains the data stored as 3-D x-ray attenuation signal patterns in the memory storage 730, processes the data as described above, and then the desired 3-D images are displayed on a 3-D display device 734

The 3-D image reconstruction array processor 732 may, for example, be comprised of an ULT A SPARC- 10 model workstation, available from Sun Microsystems, Inc of Mountain View, Calif 94043 Another system is the Mercury Computer Systems RACE Platform which is a multiprocessor-based parallel computing system scalable up to a few hundred processors I he reconstruction algorithm piesented above is well suited to such parallel processing devices, since the various terms in the reconstruction can be calculated separately and summed 1 he use ol a Storage Concept real-time storage system allows the acquisition ol up to 64 GB ol data continuously in real time

1 1 1 he patient P is placed on a patient table 706 Which is made to slide by a linear motor 738 or some such device under contiol of the system control computer 724 Alternatively, the patient P can be placed on a fixed table, and a gantry frame holding the detectoi and the source can be moved over the patient P An optional contrast solution injector 740, known in the art, can be used to inject a contrast solution for improved imaging However, the invention can be used without such an injector

An example of the operation of the CBVCT tomography system 700 will now be explained with reference to Figs 8- 1 1 As shown in Tigs 8 and 9, the patient table 706 bearing the patient P is moved into the gantry 702 so that the region of interest ROI lies between the source 710 and the detector 71 1 As shown in Fig 10, to take the arc projections, the gantry 702 is tilted, and a cone beam 704 is emitted when the angular orientation of the source 710 is at 0° and 180° from a predetermined base location As shown in Tig 1 1 , to take the circle projections, the gantry is righted, and the source 710 emits the cone beam 704 repeatedly as the gantry rotates

To decrease the total acquisition time, the sampling rate on the arcs can be reduced relative to the sampling rate on the circle In addition, or as an alternative the arc projections can be taken by using only a tilt-in of the gantry 702 A tilt-out of the gantry can be used to take additional arc projections to improve image quality Developing and optimizing an x-ray scatter control and reduction technique is one big challenge for CBVC I because CBVC I is less immune to scatter than fan-beam C I CBVC I image contrast is reduced by scatter without an effective control technique Scatter can be countered with a hybrid technique that uses an air gap technique and an antiscatter grid to control scatter and a practical sof tware correction technique lor detected scatter One of the major dif lcicnccs between Ian beam slice C I and ( BV( I is x-r y beam eoll imatiori Using

^■p vciy nai i ow slit eollimatiori in Ian beam C I reduces scattei-to-pi imaiy ratio (SPR) to 0 2 oi less On the othei hand, using a large cone colhmation in cone beam geometiy with only an air gap technique results in an average SPR up to 1 l o overcome that limitation, a software correction technique is used to correct for detected scatter and to reduce overall average SPR to 0 2 or less Convolution filtering techniques and scatter detected by the FPD are used to estimate scatter distribution and then subtract it from the total projection A known convolution filtering technique taught in Love, L A , and Kruger, R A , "Scatter estimation for a digital radiograpluc system using convolution filter," Med Phys 1987, 14(2) 178-185, was implemented for an image intensifier (IΙ)-based imaging system and produced an average percentage error of 6 6% for different anatomy and different clinical applications That is equivalent to a reduction of SPR by a factor of up to 14 Even better scatter correction results can be achieved for an FPD- based system because there is no veiling glare component, compared to an Il-based system where that is a more dominant component Based on previous studies and preliminary results, it is anticipated that the average SPR in each cone beam projection can be reduced to 0 2 That is the equivalent SPR achievable in a fan beam slice CT, using a hybrid scatter correction technique (software correction plus air gap) That analysis and the preliminary results show that with the above-noted x-ray scatter reduction and correction techniques, the FPD-based CBVCTM system provides more than adequate low contrast resolution The preferred embodiment combines an air gap technique with an antiscatter grid and a software correction technique for residual scatter A 10-15 cm air gap technique is an ef fective method to prevent laige angle scatter radiation from reaching the detector and to reduce average SPR to less than 2 It is contemplated that in the C B VC 1 system the distance Irom the rotation center to the detector will be about 40 em With that geometry the an gap is moie than 15 cm to achieve an av eiage SPR less than 2 One example of an efficient x-ray scatter rejection grid includes a focused, tantalum, air-interspaced grid with a 10: 1 grid ratio and 80 lines/inch. T he grid strips arc suspended between a pair of carbon fiber plates and aligned parallel to the axis of rotation. A scattcr-to- primary ratio (SPR) of approximately 1.0 can be achieved with 100 kVp and a moderate increase of the exposure level to keep the noise level unchanged. With a stationary grid there are grid artifacts. To avoid such grid artifacts, the grid can be reciprocated with a computer- controllable speed to blur the grid strip artifacts.

The residual scatter present within the projection images is removed based on a convolution-filtering method to estimate residual scatter distribution in each projection image. In the convolution filtering method, residual scatter is modeled as a low pass, spatially filtered version of the total projection (scatter plus primary). After estimating residual scatter in each projection, the residual scatter radiation is then subtracted to obtain primary distribution for reconstruction. That technique effectively reduces SPR from 1.0 to 0.2 or less. The conventional convolution filtering method requires two x-ray projections at each projection angle to accurately estimate residual scatter: one with a beam stop array for calculating two scaling factors and another without the beam stop array. That is not practical and would significantly increase patient dose in CBVCT. To overcome those difficulties, the preferred embodiment uses scout images for estimating scatter distribution in "real time" for each patient. Before starting to scan, one scout projection image is acquired, as in a standard fan beam CT. Traditionally, the scout images are used for positioning, and surveying body size to adjust the x-ray exposure levels in real time and reduce patient dose Before acquiring scout images, as shown in Figs. 12A and 12B, a square matrix 1204 of small lead ball bearings 1 206 is placed between the x-ray coUimator 1202 and the region of interest ROI, Both primary and sampled scatter distributions are estimated from the scout images with the lead beam stop anay I he estimated pi unaiy images arc used for a scouting pur pose I he scaling factors foi estimating scattei distnbution and the convolution kernels at sampled angle positions can be deter mined I hen the scattei distubutions aie estimated using the convolution kernel at corresponding angle positions and subtiacted from the detected projections l o reduce radiation dose to the patient and computation load, only a minimum number of required scout images are acquired Only a few scout rmages are needed because the accuracy of the method is not highly dependent on the exact shape of the convolution kernel, so long as its dimensions are large enough T he exponential kernel is used for the estimation of residual scatter because a 2D exponential kernel is an optimum formation Another technique which can be used in the present invention to improve imaging is the ultra-high-resolution volume-of inteiest (VOI) reconstruction mode That technique can be used to focus on a suspicious lesion

It is known in the art for flat panel detectors to have zoom modes One source of such flat panel detector is Varian Imaging Products of Mountain View, California, U S A The Varian PaxScan 2520 fiat panel detector has the followmg characteristics size = 19 5 x 24 4 cm, frame rate = 15 120 frames per second, image lag < 10%, pixel pitch = 127 μm, A/D = 16 bits, exposure range = 1 -3000 uR, DQE = 65% dynamic range = 2000-30,000 1 Even larger flat-panel detectors are known in the art, e g , 50 cm x 50 cm

The zoom mode of a flat panel detector such as a Varian flat panel detector is used to acquire projection data for ultra high VOI reconstruction In the zoom mode the detector can acquire a random block of 768 x 960 pixels at 30 frames/sec with the lull 4 lp/mm resolution of the sensor I he pixel si/e of the detector as noted above is 127 μm A dual-focus spot x- ray tube is used having focus spots of 0 3 and 0 6 mm Ultra-high-rcsolution VOI can use a 0 3mm focus spot so that the locus spot si/e w ill not be a limiting lactoi ol the spatial resolution lor the VOI mode I heiefoie the I OV (field ol view) ol the zoom mode is 9 75 \

5 12 2 cm l o i educe unnecessary radiation lo the patient, a colhniatoi limits the ladiation to within the ROI (icgion ol inteiest) in the VOI acquisition A nanow st p oi collimation (~2 cm wide) is needed If the ROI is larger than 12 2 cm in diameter, the projection data acquired in ultra-high VOI mode are truncated in the lateral direction I here are some streak artifacts if the reconstruction is obtained from the truncated data without preprocessing the data The conventional method to deal with truncated projection data is to tail the projection data with a cosine wave before filtering (Z H Cho, E X Wu, S K Hilal "Weighted backprojection approach to cone-beam 3D projection reconstruction for truncated spherical detection geometry," IEEE Tian Med Imaging 13(1 ), 1 10- 122, March, 1994) Fortunately, in the present case, the complete information in the region out of VOI is already available from the previous lower resolution scan That information can be used to tail the truncated projection data and then complete the VOI reconstruction Computer simulation indicates that such an algorithm eliminates the reconstruction artifacts introduced by truncated data within VOI Such a technique is anticipated to be better than the conventional method It is further anticipated that the ultra-high-resolution VOI reconstruction technique can provide up to 5 0 lp/mm resolution with a justifiable increase of the x-ray dose The above-disclosed VOI technique can be used to detect cancers, such as breast and lung cancer

A FPD-based CBVCT system will provide better contrast and spatial resolution and better geometric accuracy than an Il-based CBVCT system Recently, a new technology of large area flat panel solid state detector array has been developed by several groups A high resolution high frame rate, amorphous silicon (a-Si H) FPD using a phosphor screen and a photodiodc array to convert incident x-rays to a charge image has been developed Also, a selenium I PD has been developed by other groups using a uniform layer of an x-ray sensitive photocondiictor, selenium lor a direct conversion ol x-iays to an electioiuc image I n addition a real time I PD lor fluoioscopic images has been developed In spite ol then differences, these image sensors have some common potential advantages over other detectors: compactness, high DQE, absence of geometric distortion and veiling glare with the benefits of high resolution, high frame rate, high dynamic range, small image lag (< 1%) and excellent linearity (-1 %). The FPD has almost the same DQE as an II within the diagnostic radiation range. T hese advantages of the new FPD over an II-CCD detector make it a good candidate for the detector used in CBVCT. Therefore, a FPD-based CBVCT system will make CBVCT a superior technique. In the past two years, the development of the TFT detector has been exciting and progressed from the research phase to the production phase. Six companies have started to manufacture this type of detector. The FPD-based CBVCT angiography system has better spatial resolution and low contrast resolution than Il-based systems. The FPD-based system has better spatial resolution than a helical CT and near equal low contrast detectability in comparison to a helical CT.

Two alternatives to the circle-plus-multiple-arcs orbit can be used to obtain data sufficient for exact reconstruction. Fig. 4C shows an orbit for taking a scan over a circle plus multiple (in this case, two) lines. That orbit allows at least 25 cm coverage in the Z direction. Before starting the scan, the patient on the table is positioned to -12.5 cm from the center of the scanner to prepare for circle-plus-line (CPL) scan. While the table is moving toward the center of the scanner, the x-ray tube-detector rotates, taking projections only at 0 (on the upper line) and 180° (on the lower line) of the rotation angle positions to obtain two line projections per rotation. When the table is at the center of the scanner, the table stops moving, and the x-ray tube and detector rotate to acquire multiple circle projections. After acquisition of the circle projections, the table moves toward the position of -1- 12.5 cm from the center of the scanner, while the x-ray tube and detector are rotating, taking more line projections as above. ^"Fhe reconstruction algorithms are those taught by I i.

17 l o reduce CPL scan time, the 'quasi' spiral scan mode ol the gantry is used because during the scan, the x-ray tube and detector continue rotating on the gantiy while the table is moving and the table stops at the ccntci of the scannci to acquiie ciiclc piojcctions T his scan mode will eliminate x-ray tube-detector rotation-stops dur ing scan and reduce the transition time between line acquisition and circle acquisition It can also be noted that we actually acquire line projections along two lines the upper and lower lines, as shown in Figure 4C which shows the implementation of CPL orbit using "quasi" spiral scan on a spiral gantry with 8 line projections at the positions numbered 1 through 8 This is because this can reduce the sampling rate on a single line and increase line-scanning speed when using "quasi" spiral mode

A spiral scan will now be explained with reference to Fig 4D While the table is moving through the gantry, the x-ray tube and detector rotate, taking projections at multiple angle positions to obtain multiple spiral cone beam projections per rotation Depending on the achievable frame rate of the detector, the spiral scanning time w ill be 2-8 seconds and the total spiral rotation angle will be from 180 plus cone angle to 720 to cover 6 5 cm to 25 cm in the z-direction The reconstruction algorithms are those taught by Wang, G E , Lin, T H , Chen, P C , and Shinozaki, D M , "A General Cone-Beam Reconstruction Algorithm," IEEE Transactions on Medical Imaging Vol 12(3) 486-496 (1993), and in Wang, G E , Lin, T H , and Chen, P C , "Half-Scan Cone-Beam X-Ray Microtomography Formula," Scanning Vol 16 pp 216-220 (1994)

Based on currently available I PDs, a spiral scan should have a scanning speed of 2-8 seconds, a /-coverage of 65-250 mm dnd a slice thickness in the / direction of 0 1 7-0 67 mm l int scan oi lers the advantages ol more unif orm sampling and ease of implementation I he circle-plus ares and enele-plus-lines scans should both have a scanning speed ol 4-8 seconds a / coverage of 1 30 250 mm and the same slice thickness as tint for the spiral scan I he

18 circle-plus-lines orbit is cui icntly the best to address tr uncation. ^'Fhe ciicle-plus-arcs orbit has the advantage that it requires no patient transition during the scan; that is, the patient remains still.

The scanning times listed above are estimated based on the frame rate of currently available FPDs (60 -120 frames/s) and the spiral gantry speed for a used spiral CT gantry ( 1 s/revolution). Existing FPDs are specially designed for radiographic or fluoroscopic imaging not for fast tomographic imaging. Once a large size FPD-based CBVCT becomes feasible, a large size FPD specially designed for fast tomographic imaging with high speed and low image lag will be developed. If the frame rate of the detector is increased to 960 frames/sec. for a 25 cm x 50 cm FPD, the spiral scan time for 33 cm coverage will be 1 — 2 seconds depending on gantry speed and table moving speed.

To deal with the projection truncation problem, the following three measures can be taken. First, when determining which orbit and related algorithm will be used for reconstruction, the one with the smallest contaminated depth should be used. Second, when measuring the total dose to a patient, the dose received in the contaminated region due to projection truncation should be included Third, when acquiring projection data using the CPL or CPA, the detector in the longitudinal direction should be slightly larger than the ROI

If it is necessary for the ultra-fast readout of FPD, a subtraction algorithm can be used to reduce the effect of image lag. In such an algorithm, the previous N weighted projections will be subtracted from the current projection. The weighting factor for each previous projection will be determined by the lag measured vs. frame numbers subsequent to the frame in which it was generated. Then the final image will be reconstructed fiom image lag- eon ected projections

While a pr eferred embodiment of the present invention has been set forth above, those skilled in the ai t will recogiu/e thai other embodiments can be realized within the scope ol

V) the invention I 01 example, numet ical values and the names ol speci fic pi oducts aic illustrative iathei than limiting Also, to achieve the ciicle-plus-two-aics or ciicle-plus- multiplc-arcs orbit, any suitable equipment and mode of operating it can be used I urthermore, the particular algonthms presented herein aie illustrative rather than limiting Moreover, while the utility ol the invention has been presented with particular attention to lung cancer, it can be used for other malignancies T herefore, the invention should be construed as limited only by the appended claims

APPENDIX

A. Derivation of the Reconstruction Algorithm for Arc CB Projections

( ,, }'„,-„) i the fixed coordinate system, and (\,,V_I ,z,) is the local coordinate

system rotating rigidly in phase with the virtual detectoi plane I he arc oibits are within the

plane determined by (x_a,y„) In the local coordinate system (x^y^∑, , Grangeat's

formula can be written as

Rf OS n,ri) (A-l)

where Rf(OS n, ) is the Radon transform over the shadowed plane with norm Vector n which passes through the source focal point S, I, and Z, are the integral limits along the Tand

Z axes respectively, and P_p(}',Z) is the cone beam projection at angle β along the arc

orbits

In the local coordinate system (x_l,y_I,z_l ) ,

OS = (D, 0, 0) (A-2)

n = (sinθ cos(φ -β),sιn0 sm(φ -β),cosθ) (A-3)

p =OS /? = £>sιnθcos(φ-β) (A-4)

I OS x \² = D² - D² surθ cos^"(<P -β) = lX -p" (A-5)

OS' = T n (A-6)

I or derivation convenience by letting

/(β, /,(-)) /)h() sin Θ + /u>s(") -/)</)<// (A-7)

(Λ-l ) is converted into (Λ-8)

D - p ^' 01 Op

Taking the 1 derivative on both sides of (Λ-8) and using (A- 15) (see below) gives

(P, Θ) = - -/?/-(r-/l,/) (Λ-9)

In the local coordinate system (x_; ,y, ,∑,) , the Radon plane SD_{D₂ can be represented by the equation:

lx, +DcosΘy, +DsιnQz_L - Dl = 0 (A-10)

On the other hand, in the fixed original coordinate (x_υ,y₀,z_a) , another equation to describe

the same Radon plane can be written as

x_a sinθ cosφ + y₀ sinθ cosφ + z₀ cosθ - p =0 (A-ll) Through the relation between the local and the fixed coordinate system

and solving (A-10) and (A-l 1) simultaneously, we have:

D cos Θ cosβ + /sin β sinθ sinφ =

■ Y (A-l 4)

(D² ₊I²)

Dl p = (A- 15)

(D X ^²x)

Consequently, from (A-l ) and (A- 14), we have / co Θ co -(- / sin β tanφ = — (A-17)

- / cosΘ sin - cos

Considering the variable change from (O ,φ) →- (θ, β) , we get

sin OJOJφ (Λ-I8) Further, by introducing (A- 15) into (A-9), wc get

(A-19)

According to the 3D Radon inverse transform (27), eventually, wc have

where H β, /, Θ) is the window function for the sub-domain missed by the circular orbit in

the Radon domain, = {1,2} conesponds to arc orbit 1 and arc orbit 2 respectively, and β,.

determines the arc sub-orbit spanning range. B. Derivation of the Window Function

By referring to Fig. 3, the section in Radon domain that can not be covered by the radon transform of the circular CB projections is

Actually, we have (see Appendix A)

D cos Θ cos β + / sin β tanφ = (B-4)

D cos Θ in β 4- /cos β Then, from (B-3) we get

²cos²θ + /² sin θ = 1 -cos'O = (B-5)

D²xl² and from (B-4) we get

Incorporating (B-2), (B-5) and (B-6) in (B-1) we get

|/|> JD²4J²-(Z⁾ cos Θ cosβ +/sinβ)² (B-8)

l² >£>²+/²-(£>cosΘcosβ+/sinβ)² (B-9)

D² <(Z)cosθcosβ -f/sinβ)² (B-10) Finally, the window function can be written as

1 /sinβ >D-(l-cosΘcosβ)

*{β ,/,©) = 1 / sin β < -D ^■ (1 + cos Θ cos β ) (B-ll) 0 elsewhere

Claims (1)

1. I claim:

   1. A method of imaging an object to form a reconstructed image, the method comprising:

   (a) scanning the object using a source of radiation and a detector of the radiation, the source and the detector being moved around the object to define an orbit comprising (i) a circle orbit for providing a first set of data signals and (ii) a plurality of arc orbits for providing a second set of data signals;

   (b) performing a first reconstruction from the first set of data signals to generate a first reconstruction result; (c) performing a second reconstruction from the second set of data signals to generate a second reconstruction result; and (d) summing the first reconstruction result and the second reconstruction result to obtain the reconstructed image as a sum of the first reconstruction result and the second reconstruction result. 2. The method of claim 1, wherein the source of radiation is a source of cone- beam radiation.

   3. The method of claim 2, wherein the first reconstruction result is a sum of a Feldkamp reconstruction and a complementary term used to conect the Feldkamp reconstruction for use of the cone-beam radiation on the circle. 4. The method of claim 2, wherein the second reconstruction result is generated by summing individual arc reconstruction results for the arc orbits.

   5. ^"Fhe method of claim 4, wherein two arc orbits are used.

   6. ^'Fhe method of claim 5, wherein, for each of the are orbits, the individual arc reconstruction result is calculated using a window function to account for a portion ol a Radon domain which cannot be covered by a Radon tiansfoim of the circle orbit The method of claim 6, wherein, foi any point T in the object

   (λ_/ fi zι) is a detector coordinate system which rotates rigidly with the detector, β is an angle along the arc orbits at which the source is located, D is a radius of the aic orbits, r and a locatron of the source define a plane which intersects a plane of the detector at a line of intersection, the line of intersection having a point C of closest approach to an origin O of the detector coordinate system such that a line segment connecting O and C has a length / and forms an angle Θ with a yj axis of the detector coordinate system, and the window function is given by

   /sinβ > D (1-cosΘcosβ)

   M'(β,/,Θ) /sinβ <~D (1 + cosΘcosβ). elseiiheie

   The method of claim 7, wherein

   (Y, Z) is a projection of ;^" onto the detector coordinate system,

   Y, and Z, are integration limits determined by dimensions of the detector, β, is an integration limit determined by dimensions of the arc orbits,

   / ) /,(p,ΛΘ)= \ |/'_p,(>^/,Z> (rsιnΘ + ZcosΘ-/>/> Z,

   /'„([! /Θ) I Θ),and the individual arc reconstruction results are given by

   /..(') ,π ' , J, „ j^J „ (!'> <->>Λ- ⁱ 1 he method of claim 8, wheiein

   (Do is an integiation limit deteimmed by a spatial sampling liequency ol the detector,

   //is an integration limit along a Z direction,

   P_Φ( Y,Z) is a cone-beam projection at a point (Y.Z on the detector,

   P_Φ{ ,Z)= d=h_M(Z-z)P_φ{Y,z),

   the Teldkamp reconstruction is given by

   f ' _x- j °^{2 p} _φ(χ(r (r)),

   P_φ (y ) = ±._{σ φ} (} ) = )h_jm (}'-> _φ (Y)dy ,

   the complementary term is given by

   the first reconstruction result is given by

   / (') = /„(^/ )1 /, ('^"")

   10. T he method of claim 9, wherein step (b) is performed through a digital signal processing operation which assumes:

   and

   1 1. The method of claim 1 , wherein the detector is a flat panel detector.

   12. The method of claim 1 , wherein at least one of steps (b) and (c) comprises scattering correction.

   13. The method of claim 1, wherein the first reconstruction result and the second reconstruction result are both in a filtered backprojection format.

   14. The method of claim 1, wherein steps (b)-(d) are performed through parallel cone beam reconstruction.

   15. The method of claim 1, wherein the object is longitudinally unbounded, and wherein step (d) comprises providing the reconstructed image as an exact reconstruction of the longitudinally unbounded object.

   16. The method of claim 1 , wherein step (d) comprises forming a 3D matrix of attenuation coefficient distribution of the object.

   1 7. The method of claim 1 , wherein the object is a patient or a region of interest in a patient. 1 . ^'fhe method of claim 1 , wherein the reconstructed image is formed for nondestructive testing of the object. 19 I he method of claim I , wherein step (a) comprises pei foi m g a quasi-spii ul scan ol the object

   20 I he method of claim 19, wherein the quasi-spiral scan comprises a tilt in plus circle scan 21 1 he method ol claim 20, wherein the quasi-spiral scan further compiiscs a tilt out scan

   22 The method of claim 1 , wherein the first set of data signals has a higher sampling rate than the second set of data signals

   23 T he method of claim 1 , further comprising (e) locating a volume of interest in the object,

   (f) scanning the volume of interest, and

   (g) performing steps (b) (d) again for the volume of interest

   24 The method of claim 23, wherein the detector has a first resolution and a second resolution higher than the first resolution, and wherein the first resolution is used in step (a) and the second resolution is used in step (e)

   25 A device for imaging an object to form a reconstructed image, the device comprising a source of radiation, a detector of the radiation, a gantry for supporting the source and the detector and for moving the source and the detector around the object to define an oibit compi is g (ι) a circle oibit for piovidmg a lust set of data signals and (n) a plurality of arc or bits for providing a second set of data signals, and a computing device, receiving the fir st and second sets ol data signals foi ( I ) per for ming a fir st reconstr uction fr om the fir st set ol data signals to gener ate a fir st reconstruction result, (ii) performing a second reconstruction from the second set of data signals to generate a second reconstruction result and (iii) summing the first reconstruction result and the second reconstruction result to obtain the reconstructed image as a sum of the first reconstruction result and the second reconstruction result. 26. The device of claim 25, wherein the source of radiation is a source of cone-beam radiation.

   27. The device of claim 26, wherein the first reconstruction result is a sum of a Feldkamp reconstruction and a complementary term used to correct the Feldkamp reconstruction for use of the cone-beam radiation on the circle. 28. The device of claim 26, wherein the second reconstruction result is generated by summing individual arc reconstruction results for the arc orbits.

   29. The device of claim 28, wherein two arc orbits are used.

   30. The device of claim 29, wherein, for each of the arc orbits, the individual arc reconstruction result is calculated using a window function to account for a portion of a Radon domain which cannot be covered by a Radon transform of the circle orbit.

   31. The device of claim 30, wherein, for any point r in the object:

   (x_L, y> , ∑i is a detector coordinate system which rotates rigidly with the detector; β is an angle along the arc orbits at which the source is located;

   D is a radius of the arc orbits; r and a location of the source define a plane which intersects a plane of the detector at a line of intersection, the line of intersection having a point C of closest approach to an origin O of the detector coordinate system such that a line segment connecting O and C has a length / and forms an angle Θ with a V/. axis of the detector coordinate system; and the window function is given by 1 /sin > /)-(l-cosθeo ) u(β, Θ) = 1 /sin <-/)-(l+cosθco ), 0 elsewhere

   32. The device of claim 31 , wherein:

   (}' Z) is a projection of r onto the detector coordinate system;

   Y, and Zs arc integration limits determined by dimensions of the detector; β, is an integration limit determined by dimensions of the arc orbits; / -., r, β^Θ)= f Jl ]p^,(Y,Z5(YsmΘ + ZcosΘ-l)dYdZ

   the individual arc reconstruction results are given by

   , P, ^πA f_aι(r) = --~r J jP_aι(β,l,θ)dΘd&.

   33. The device of claim 32, wherein: ωo is an integration limit determined by a spatial sampling frequency of the detector;

   Lχ is an integration limit along a Z direction;

   P_Φ(Y,Z) is a cone-beam projection at a point (Y,Z) on the detector;

   h_M{Z)= f|ω|eΛoexp(/ωZ);

   tlie Feldkamp leeonstruelion is given by

   ^lf_<Λ^y) = j/ωexp(/ωr)cω

   ^ o = - d^l • = ^(r - -^ • ^(r • the complementary term is given by

   x X- i dΦ- y, v P_φ (7(F)), and

   4π [θ 2π ] ( -F x,)²

   the first reconstruction result is given by

   34 The device of claim 33, wherein the computing device generates f_c(r) through a

   digital signal processing operation which assumes

   = 0 h n) = 4 /? with 1 -(-!)" 1 n≠O 8π ² n² and

   35 T he device of claim 25, wherein the detector compi rses a fiat-panel detector 36 ^'fhe device of claim 35, wherein the flat-panel detector has a flame rate of at least 30 frames per second 37 The device ol claim 35, wheiein the flat-panel detector has an image lag of less than 2%

   38. T he device of claim 35, wherein the ilut-pancl detector lias a dynamic range of at least 4000: 1.

   39. ^'Fhe device of claim 35, wherein the flat-panel detector has a size of at least 19.5 cm x. 24.4. cm. 40. The device of claim 25, lurther comprising a device for correcting for scatter in the reconstructed image.

   41. The device of claim 40, wherein the device for correcting scatter comprises an antiscatter grid disposed between the source and the object.

   42. The device of claim 41, wherein the device for correcting scatter further comprises a coUimator for collimating the radiation.