METHOD OF PROCESSING COMPUTER TOMOGRAPHY (CT) DATA FOR FILTER BACK PROJECTION (FBP)

Abstract

The present invention relates to a method of processing CT data for suppressing image cone beam artefacts (CBA) in CT images, which are reconstructed from said CT data. For the reconstruction the Frequency Split method is used. However, a straightforward use of this method can lead to an un-desired increase of the residual low-frequency noise left in the basis image after applying image domain de-noising methods. This residual noise then propagates rather linearly to the spectral results. In order to avoid this increase of the noise, the method presented here uses the FS method selectively and yet effectively. Thus, in a first aspect of the invention there is provided a method of processing computer tomography (CT) data for suppressing image cone beam artefacts (CBA) in CT images to be reconstructed from said CT data. The method comprises the steps of obtaining CT data generated during a CT scan of a patient (step S1); decomposing the obtained CT data in the projection domain resulting in a plurality of decomposed sinograms (step S2); and non-uniformly spreading between said decomposed sinograms noise and/or inconsistencies that would lead to image cone beam artefacts (step S3).

Claims

1. A method of processing computer tomography (CT) data for suppressing image cone beam artefacts (CBA) in CT images, the method comprising: obtaining the CT data generated during a CT scan; decomposing the obtained CT data in a projection domain resulting in a plurality of decomposed sinograms; non-uniformly spreading, between the decomposed sinograms, noise and/or inconsistencies that would lead to image cone beam artefacts; and reconstructing one or more base images by applying a filter back projection to the decomposed sinograms.

2. The method according to claim 1, further comprising applying a unitary basis transformation on the different sinograms decomposed in the projection domain, wherein the noise and/or inconsistencies that would lead to the image cone beam artefacts are as non-uniformly spread between the decomposed sinograms.

3. The method according to claim 1, wherein at least some low frequencies of the base image are reconstructed using not all data of the obtained CT data, while high frequencies of the base image are reconstructed using all data of the CT data.

4. The method according to claim 1, wherein a Frequency Split method is selectively applied to the plurality of sinograms.

5. The method according to claim 4, further comprising varying an aggressiveness of the Frequency Split method for the different sinograms.

6. The method according to claim 5, wherein the aggressiveness of the Frequency Split method is reduced for at least one sinogram having a high low-frequency noise.

7. The method according to claim 5, wherein the aggressiveness of the Frequency Split method is reduced for at least one sinogram having a low level of cone angle inconsistencies.

8. The method according to claim 5, further comprising controlling the variation of the aggressiveness of the Frequency Split method for the different sinograms by varying a cut off and/or shape of a low-frequency filter used in the Frequency Split method.

9. The method according to claim 5, further comprising controlling the variation of the aggressiveness of the Frequency Split method for the different sinograms by modifying a back projection weighting scheme used to generate a low-frequency image.

10. The method according to claim 1, wherein the CT data originate from a non-gated helical scan.

11. A system for processing computer tomography data for suppressing image cone beam artefacts in CT images, the system comprising: a memory that stores a plurality of instructions; and processor circuitry that coupled to the memory and is configured to execute the plurality of instruction to: obtain CT data generated during a CT scan; decompose the obtained CT data in the projection domain resulting in a plurality of decomposed sinograms; non-uniformly spread between the decomposed sinograms noise and/or inconsistencies that would lead to image cone beam artefacts; and reconstruct one or more base images by applying a filter back projection to the decomposed sinograms.

12-14. (canceled)

15. A non-transitory computer-readable medium for storing executable instructions, which cause a method to be performed to process computer tomography (CT) data for suppressing image cone beam artefacts in CT images, the method comprising: obtaining the CT data generated during a CT scan; decomposing the obtained CT data in a projection domain resulting in a plurality of decomposed sinograms; non-uniformly spreading, between the decomposed sinograms, noise and/or inconsistencies that would lead to image cone beam artefacts; and reconstructing one or more base images by applying a filter back projection to the decomposed sinograms.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0077] FIG. 1 shows a flow diagram of a method of processing computer tomography (CT) data for suppressing image cone beam artefacts (CBA) in CT images to be reconstructed from said CT data according to an exemplary embodiment of the invention.

[0078] FIG. 2 shows flow diagram of a method of processing CT data for suppressing CBA in CT images that are reconstructed from said CT data according to an exemplary embodiment of the invention.

[0079] FIG. 3 shows typical scatter plots of the noise components which can be used in exemplary embodiments of the present invention.

[0080] FIG. 4 shows a CT system for processing CT data for suppressing image cone beam artefacts (CBA) in CT images according to an exemplary embodiment of the present invention.

[0081] FIGS. 5a-c show results of an exemplary embodiment of the method of the present invention over the prior art technique of reconstructing CT images.

DETAILED DESCRIPTION OF EMBODIMENTS

[0082] FIG. 1 shows a flow diagram method of processing CT data for suppressing image cone beam artefacts (CBA) in CT images, which are reconstructed from said CT data. For the reconstruction the FS method is used. However, a straightforward use of this method can lead to an un-desired increase of the residual low-frequency noise left in the basis image after applying image domain de-noising methods. This residual noise then propagates rather linearly to the spectral results. In order to avoid this increase of the noise, the method shown in FIG. 1 uses the FS method selectively and yet effectively. This will be explained in more detail hereinafter, also in combination with the other FIGS. 2 to 4.

[0083] The method of FIG. 1 comprises the steps of receiving/providing/obtaining CT data generated during a CT scan of a patient in step S1. As a further step the obtained CT data are decomposed in the projection domain resulting in a plurality of decomposed sinograms in step S2. Moreover, a non-uniform spreading between said decomposed sinograms with respect to noise and/or inconsistencies that would lead to image cone beam artefacts is carried out in step S3. After step S3 the resulting data, i.e. the sinograms with the distributed noise/inconsistencies are used in step S4. In this step a reconstruction of one or more base images is carried out by applying a filter back projection (FBP) to the decomposed sinograms, to which the non-uniformly spreading was applied in step S3, thereby using the Frequency Split (FS) method in step S4.

[0084] In other words a practical method for suppressing image CBA in wide cone angle spectral CT is proposed here. As opposed to the original FS method, the method of the present invention helps to restrain the low-frequency noise in these images, as will be explained in more detail hereinafter, especially in the context of the embodiment shown in FIG. 2.

[0085] It should be noted that the method of FIG. 1 is preferably carried out on a computer, e.g. a reconstruction server, which is typically used for reconstructing CT images. Moreover, possible applications of this method presented here are all non-gated helical scans in a variety of wide cone angle spectral CT systems, like Dual-energy systems like the dual-layer detector, the fast kVp switching or the dual source, as well as photon counting systems.

[0086] The result of the method steps S1 to S3 as described hereinbefore will result in sinograms, in which the noise and/or inconsistencies that would lead to image cone beam artefacts are non-uniformly, i.e. unevenly spread. Preferably, the noise and/or inconsistencies are spread as non-uniformly as possible, i.e. with a maximum in non-uniform distribution of said noise and/or inconsistencies that would lead to image cone beam artefacts. This will be explained in more detail in the context of FIG. 2.

[0087] Again, the Frequency Split (FS) method as used in the context of FIG. 1 can be understood as a filter back projection (FBP) in which at least some low frequencies of the base image are reconstructed using not all data of the obtained CT data, while high frequencies of the base image are reconstructed using more, preferably all data of the CT data, as will be explained now in the context of FIGS. 2 and 3.

[0088] FIG. 2 shows a flow diagram of a method of processing CT data for suppressing CBA in CT base images that are reconstructed from said CT data according to an exemplary embodiment of the invention. As will become apparent from the following explanations, FIG. 2 shows a practical method for suppressing image CBA in wide cone angle spectral CT, since it helps to restrain the low-frequency noise in these images. The embodiment shown in FIG. 2 can be applied to all non-gated helical scans in a variety of wide cone angle spectral CT systems like dual-energy systems like the dual-layer detector, the fast kVp switching or the dual source, as well as photon counting systems.

[0089] In the method 200 of FIG. 2 a pre-calculated basis for transformation 201 is used to non-uniformly spread, between the decomposed sinograms 202, noise and/or inconsistencies that would lead to image cone beam artefacts. This results in a change of base, as will be explained in the detailed exemplary embodiment following hereinafter. There are of course different ways to pre-calculate the basis transformation 201. For example a-priory knowledge with the intention to spread the noise in a non-uniform manner between the different sinograms can be used. The idea here is to reconstruct each sinogram to an image using the FS method selectively for each basis element, i.e. to reduce the aggressiveness of the FS sinograms known to have higher low frequency noise than the others. Alternatively, a different a-priory knowledge can used, now with the intention to spread the inconsistencies originating from the wide cone angle in a non-uniform manner between these different sinograms. In this case, one should reconstruct the sinograms, reducing the aggressiveness of the FS for those known to contain less cone angle inconsistencies than the others. Using either one of these two approaches, or a combination of both of them, one can manage to have a satisfying reduction of CBA and at the same time to avoid increasing the residual low-frequency noise in the spectral results.

[0090] In FIG. 2 there are also the plurality of decomposed sinograms 204a, 205a, and 206a shown to which the change of base is applied for non-uniformly spreading, between the decomposed sinograms 202, noise and/or inconsistencies. Moreover, FIG. 2 shows that the FS method is applied differently to the different sinograms with respect to the aggressiveness of the FS method, see 204b, 205b, 206b. This then results in the reconstructed basis images 206, which can be used to produce the spectral results. The principle of the embodiment shown in FIG. 2 will be elucidated now with a detailed further embodiment.

Detailed Exemplary Embodiment

[0091] Industrial dual energy CT scanners consist of collecting signals at two energy bins. In photon counting CT systems the number of bins denoted by n.sub.bin can increase for example to 5. By projection domain decomposition a number of n.sub.m equivalent paths are decomposed numerically, where n.sub.m≤n.sub.bin. This can be done by either inverting an analytic expression, or by maximizing the likelihood function. Let us denote these equivalent paths by A.sub.α; α=1, 2 . . . n.sub.m.

[0092] For convenience, we translate the equivalent paths to dimensionless line integrals denoted by L.sub.α as follows. Here μ.sub.α is the attenuation coefficient of the material corresponding to A.sub.α at some fixed energy, e.g. at 70 keV.

L.sub.α=A.sub.α.Math.μ.sub.α; α=1,2 . . . n.sub.m.  (1)

[0093] Basis images denoted by I.sub.α are then reconstructed from the sinograms of these line integrals by the filter-back-projection (FBP) method. These images provide all spectral results e.g. virtual mono-energetic images, iodine no water images, K-edge material images, etc. To allow an accurate quantitative imaging, these images must be free of CBA. Here, the FS method can be used. However, a straightforward use of this method can lead to an un-desired increase of the residual low-frequency noise left in I.sub.α after applying image domain de-noising methods. This residual noise then propagates rather linearly to the spectral results. In order to avoid this increase of the noise, this embodiment suggests the use of the FS method selectively and yet effectively. For this purpose, we first apply in this exemplary embodiment a unitary basis transformation on L.sub.α.

L.sub.β=Σ.sub.α=1.sup.n.sup.mU.sub.βα.Math.L.sub.α∀β∈1,2 . . . n.sub.m.  (2)

[0094] The basis transformation matrix U.sub.βα can be selected using a-priory knowledge with the intention to spread the noise in a non-uniform manner between the different sinograms L.sub.β. The idea here is to reconstruct each sinogram L.sub.β to an image I.sub.β using the FS method selectively for each basis element β. I.e. to reduce the aggressiveness of the FS for L.sub.β sinograms known to have higher low frequency noise than the others.

[0095] The transformation matrix U.sub.βα can also be selected using a different a-priory knowledge, now with the intention to spread the inconsistencies originating from the wide cone angle in a non-uniform manner between these different sinograms. In this case, we reconstruct the L.sub.β sinograms, reducing the aggressiveness of the FS for those known to contain less cone angle inconsistencies than the others.

[0096] Using either one of these two approaches, or a combination of both of them, we manage to have a satisfying reduction of CBA and at the same time to avoid increasing the residual low-frequency noise in the spectral results.

[0097] Controlling the FS aggressiveness according to this exemplary method is carried out by varying the cut-off or shape of the low-frequency filter used by the FS method, as mentioned in the FS method paper cited hereinbefore. Alternatively, the aggressiveness can be changed by modifying the BP weighting scheme used to generate the low-frequency image.

[0098] Since transforming the basis L.sub.α to L.sub.β is done linearly, we do not need to apply later on the inverse transformation to get I.sub.α from I.sub.β. Instead, we can extract the spectral results directly from I.sub.β. The flow chart of this is shown in FIG. 2. We will now demonstrate exemplary embodiments of this method in more details.

[0099] This method is designed for various numbers of decomposed equivalent paths. Yet, to demonstrate it visually we address here by an example a dual energy system where n.sub.m=n.sub.bin=2. We choose the basis L.sub.α so that L.sub.α=1 represents the line integral through a virtual material having an energy-dependent attenuation profile that is similar to the attenuation profile of the Compton scatter mechanism in water. We complete the basis, choosing L.sub.α=2 as the line integral through the virtual material having an energy-dependent attenuation profile that is similar to the sum of the attenuation profiles of the Rayleigh scatter and photoelectric mechanisms in water.

[0100] In FIG. 3 we show typical scatter plots of the noise components of L.sub.α. To obtain these, we use a simulation of the NCAT mathematical phantom scan. The noise components are obtained after omitting from the noisy L.sub.α their values obtained by a noiseless simulation. In (a) of FIG. 3 we show a water like sinogram of L.sub.α=1+L.sub.α=2 of a given detector row. We define within it two regions of interest (ROIs), see the oval contours. In (b) of FIG. 3 we show the noise components of the readings belonging to these ROIs. FIG. 3 provides two important observations. First, a clear anti-correlated behavior between L.sub.α=1,2.sup.noise with a major principal axis oriented at about −45°. Second, insensitivity of this axis with respect to the location of the readings within the sinogram. In fact, for given spectra of the system in the two energy bins, this axis also hardly changes between sinograms of different scanned objects. Following this notion we choose U.sub.βα as in (3). This allows spreading the noise between the L.sub.β sinograms in the most non-uniform manner.

[00001]$\begin{array}{cc}{U}_{\beta \alpha }=\frac{1}{\sqrt{2}}.Math.\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right].& \left(3\right)\end{array}$

[0101] Generalizing these observations back to n.sub.m≥2 we introduce now the covariance matrix denoted by Σ.sub.αα, that describes the noise correlation between the different L.sub.α. The unitary transformation matrix U.sub.βα used in (2) helps to diagonalize U.sup.TΣU. Its columns are taken as the right eigenvectors of Σ.sub.αα′. Ordering them according to their eigenvalues in a descending order, the noise within the sinograms of the paths L.sub.β are decreasing β with as designed.

[0102] Choosing the matrix U.sub.βα according to the covariance matrix Σ.sub.αα′ is basing on the underlying assumption by which the amount of wide cone angle inconsistencies diffusing into the spectral results through the different path sinograms L.sub.β is roughly the same. However, as mentioned briefly before, another approach is to use a-priory knowledge on the patient anatomy in order to deliberately construct sinograms of L.sub.β that contain different amounts of wide cone angle inconsistencies. An example for such a-priory knowledge is the fact that most of the image CBA originate from the strong gradients of the cortical bone content of the patient along the rotation axis z. Here we neglect the air to soft tissue interfaces at the diaphragm region. The cortical bone X-ray attenuation can be described within the approximation involved within the two base model as a linear combination of the two virtual materials described before that define the dual-energy basis elements L.sub.α=1,2 With this input, we can use the basis transformation matrix U.sub.βα.sup.CB given in (5).

[00002]$\begin{array}{cc}{\mu }_{CB}\left(E\right)=c_1.Math.{\mu }_{\alpha =1}\left(E\right)+c_2.Math.{\mu }_{\alpha =2}\left(E\right).& \left(4\right)\end{array}$$\begin{array}{cc}{L}_{\beta }={.Math.}_{\alpha =1}^{n_m}{U}_{\beta \alpha }^{CB}.Math.L_{\alpha };U_{\beta \alpha }^{CB}=\frac{1}{\sqrt{c_1^2+c_2^2}}.Math.\left[\begin{array}{cc}{c}_1& c_2\\ c_2& -c_1\end{array}\right].& \left(5\right)\end{array}$

[0103] The inventor of the present invention could also demonstrate in tests shown in FIGS. 5a to 5c the advantages offered by the method presented herein. The sagittal brain images shown in FIGS. 5a to 5c are reconstructed from a simulated dual-energy helical scan of 8-cm beam opening at rotation center, pitch factor of 0.3, and 340 mAs. If no FS method is applied for the reconstruction as shown in FIG. 5 a, an unacceptable strip-shaped CBA appear around the cerebellum. In FIG. 5b the inventor used the FS method to reconstruct the original basis elements L.sub.α=1,2 with a low frequency filter that roles down to zero at 4 line pairs per cm (LPP). Here, the suppression of CBA is priced by an increase of the residual low-frequency noise. This noise increase is sabotaging the differentiation between gray and white matter and is damaging the image more than the original CBA. The residual low-frequency noise (in x-y) is also responsible for the fuzziness of the image around the cerebellum. In FIG. 5c, the inventor non-uniformly spreads, between the decomposed sinograms, noise and/or inconsistencies that would lead to image cone beam artefacts. As an example, he switched to a new basis using U.sub.βα described in formula (3) below. While reconstructing the sinogram of L.sub.β=2 with the FS method settings used to get FIG. 5b, the L.sub.β=1 sinogram is reconstructed without using the FS method. Due to the selective use of the FS in the test of FIG. 5c, no increase of the residual low-frequency noise is observed with respect to FIG. 5a. At the same time, a clear suppression of CBA is still accomplished. Thus, as is confirmed by these tests, the method of processing computer tomography (CT) data for suppressing image cone beam artefacts (CBA) in CT images to be reconstructed from said CT data provides improved reconstruction results as compared to the prior art.

[0104] FIG. 4 shows a CT system 400 for processing CT data for suppressing image cone beam artefacts (CBA) in CT images according to an exemplary embodiment of the present invention. The system 400 comprises a CT imaging system 401, 402, and system 403 with a calculation unit (406), which is configured for: [0105] receiving CT data generated during a CT scan of a patient; [0106] decomposing the provided CT data in the projection domain resulting in a plurality of decomposed sinograms; and [0107] non-uniformly spreading between said decomposed sinograms noise and/or.

[0108] Also the computer program element 404 is shown, which, when being executed by at least one processing unit (PU), is adapted to cause the processing unit (PU) to perform the method as described herein.

[0109] With such a calculation unit 406 one can cure the problems in the prior art of reconstructing CT images, in which the frequency split method is applied, but brings in the disadvantage that the low frequency noise components of the image increase. This increase of this noise becomes even trickier in spectral CT images reconstructed after projection domain decomposition. These disadvantages are overcome with the calculation unit 406, since after processing the sinograms with the FS method the increase of the low frequency noise components in the image to be reconstructed will be avoided or at least be reduced.

[0110] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing a claimed invention, from a study of the drawings, the disclosure, and the dependent claims.

[0111] In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfill the functions of several items re-cited in the claims. The mere fact that certain measures are re-cited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.