CN106447740A - Relatively parallel line CT region-of-interest image reconstruction method - Google Patents

Abstract

The invention relates to a relatively parallel line CT region-of-interest image reconstruction method which comprises the following steps: (S1) obtaining projection data; (S2) performing differential back projection of the projection data; and (S3) performing Hilbert inverse transformation of the data obtained by the back projection to obtain a reconstructed image. In the invention, a nearly complete object image can be reconstructed when truncation is not very serious, and a region-of-interest image can be accurately reconstructed by use of a no-truncation artifact in the truncation data collected by a PTCT system. Moreover, the invention also provides a practical weight function to cut down the redundant information generated by a general repeated linear scanning model.

Description

Opposing parallel straight line CT area-of-interest image rebuilding method

Technical field

The present invention relates to image reconstruction field, and in particular to a kind of opposing parallel straight line CT area-of-interest image reconstruction side Method.

Background technology

A kind of new CT system for moving in parallel (PTCT) based on x-ray source and detector in different directions being recently proposed System structure, and have confirmed that it has huge potentiality in inexpensive CT scanner.However, in order to optimize PTCT system, related Image reconstruction should be by primary study.

Before for FBP algorithm under PTCT system, the image reconstruction [3] under data that are complete and no blocking mainly is processed. However, detector can only often cover a part for object in PTCT system, this causes data to be truncated, further results in Exact image reconstruction complexity, or even image reconstruction can not be carried out.

Content of the invention

In view of this, it is an object of the invention to provide a kind of opposing parallel straight line CT area-of-interest image reconstruction side Method.

The purpose of the present invention is achieved through the following technical solutions,

A kind of opposing parallel straight line CT area-of-interest image rebuilding method, comprises the following steps：S1. projection number is obtained According to；S2. differential back projection is carried out to data for projection；S3. the data for back projection being obtained carry out Hilbert inverse transformation, obtain weight Build image.

Further, step S2. back projection step be in line style PI lineHilbert image letter in the middle of upper generation one Number Wherein

λ shows radiographic source to the vector of initial point in the angle of y-axis, and h is distance of the initial point to x-ray source track, and SDD is ray Source track is to the distance of detector trajectory, and ψ is the angle of radiographic source track and x-axis, λ_bAnd λ_eIt is that x-ray source track starts and ties The angle of beam position, p refers to data for projection.

Further, in step s 2, the once linear that Hilbert inverse transformation is obtained scans obtained image：

Or

Wherein L ＞ l >=max (x_e|,|x_b|), k (L, l, x) is expressed as follows

Further, the l=max (| x_b|,|x_e|)+(2～3pixels), L=(1.1～1.3) max (| x_e|,|x_b|).

Further, the true picture for obtaining from Hilbert image is：

ε is a minimum, and span is (10^-3, 10^-2).

Further, multiple linear scanning is carried out, then under multiple linear scan pattern, reconstruction image is：

Or

Further, also include that step S3. cuts down the redundancy of multiple linear scanning model generation using weighting function, The weighting function is：

Further, in order to avoidDiscontinuity, then

Be one smooth Positive function,

Due to adopting above technical scheme, the present invention has advantages below：

Proposed by the present invention can not only block be not very serious in the case of rebuild approximately complete subject image, and No gibbs artifact accurate reconstruction region of interest area image in the truncated data of PTCT systematic collection can be used.

Description of the drawings

In order that the object, technical solutions and advantages of the present invention are clearer, below in conjunction with accompanying drawing the present invention is made into The detailed description of one step, wherein：

Fig. 1 is the general linear scanning model of PTCT system；

Fig. 2 obtains model for PTCT system data；

Fig. 3 is that assigned direction passes through data for projection of the terminal with regard to different scanning track under parallel lines scanning；

Fig. 4 blocks area-of-interest image reconstruction for detector；

Fig. 5 is the Sheep-Slogan figure for rebuilding and smiling face's figure；

If Fig. 6 is respectively using the FBP algorithm of formula (8), formula (14), the MP-BPF algorithm of formula (26), and formula (27) MZ-BPF algorithm carries out the image reconstruction of noiseless fladellum non-truncated data to Shepp-Logan figure, and the first row is arrived The third line is represented 1 time respectively, 2 times and 3 scan model；

Fig. 7 is that 2 scan model have weighting function and the reconstructed results of no weighting function to contrast；

Fig. 8 is the image profile figure of MP-BPF, MZ-BPF and FBP algorithm under different scan model on y=0 straight line Gray value size；

Fig. 9 is the FBP algorithm of formula (8), formula (15), the MP-BPF algorithm of formula (27), and the MZ- of formula (28) BPF algorithm carries out the image reconstruction of noiseless fladellum non-truncated data to Shepp-Logan figure；

Figure 10 is the FBP algorithm using formula (8), formula (14), the MP-BPF algorithm of formula (26), and formula (27) MZ-BPF algorithm carries out the image reconstruction of noiseless fladellum truncated data to Shepp-Logan figure, and the first row is divided to the third line Do not represent 1 time, 2 times and 3 scan model；

Figure 11 is area-of-interest image reconstruction；

Figure 12 is the profile in y=0 direction in Figure 10；

Figure 13 is that the image reconstruction for having noise fladellum truncated data is；

Figure 14 is profile of the Figure 13 along y=0 direction.

Specific embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.

PTCT model is looked back first.In PTCT, target hovering, x-ray source and detector are moved in opposite direction, are such as schemed Shown in 1.Now, using target's center as the initial point of cartesian coordinate system.Radiographic source track is expressed as follows

λ shows radiographic source to the vector of initial point in the angle of y-axis, and h is distance of the initial point to x-ray source track, and SDD is ray Source track is to the distance of detector trajectory.ψ is the angle of radiographic source track and x-axis.Under this work, it is assumed that image function

Now, a moving coordinate system with ray source point as the center of circle is described.In this system, two units to Amount is as follows

It is true that adopting flat panel detector in PTCT system.However, only considering fan-shaped beam scanning herein.On detector Any parameter all represented with t.Projection p (t, λ, ψ) is to pass through the point on radiographic source track and detector unit along the X-ray that specifies The line integral of plain t point.Therefore it is expressed as follows in image Function Projective p (t, λ, ψ) of t point

Represent the unit vector in the point direction from ray source point to image, be expressed as follows

According to above-mentioned equation,

λ_bAnd λ_eIt is the angle of X-ray track beginning and end position.It is reconstruction point to X ray source scanning rail The distance of mark.G (t) is ramp filter.

For multiple opposite linear scan pattern, equation is amended as follows

According to classical BPF algorithm, object function is become by the chord group for scanning track, and object can be obtained by these strings. But for PTCT system, because all of string covers the classic BP F algorithm phase on identical line segment, with general scanning track Seemingly, it is believed that these special strings are linear type PI line, and cross point with line style PI line and object function is to support Section.

Back projection's step of BPF algorithm is in line style PI lineHilbert image function in the middle of upper generation one

In order to simplify above-mentioned equation, the differential G (t, λ, ψ) of data for projection is expressed as follows

Obtained by equation (5)

By equation (11), (12) bring equation (10) into

By equation (1), (8), (13) bring equation (9) into

B. Hilbert inverse transformation

F (x) is finite interval [x_b,x_e] on smooth function.It is its one-dimensional Hilbert transform, Xi Er Bert is converted to as follows

Pv is the Cauchy's principal value of integration.Because target is in finite interval [x_b,x_e], true picture can use limited Xi Er Bert transformation equation is obtained.In the present invention, two limited Hilbert inverse transformation formula are employed, respectively

Wherein L ＞ l >=max (| x_e|,|x_b|), k (L, l, x) is expressed as follows

Wherein f (ψ, λ_b,λ_e, it is x) that f (x) scans the substantially image for being obtained in once linear, is not accurate figure in theory Picture.In equation (18), the parameter to true picture sensitivity is L and l.In practice, under a scope, one can be selected to fit When value l=max (| x_b|,|x_e|)+(2～3pixels), L=(1.1～1.3) max (| x_e|,|x_b|)

It is true that true picture can be obtained using these equations from Hilbert image.However, these equations have one Individual singular point, in order to avoid the singular point for integrating, equation can make following modification

ε is a minimum, and span is (10^-3, 10^-2).

Based on the result for obtaining, under multiple linear scan patternCan be reconstructed by BPF algorithm

Two formula are respectively designated as MP-BPF algorithm and MZ-BPF algorithm above.

Now, it is assumed that have n times linear scanning track.For convenience, i ＆ lt and jth time linear scanning track are only considered, As shown in Figure 3.It is defined as follows.It is a weight, in order to calculate in multiple linear scanning mould The redundancy of the data set for obtaining in type.Obviously, when ray passes through under different scanning tracksTerminal fan beam projections meeting There is provided, for the reconstruction of object function, the information for repeating.

p(t_i,λ_i,ψ_i)=p (t_j,λ_j,ψ_j)s.t 1≤i,j≤N (23)

WeightIt is used for processing redundancy.

It isThe number of hits in line and all linear scanning paths,For scanning On track by the fixing straight line in cross point be Φ (ψ_i,λ_i),Therefore, Weighting Functions Definitions are as follows：

SelectAs weighting function.However, in fact, in order to avoid's Discontinuity, takes following methods.

It is a smooth positive function, is denoted herein as

Finally, with MP-BPF algorithm and MZ-BPF algorithm, image reconstruction is realized respectively.

Generally speaking, the general BPF algorithm from a series of reconstruction image fladellum parallel lines scan datas is obtained.

In discussed above, such a situation is only only accounted for, be exactly that whole object can be covered (nothing section by detector Disconnected projection).It is however quite easy to run into such case.In PTCT system, target object can not be completely covered by the visual field.(projection Block), as shown in Figure 5.

Linear type PI line is by parameter group (ψ_i,λ_b,λ_e) represent, as formula (26) and (27), area-of-interest figure to be rebuild As needing only to know in [x_b,x_e] and [- L, L] on back projection's image.Although anti-throwing can not be obtained from single pass model Shadow image, but the method that can be by increasing scan lines projects, to obtain completely, the reconstruction for realizing complete image.Such as two Secondary and three scan model, if extending this conclusion, using the condition that BPF algorithm accurate reconstruction image is necessary and sufficient For：Any point in principal function will be expressed the scan angle at least needing 180 degree.If it is complete that area-of-interest is scanned line segment Illuminate, it is possible to use BPF algorithm proposed by the present invention realizes area-of-interest image reconstruction, and without gibbs artifact.

MP-BPF the and MZ-BPF algorithm for proposing for fladellum PTCT system is schemed by an improved Shepp-Logan Its effectiveness is found that with smiling face's graph evaluation, as shown in Figure 6.The region that smiling face's in figure is covered by red squares is exactly Area-of-interest, it is selected to test table of the MP-BPF and MZ-BPF algorithm under truncated projection with the comparison of FBP algorithm Existing.It is 1 × 1mm that the pixel of two images is all the area size of 256 × 256 their coverings².For other 1 times, 2 times, 3 The parameter of secondary scanning is as shown in Table 1.By the detector array of 1000mm length respectively at 1 time, 2 times, produce under 3 scan patterns The PTCT data of raw non-truncated.The data that blocks are obtained by the detector array of 350mm length.It is added to also by Gaussian noise and no makes an uproar The data with noise are produced in the data of sound.In order to prove significantly low contrast district, the maximum of noise free data is surveyed in choosing 0.37% as Gaussian noise standard deviation.By set forth herein BPF algorithm and FBP algorithm non-truncated and truncated data are divided Do not do full images reconstruction and area-of-interest image reconstruction is contrasted.

1 simulation parameter of table

If Fig. 6 is respectively using the FBP algorithm of formula (8), formula (14), the MP-BPF algorithm of formula (26), and formula (27) MZ-BPF algorithm carries out the image reconstruction of noiseless fladellum non-truncated data to Shepp-Logan figure.The first row is arrived The third line is represented 1 time respectively, 2 times and 3 scan model.In order to confirm set forth herein weighting function effectiveness, in Fig. 7 point Not giving 2 scan model has weighting function and the reconstructed results of no weighting function to contrast.Fig. 8 gives MP-BPF, MZ- The gray value size of image profile figure of the BPF and FBP algorithm under different scan model on y=0 straight line.In order to do distinctness Contrast, really the profile gray value of books is also presented in Fig. 8.In order to assess the quality of reconstruction image further, arrange in table 2 The mean square error of each algorithm is gone out.

2 PTCT system of table is using the mean square error of FBP and BPF algorithm

From the above analysis, it will be apparent that 2 times and three times scanning can be passed through and obtain accurate reconstruction image, 3 scanning Picture quality better than 2 times scanning picture quality.The main cause for causing this result is the projection that is collected by 3 scanning Data scan 360 degree around object as circular scan model, and weighting function is a simple constant 1/2 here.From another One angle is seen, 2 scan model are considered as a typically short scanning, and therefore weighting function is difficult to determine.But, herein The weighting function of proposition can process these redundancies to a certain extent, as shown in Figure 7.In addition, in three scan model Under, for no truncated projection data BPF algorithm quality less than FBP algorithm because face can be carried out to image using BPF algorithm Remote replacement, this can reduce picture quality.Finally, as a result prove MP-BPF algorithm and MZ-BPF algorithm in terms of suppression picture noise There is good performance.

Smiling face's picture has been applied set forth herein BPF algorithm carry out the area-of-interest of reconstruction image.In this part, Need to observe the acquisition of complete approximate image, as shown in Figure 10, respectively using the FBP algorithm of formula (8), formula (14), formula (26) MP-BPF algorithm, and the MZ-BPF algorithm of formula (27) carries out noiseless fladellum truncation number to Shepp-Logan figure According to image reconstruction.The first row is represented 1 time respectively to the third line, 2 times and 3 scan model.

As shown in the figure, it can be seen that the reconstruction image of no gibbs artifact can be obtained using BPF algorithm, FBP algorithm is compared Just there is gibbs artifact.In addition, if projection be not seriously block very much if, BPF algorithm can be rebuild beyond area-of-interest model The complete coarse image that encloses.

In order to study further set forth herein performance of the BPF algorithm in terms of area-of-interest image reconstruction.As Figure 11 Respectively show, region of interest area image is obtained from Figure 10.In order to compare the quality of area-of-interest image reconstruction, also in figure In 12 there is provided y=0 position in Figure 11 profile.

Can see, the gibbs artifact for being marked with red squares in fig. 11 is to carry out region of interest using FBP algorithm Domain is produced when rebuilding.Compare, accurate reconstruction area-of-interest that but can be without gibbs artifact using BPF algorithm.Sweep at 1 time Retouch under model, because the loss of projection, three kinds of algorithms can not all rebuild region of interest area image.Redundancy under 2 scan model Information is a difficult problem, in addition can be obtained under 3 scan patterns using BPF algorithm more complete than under 2 scan patterns Area-of-interest reconstruction image.

In order to explore further set forth herein PTCT system BPF algorithm to suppress picture noise in ability.As schemed The 13 FBP algorithms for using formula (8), formula (14), the MP-BPF algorithm of formula (26), and the MZ-BPF algorithm pair of formula (27) Shepp-Logan figure carries out the area-of-interest image reconstruction for having noise fladellum truncated data.Figure 14 is cuing open for y=0 direction Face figure.These figures prove set forth herein algorithm have good performance in terms of suppression picture noise.

Finally illustrate, preferred embodiment above is only unrestricted in order to technical scheme to be described, although logical Cross above preferred embodiment to be described in detail the present invention, it is to be understood by those skilled in the art that can be Various changes are made in form and to which in details, without departing from claims of the present invention limited range.

Claims (8)

1. a kind of opposing parallel straight line CT area-of-interest image rebuilding method, it is characterised in that：Comprise the following steps：

S1. data for projection is obtained；

S2. differential back projection is carried out to data for projection；

S2. the data for back projection being obtained carry out Hilbert inverse transformation, obtain reconstruction image.

2. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 1, it is characterised in that：Described Step S2. back projection step be in line style PI lineHilbert image function in the middle of upper generation one Wherein

λ shows radiographic source to the vector of initial point in the angle of y-axis, and h is distance of the initial point to x-ray source track, and SDD is radiographic source rail Mark is to the distance of detector trajectory, and ψ is the angle of radiographic source track and x-axis, λ_bAnd λ_eIt is x-ray source track beginning and end position The angle that puts, p refers to data for projection.

3. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 2, it is characterised in that：In step In rapid S2, the obtained image of once linear scanning that Hilbert inverse transformation is obtained is：

Or

Wherein L ＞ l >=max (| x_e|,|x_b|), k (L, l, x) is expressed as follows

$k(L,l,x)=\left\{\begin{array}{cc}-\sqrt{L^2-x^2}& l\≤\left|x\right|\≤L\\ \sqrt{l^2-x^2}-\sqrt{L^2-x^2}& \left|x\right|\≤l\\ 0& otherwise\end{array}\right.$

Wherein, L, l, represent length, and they refer to the compact schemes region that linear PI line should run through object.

4. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 3, it is characterised in that：Described L=max (| x_b|,|x_e|)+(2～3pixels), L=(1.1～1.3) max (| x_e|,|x_b|).

5. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 4, it is characterised in that：From uncommon In your Bert image, the true picture of acquisition is：

$f(\mathrm{\ψ},{\mathrm{\λ}}_b,{\mathrm{\λ}}_e,x)=\frac{1}{2\mathrm{\π}}\sqrt{\frac{x-x_b}{x_e-x}}{\∫}_{x_b}^{x_e}\sqrt{\frac{x_e-x}{x-x_b}}\frac{(x-x^{\′})b_{(\mathrm{\ψ},{\mathrm{\λ}}_b,{\mathrm{\λ}}_e)}\left(x^{\′}\right)}{{(x-x^{\′})}^2+{\mathrm{\ϵ}}^2}{\mathrm{dx}}^{\′}$

$f(\mathrm{\ψ},{\mathrm{\λ}}_b,{\mathrm{\λ}}_e,x)=\frac{1}{2\mathrm{\π}}\frac{1}{\sqrt{L^2-x^2}-\sqrt{l^2-x^2}}{\∫}_{-L}^L\frac{(x-x^{\′})k(L,l,x^{\′})b_{(\mathrm{\ψ},{\mathrm{\λ}}_b,{\mathrm{\λ}}_e)}\left(x^{\′}\right)}{{(x-x^{\′})}^2+{\mathrm{\ϵ}}^2}{\mathrm{dx}}^{\′}$

ε is a minimum, and span is (10^-3, 10^-2).

6. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 5, it is characterised in that：Carry out Multiple linear scanning, then under multiple linear scan pattern, reconstruction image is：

Or

$f\left(\stackrel{\→}{r}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{1}{2\mathrm{\π}}\frac{1}{\sqrt{L^2-x^2}-\sqrt{l^2-x^2}}{\∫}_{-L}^L\frac{\left(x-x^{\′}\right)k\left(K,l,x^{\′}\right)b_{\left({\mathrm{\ψ}}_i,{\mathrm{\λ}}_b,{\mathrm{\λ}}_e\right)}\left(x^{\′}\right)}{{\left(x-x^{\′}\right)}^2+{\mathrm{\ϵ}}^2}{\mathrm{dx}}^{\′}.$

7. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 6, it is characterised in that：Also wrap The redundancy that step S3. cuts down the generation of multiple linear scanning model using weighting function is included, the weighting function is：

8. opposing parallel straight line CT area-of-interest image rebuilding method according to claim 7, it is characterised in that：In order to AvoidDiscontinuity, then It is a smooth positive function, It is used for describing in supporting zone any point each The weighting function in individual direction, before two parameters statement weight component come from the component of radiographic source position.