DE102007040549A1 - Method for reducing image noise and spirit of artifacts in frame of recorded radioactive-based image of image receiving area, involves taking raw image of image receiving areas with both different radiation spectrums - Google Patents

Abstract

The method involves taking raw image of the image receiving areas with both different radiation spectrums with a pair of measured values that are assigned to each other. A reconstructed value pair is determined by considering regeneration between a result and measuring value pair for separation of different materials in image receiving area. The reconstructed value pair is assigned to a measuring value pair as the result of the separation.

Description

The The invention relates to a method of reducing image noise and / or ghost artifacts in the context of the inclusion of at least one radiation-based Image of an image pickup area with two different radiation spectra, in particular with two different X-ray spectra.

at the dual-energy material decomposition or formation (DE material decomposition or imaging) is an object to be irradiated, ie z. B. a Patient, at two different x-ray voltages and thus taken with two different X-ray spectra. Within this frame, two projection images, ie raw images, generated for the different voltages.

The Recording with two different spectra instead of a single one Spectrum has the advantage that radiologically different materials, For example, soft tissue and bone, separate or separate by combining the two raw images appropriately.

Quantitative DE imaging reconstructs physical quantities such as material thicknesses (in cm) or mass population densities (in g / cm ² ) as reconstruction values, with a disadvantage of dual energy imaging being the large increase in image noise compared to the raw images is.

To cope with this, various noise filtering techniques are used. However, these either do not start from the physically correct nonlinear model or are based on a pure image postprocessing method which skilfully exploits negative correlations between the two separated material images for the purpose of noise reduction. To name for such approaches to noise filtering are the articles "Quantitative evaluation of noise reduction strategies in dual-energy imaging" by RJ Warp and JT Dobbins of Med. Phys. 30 (2), Feb 2003 , such as "An Algorithm for Noise Suppression in Dual Energy CT Material Density Images" by WA Kalender, E. Klotz and L. Kostaridou of IEEE Trans. Med Imaging, Vol. 7, No. 3, September 1988, 218-224 , and CH McCollough, MS Van Lysel, WW Peppler and CA Mistretta of Med. Phys. 16 (6), Nov / Dec 1989, 873-880 ,

A review the results obtained in the filtering, with regard to however, the actual measurement data does not take place.

To note further that structures with higher spatial frequencies, For example, edges of a material image, such as a Bone image, in the second material image, for example, a soft tissue image, can be transported in (as so-called "ghosts"). These so-called "ghost images" can become z. B. interfere with an evaluation.

Of the Invention is thus the object of a basis in this respect improved method for reducing image noise and / or of ghost artifacts in the context of the inclusion of at least one radiation-based Image of an image pickup area with two different radiation spectra, especially with two different X-ray spectra, specify.

• – Aufnahme von Rohbildern des Bildaufnahmebereichs mit den beiden unterschiedlichen Strahlungsspektren mit jeweils paarweise einander zugeordneten Messwerten und
• – zur Separation unterschiedlicher Materialien im Bildaufnahmebereich Bestimmung wenigstens eines einem Messwertepaar als Ergebnis der Separation zuzuordnenden Rekonstruktionswertepaars unter Berücksichtigung einer Rückkopplung zwischen dem Ergebnis und dem Messwertepaar.

To achieve this object, such a method is provided which comprises the following steps:

• - Recording of raw images of the image pickup area with the two different radiation spectra with pairs of mutually associated measured values and
• For the separation of different materials in the image recording area, determining at least one reconstruction value pair to be assigned to a measured value pair as a result of the separation, taking into account a feedback between the result and the measured value pair.

Provided becomes thereby that the measuring data except noise no systematic Inaccuracies contain more so that all calibrations and usual Corrections have already been made, and that the scattered radiation has been eliminated with a suitable method.

According to the invention So raw images of the image pick-up area, so for example one specific area of a patient, with two different ones Radiation spectra recorded. These radiation spectra correspond different voltages of the x-ray tube or another radiation generator for image acquisition.

at The images showing the same image pickup area are respectively identical pixels associated with measured values, which are summarized as a pair of measured values to let.

In addition, methods are also conceivable in which, instead of dual-energy imaging, imaging is carried out with more than two different spectra, so that measured value pairs are generated instead of pairs of measured values, which are also included in the noise reduction method according to the invention for the purpose of determining reconstruction score. In the following, only couples are entered to the description fold. However, the scope of the invention also includes methods with more than two acquisition spectra and values obtainable therefrom.

Around now a separation of the different materials in the image pickup area, for example, of bones and soft tissues, to reach becomes a pair of measured values by calculation a pair of reconstruction values assigned, which is for example a material thickness or a mass occupation density, but also other suitable reconstruction values can act.

These Assignment of a reconstruction value pair to a pair of measured values takes place according to the invention under consideration a suitable feedback between the result and the measured value pair, ie the reconstruction value and the actual value Reading. Such a feedback allows it, the result images in terms of actually recorded measured data to check to reduce the noise and the appearance of ghosting to suppress. It will be through the feedback thus possible, a noise reduction without an occurrence to achieve ghost artifacts.

The Method refers to the image data recording, so a recording physical measurement data for processing and evaluation, so first to get a usable or optimal picture.

In particular, in the context of consideration of the feedback, the result can be determined by specifying a tolerance interval for the compatibility with the measured value pair. Thus, a so-called "feasibility problem" can be formulated in which it is assumed that the measured values, ie measured value pairs p = (p ₁ , p ₂ ), are subject to errors due to noise, ie it can be specified that certain pairs of reconstruction value pairs, for example material thickness pairs or material thickness vectors of the form b = (b ₁ , b ₂ ) are accepted as compatible solutions ("feasible solution"), provided they represent a solution of an inequitable equation to be formulated within a certain error fluctuation range of the measured value pairs p .

there can be a tolerance interval for a range of deviation up and down (+/-) can be specified.

Especially can the tolerance interval depending on a standard deviation for a noise of the measured values of the raw images and a Tolerance factor can be specified, especially as a product of Standard deviation with the tolerance factor.

The tolerance interval, which defines a deviation of the result values in the form of the reconstruction values with regard to the underlying measured values, is therefore predetermined in this case by a standard deviation and a tolerance factor. In particular, this interval can be defined by the product of a standard deviation with this tolerance factor. The standard deviation is expediently the standard deviation of the noise of the raw data, which is referred to as σ ( p ) = (σ (p 1 ), σ (p 2 )) given is.

Of the Tolerance factor can then be denoted by t. The product formation causes for the special case t = 0 only the exact solution is compatible. Will the tolerance factor chosen to t = 1, this means that as so-called "compatible Solutions "all solutions that are approved within a tolerance band of +/- one standard deviation σ. The standard deviation or its components can be as follows easy to estimate.

Mit Ik = Ik0e–p k und e–p k << 1folgt:

mit k = 1, 2, wobei σ die Standardabweichung für eine Komponente p_k eines Messwertepaars, e die Eulersche Zahl und I_k0 die ungeschwächte Intensität ohne Objekt bezeichnet.Advantageously, the standard deviation for the noise is determined using Poisson's statistics. This is due to the fact that two (logarithmic) measured values p ₁ , p ₂ , which were obtained with two different tube voltages, are the quotients of the measured intensities before and after the object to be recorded for the same detector pixel by the equations P 1 = -Ln (I 1 / I 10 ) P 2 = -Ln (I 2 / I 20 ) where I _k or I _{k0 denote} the measured intensities behind or in front of an object to be recorded, ie with and without attenuation. If these quantities correspond to registered photon numbers I _k , then they satisfy the Poisson statistic with a standard deviation

With I k = I k0 e -p k and e -p k << 1 follows:

with k = 1, 2, where σ denotes the standard deviation for a component p _{k of} a measured value _pair , e the Euler number and I _k0 the _unattenuated intensity without an object.

Thus, the standard deviation for each pixel (x, y) can be determined from a projection data pair p ₁ (x, y), p ₂ (x, y).

As a tolerance factor, a factor in the range greater than 0 and up to and including 3 can be specified. Of course, other factors are also conceivable, but a choice according to the inequality 0 <t ≤ 3 is preferable, ie a tolerance factor, which in the case t = 3 includes all solutions that are in the range of a deviation of 3σ, while in the (excluded) case t = 0 only the exact solution would be allowed. For the case t = 1, all (compatible) solutions must be within a tolerance band of one standard deviation.

The Compatibility of the result with the measured value pair can as the amount of difference between the measured value pair and the product one the transition from the reconstruction value pair to the Measured value pair describing coefficient matrix.

This coefficient matrix results from the fact that for a theoretical measured value pair (M ₁ , M ₂ ) with M 1 (b 1 , b 2 ) = -Ln (∫e -α₁ (E) b₁-α₂ (E) b₂ W 1 (E) dE) M 2 (b 1 , b 2 ) = -Ln (∫e -α₁ (E) b₁-α₂ (E) b₂ W 2 (E) dE) where b = (b ₁ , b ₂ ) denotes a pair of reconstruction values, e stands for the Euler number, E indicates the energy and the two spectra are denoted by W ₁ (E) and W ₂ (E) respectively, while α ₁ and α _{2 represent} mass attenuation coefficients, linear relationships of the form M 1 (b 1 , b 2 ) = α 1 (e 1 ) b 1 + α 2 (e 1 ) b 2 M 2 (b 1 , b 2 ) = α 1 (e 2 ) b 1 + α 2 (e 2 ) b 2 based on the assumption that each pair of reconstruction values (b ₁ , b ₂ ) has "equivalent discrete energies" e 1 = E 1 (b 1 , b 2 ) such as e 2 = E 2 (b 1 b 2 ) can be assigned.

It is assumed that the effective spectra W ₁ (E) and W ₂ (E) can be assumed to be known. These spectra include the emission spectra of the X-ray tube at two different voltages, the spectral filters and the energy-dependent detector response. They are normalized such that their integral is 1 in each case.

mit

The linear relationship for the theoretical measured values (M ₁ , M ₂ ) has as coefficients the coefficients α _i , which depend on the discrete energies. The coefficient matrix to be assigned to these coefficients can be denoted by A. This matrix, as expressed by the index used below, depends on the reconstruction value pairs b = (b ₁ , b ₂ ). The coefficient matrix thus has the form

With

erfolgen.The inversion, ie the recalculation of a pair of measured values to the associated pair of material thicknesses or other reconstruction values, can basically be done by inversion of this matrix

respectively.

zugeordnet ist.In order to be able to determine a suitable solution with various algorithms, it is expedient to first of all calculate and store a table in which each measured value pair p = (p ₁ , p ₂ ) contains the associated matrix, ie the four coefficients of the matrix, A =

assigned.

The Forecasting, in contrast to real-time calculation, offers the Advantage that in terms of computational effort no restrictions available. So it is possible, for example, first the measured value pairs corresponding to an expected value range, So z. B. the maximum water thickness plus the maximum bone thickness, to discretize in fine steps, for example of 0.01.

Then For each pair of measured values, an associated pair of reconstruction values can be used by inversion of the corresponding nonlinear system of equations, z. B. using the Newton method determined.

bilden, ermittelt werden.For a pair of reconstruction values, the corresponding "equivalent discrete energies" are determined, for which then the mass attenuation coefficients of the two materials, which are the four coefficients of the matrix

form, be determined.

gilt.Since the starting point of the determination of the matrix A is the measured value pair p , the matrix can be determined also mark with the index p , so that

applies.

kann somit die Verträglichkeit des Ergebnisses mit dem Messwertepaar bestimmt werden, worauf im Folgenden noch ausführlich eingegangen wird.By means of this matrix

Thus, the compatibility of the result with the measured value pair can be determined, which will be discussed in more detail below.

As has already been described, a pair of measured values to be identified with the pair of measured values can thus be assigned to each pair of measured values recorded with the different radiation spectra, and a pair of (equivalent) discrete energies can be assigned to each pair of reconstruction values, of which Depend on coefficients of the coefficient matrix. The coefficient matrix is accordingly given by the linear relationships for the theoretical value pairs, ie by the dependence of the components M ₁ and M _{2 of} the theoretical value pair on the components of the reconstruction value pair b ₁ and b ₂ .

The Reconstruction value pair may take into account a associated reference distribution, in particular as an optimization specification, be determined.

the is due to that in the mathematical formulation of the problem if possible, all available prior knowledge should be considered. consideration has found in the Feasibilitätserwägungen already the statistical uncertainty of the measured data. Furthermore it must be considered extremely unlikely that the reconstruction values associated with neighboring pixels, So for example, material thickness, randomly strong at random differ from each other. This means that local smoothness properties are to be expected.

such Properties or other properties that must be given or with a certain probability, can by the specification of a suitable reference distribution, here one relatively smooth reference distribution. Then it is time to find a solution that meets both the feasibility condition, as compatible with the reference distribution, so this is as similar as possible is.

The Reference distribution can be determined by determining one in the smallest Squares minimum deviation from the pair of reconstruction value and / or Specification of a non-quadratic deviation rule taken into account become.

there can be used as a reference distribution a highly smooth version a standard reconstruction can be used.

Given is therefore a pair of measured raw data images with the measured value pairs p and a standard deviation σ ( p ). Provide a reference distribution, so for example, a pair of material thickness images, according to b ^(ref) for the reconstruction value pairs and a tolerance factor t.

erfüllt, und das
des Weiteren z. B. im Sinne der kleinsten Quadrate minimal vom Referenzpaar b ^(ref) abweicht, also zudem ein Optimierungsproblem gemäß |b – b (ref)|2 = Minimumlöst.To determine a reconstruction value pair b, which is specified first, within a tolerance interval t with the tolerance factor, is compatible with the raw image data, so the Feasibilitätsbedingung

fulfilled, and that
further z. B. in the sense of least squares minimally differs from the reference pair b ^(ref) , so also an optimization problem according to | b - b (Ref) | 2 = Minimum solves.

Of course may have different rules regarding derogation the reference distribution is given by the pair of reconstruction values, which may be better or better in certain cases can lead to more suitable results.

Preferably, the reconstruction value pair is determined using an iterative algorithm, in particular using an Algebraic Reconstruction Technique (abbreviated to ART, in which case in particular an ART 3 or ART 4 algorithm can be used) and / or a multiplicative algebraic reconstruction -Technique and / or a maximum entropy algorithm. For example, the ART4 algorithm is the article "A family of iterative quadratic optimization algorithms for pairs of inequalities with application in diagnostic radiology" by GT Herman and A. Lent of Math. Prog. Study 9 (1978), pp. 15-29 , to call.

During the iteration, the abbreviations can be set for the limits of the tolerance interval ε 1 = tσ (p 1 ) and ε 2 = tσ (p 2 ) introduce, wherein the error bounds ε ₁ and ε _{2 are} pixel dependent. In this case, an iteration loop is to be carried out for each pixel (x, y), for example with an iteration start according to FIG b (0) = b (Ref) and values for a companion vector according to λ (0) 1 = λ (0) 2 = 0.

In the following, the iteration loop with n ≥ 0 for the two matrix lines k = 1 and k = 2 corresponding to the two energies is run through, the reprojection by q = <a k . b > is given (here the square brackets denote the formation of the scalar product). a _k is the row vector k of the matrix A.

angesetzt. Dementsprechend wird eine Korrektur gemäß b (n+1) = b (n) + cak durchgeführt.The residual error results too δ = p k - q, and a correction value is included

stated. Accordingly, a correction according to b (N + 1) = b (N) + approx k carried out.

It Thus, it is preferably an iterative algorithm with a correction step used. This correction step can vary depending on the algorithm used be different.

For the accompanying vector in step n + 1 λ (N + 1) k = λ (N) k - c.

Subsequently, the index according to n = n + 1 elevated. If the correction step involves only a negligible change, the iteration loop is aborted. The end of the iteration has been reached.

The Use of such algorithms for an application, as here only the solution of two equations for involves two energies, the equations being independent for each pixel (since the coefficient matrix depends on the measured value pair of the pixel) and to solve are in this form a hitherto completely unknown area represents.

Farther can be used during the correction step to influence the convergence speed a relaxation factor is taken into account. The introduction of such a factor thus allows the convergence behavior of the iteration process in a desired manner to influence or change.

The Different algorithms used to solve feasibility problems can be used differ by the type the correction step or by each deviating, for example non-quadratic, optimization functions or specifications. These different algorithms can be applied alternatively become. Ultimately, it is only decisive that the invention present problem of noise reduction or Geistartefaktvermeidung when recording with two different spectra as an optimization problem one Interval inequality is formulated.

According to the invention each one recorded with the two different radiation spectra Pair of measurements as at least one pair of reconstruction values associated with a pair of mass occupation densities and / or material thicknesses become. Of course, others can as well Reconstruction values are determined based on the raw data.

Farther can for at least one reconstructed value pair obtained as a result an adaptive correlated post-filtering, in particular a variant a median filtering, in particular in the filter mask, to be considered those pixel pairs that are negative are correlated.

the is based on the result images of a proposed iteration method especially when choosing larger tolerance interval parameters t tend to have a fine-grained so-called "salt-and-pepper" noise in isolated pixels. Suitable for the reduction of this Effects is a median filtering with a 3 × 3 mask.

Around only isolate isolated noise pixels in this way and not to change the structures themselves, it is appropriate to use a variant of median filtering, referred to here as "adaptive Correlated median filtering. "This filtering is based on the basic idea that the noise in the complementary Material images is strongly negatively correlated. It should only such Pixels are corrected with complementary sign deviate from their surroundings.

A corresponding algorithm can work in such a way that, for an image size of N × N, a 3 × 3 mask with the pixel as the center is formed for each pixel, the mask centers in both FIGS which have certain values dependent on this pixel.

Subsequently, the median values in the respective mask are determined. If the deviations of the central values from the median values, which can be denoted by d ₁ and d ₂ , have different signs, the central values are replaced by the median values.

This Method is performed for all pixels from (1, 1) to (N, N).

zu jedem Messwertepaar gemäß der Erfindung eine große Flexibilität hinsichtlich unterschiedlicher Verfahren zur Rauschfilterung ermöglicht.In summary, it should be noted that the tabulation of the four coefficients of the 2 × 2 matrix

for each pair of measured values according to the invention allows great flexibility with regard to different methods for noise filtering.

One iterative algorithm enforces the invention Consistency with the measurement data as part of their statistical inaccuracy.

At the Iterationsstart can by specifying a reference image as an example, the image properties are influenced. A gray scale change is not connected to it. For a suitable choice of the reference picture the image results are significantly reduced noise, so that practically no Ghosts occur more. Suitable reference images are, for example a strongly smoothed version of a standard reconstruction and the same.

different Iterative algorithms can be used according to the invention Find. The post-processing, for example, by an "adaptive Correlated median filtering "may have residual salt-and-pepper noise in isolated pixels. An application of the method on projection image series for a computer tomographic Image reconstruction is possible.

Further Advantages, features and details of the invention will be apparent from the following embodiments and from the drawings. there demonstrate:

1 Normalized spectra for dual energy imaging for different voltages and prefilters,

2 Mass attenuation coefficients for different materials,

3 a representation for determining an equivalent discrete energy for polychromatic spectra,

4 and 5 Representations of a water or bone image for different tolerance factors when using a method according to the invention and

6 and 7 the pictures of 4 and 5 after a subsequent adaptive correlated median filtering.

In the 1 Normalized spectra for dual-energy imaging for different voltages and prefilters are shown. It is on the x-axis 1 the quantum energy is plotted in keV while on the y-axis 2 the normalized intensity is plotted. The curve 3 indicates the spectrum at a voltage of 60 kV (kilovolts) and a pre-filtering of 0.01 mm copper, while the curve 4 the spectrum at the same voltage and a prefilter of 0.3 mm copper shows.

The curves 3 and 4 each show relatively narrow spectra with a peak lying at a low energy in the range of 40 and 45 keV peak.

The curve 5 corresponds to a spectrum with a voltage of 150 kV in a prefilter with 0.1 mm copper, the curve 6 a voltage of 150 kV in a prefilter with 0.3 mm copper. The curves 5 and 6 describe much broader spectra with narrower peaks, which are also found at higher energies.

logarithmisch aufgetragen ist.In the 2 mass attenuation coefficients μ / ρ (E) are plotted for different substances (ρ denotes the thickness, E the energy and μ the weakening). It is on the x-axis 7 the photon energy is given in keV (kilo-electron volts), while on the y-axis 8th the mass attenuation coefficient in

is plotted logarithmically.

The curve 9 corresponds to the course of the mass attenuation coefficient for iodine, the curve 10 the course for calcium, the curve 11 that for bones as well as the curves 12 and 13 in each case the course for water and fatty tissue. In this case, iodine according to the curve 9 For all energies a higher mass attenuation coefficient than the other materials. The mass attenuation coefficient for water according to the curve 12 is similar to that for adipose tissue according to the curve 13 , For higher energies, the mass attenuation coefficient for bones also increases according to the curve 11 comparably low values. Slightly higher are the values for calcium according to the curve 10 , The values, with the exception of iodine, are strictly monotonic for increasing energies.

In the 3 a plot for determining equivalent discrete energy for polychromatic spectra is shown. It is on the y-axis 14 the logarithmic weakening, on the x-axis 15 the energy as photon energy in keV applied. The example corresponds to a situation with 20 cm water and 5 g / cm ² bone.

The curve 16 returns the situation in the monochromatic case, while the curves 17 respectively. 18 refer to polychromatic spectra of 70 kV and 150 kV, respectively. The intersections of the curves 17 respectively. 18 with the curve 16 for the monochromatic case, the discrete energies are E ₁ and E ₂ .

In the 4 and 5 are representations of a water or bone image 19 . 20 shown for different tolerance factors when using a method according to the invention. As a simulation object serve bone slices with a material thickness of 50-250 mg / cm ² , wherein the increment is 50 mg / cm ² . These bone disks are over 20 cm of water. A two-spectra method with 70 kV and 150 kV tube voltage is used. The noise is given by the NEQ value 1000 (NEQ = noise equivalent quanta), ie the standard deviation is 3.16%. The material separation is achieved by a matrix inversion.

The top line 21 of the 4 indicates the iteration start, which is a heavily smoothed version of the result of direct matrix inversion as a reference. The second line 22 shows a corresponding exact inversion without noise filtering, ie with tolerance factor t = 0, ie the state of the line 21 before smoothing it with an averaging mask of 25x25 pixels.

at As shown, this smoothing does not produce ghosting. The restoration of the picture sharpness can over the Tolerance thresholds are influenced.

The third line 23 shows the result in an inventive application of an iteration algorithm with a tolerance interval of +/- 1σ. Ghost pictures are in this line 23 not recognizable. In addition, the noise is advantageously greatly reduced and the image sharpness restored.

The other lines 24 and 25 show for the water picture 19 the results at larger tolerance intervals +/- 1.5σ and +/- 2σ. In this case, the noise reduction is stronger, but the sharpness gain is lower.

Accordingly, the shows 5 in the case of the bone picture 20 in line 26 the startup image for the iteration, which is a heavily smoothed version of the line 27 equivalent. The line 28 shows the result with a tolerance factor 1 , the line 29 the result for a tolerance factor 1 . 5 and the line 30 finally the result with a tolerance factor of 2.

In the 6 and 7 are each the pictures of the 4 and 5 shown after an (additional) subsequent adaptive correlated median filtering.

Accordingly, in the 6 that correlates filtered water picture 31 , in the 7 the subsequently correlated median filtered bone image 32 shown.

The lines 33 respectively. 38 give each of the smoothed startup images again, by smoothing the lines 34 and 39 have arisen. The lines 35 and 40 show the result of applying an iteration algorithm with a tolerance interval of +/- 1σ, the rows 36 and 41 the result with a tolerance factor of 1.5 and the lines 37 and 42 with a tolerance factor of 2. The median post-filtering according to the 6 and 7 Almost eliminates the "salt and pepper" noise by repeating the filtering and eliminating the remaining "noise grains".

In principle, it is worth considering whether some small amount of noise is not yet acceptable or even desirable in order to reduce the visibility of very low low-frequency noise in the picture 6 and 7 from the strong low-pass filtering of the noise in the start image, to mask and to obtain a correspondingly "natural" image representation.

One Inventive iteration method of the Further on standard methods for noise filtering are set up for example, such that the start images the results of a so-called "Correlated Noise Reduction" algorithm, which provides a strong noise filtering, but the problem of ghosting brings with it. In one application of the iteration, as above described in addition to this filtering the ghost images are greatly reduced. Furthermore, there is an additional Noise reduction achievable.

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited non-patent literature

• - "Quantitative evaluation of noise reduction strategies in dual-energy imaging" by RJ Warp and JT Dobbins of Med. Phys. 30 (2), Feb 2003 [0005]
• "An Algorithm for Noise Suppression in Dual Energy CT Material Density Images" by WA Kalender, E. Klotz and L. Kostaridou of IEEE Trans. Med Imaging, Vol. 7, No. 3, September 1988, 218-224 [0005]
• - "A correlated noise reduction algorithm for dual-energy digital subtraction angiography" by CH McCollough, MS Van Lysel, WW Peppler and CA Mistretta of Med. Phys. 16 (6), Nov / Dec 1989, 873-880 [0005]
• - "A family of iterative quadratic optimization algorithms for pairs of inequalities with application in diagnostic radiology" by GT Herman and A. Lent of Math. Prog. Study 9 (1978), pp. 15-29 [0045]

Claims (16)

Method for reducing picture noise and / or of ghost artifacts in the context of the inclusion of at least one radiation-based Image of an image pickup area with two different radiation spectra, especially with two different X-ray spectra, with the steps - Capture raw images of the image capture area with the two different radiation spectra, respectively pairwise assigned measured values and - to Separation of different materials in the image recording area Determining at least one pair of measured values as a result of Separation of reconstructive value pairs to be taken into account a feedback between the result and the measured value pair. Method according to claim 1, characterized in that that in the context of consideration of feedback the result given a tolerance interval for the compatibility with the measured value pair is determined. Method according to claim 2, characterized in that that the tolerance interval depends on a standard deviation for a noise of the measured values of the raw images and a Tolerance factor is specified, in particular as a product of the standard deviation with the tolerance factor. Method according to claim 3, characterized that the standard deviation for the noise under application Poisson statistics is determined. Method according to claim 3 or 4, characterized that as a tolerance factor, a factor in the range larger 0 and up to and including 3 is specified. Method according to one of claims 2 to 5, characterized in that the compatibility of the Result with the measured value pair as the amount of the difference between the pair of measured values and the product of the transition from Reconstruction value pair on the pair of measured values describing coefficient matrix is determined. Method according to one of the preceding claims, characterized in that each one with the different Radiation spectra recorded pair of readings with the pair associated with measured values to be identified theoretical value pair becomes. Method according to one of claims 6 to 7, characterized in that each reconstruction value pair Pair of discrete energies is assigned, of which the coefficients depend on the coefficient matrix. Method according to one of the preceding claims, characterized in that the reconstruction value pair under Consideration of an associated reference distribution, in particular as an optimization specification. Method according to claim 9, characterized that the reference distribution is determined by determining one within the meaning of least squares minimal deviation from the reconstruction value pair and / or Specification of a non-quadratic deviation rule taken into account becomes. Method according to one of claims 9 or 10, characterized in that as reference distribution a highly smoothed Version of a standard reconstruction is used. Method according to one of the preceding claims, characterized in that the reconstruction value pair under Use of an iterative algorithm is determined, in particular using an Algebraic Reconstruction Technique, in particular ART 3 and / or ART 4, and / or a multiplicative algebraic reconstruction technique. and / or a maximum entropy algorithm. Method according to claim 12, characterized in that that uses an iterative algorithm with a correction step becomes. Method according to claim 13, characterized in that that during the correction step for influencing the convergence speed Relaxation factor is taken into account. Method according to one of the preceding claims, characterized in that each one with the two different Radiation spectra recorded pair of measurements as at least a reconstruction value pair a pair of mass occupation areas densities and / or material thicknesses. Method according to one of the preceding claims, characterized in that for at least one as a result obtained reconstruction value pair an adaptive correlated post-filtering, in particular a variant of a median filtering, in which in a corresponding Filter mask only those pixel pairs are taken into account, which are negatively correlated, is performed.