METHOD AND SYSTEM FOR IMAGE RECONSTRUCTION FOR COMPUTER TOMOGRAPHY

Abstract

The present invention pertains to a method and system for image reconstruction for computer tomography, in particular for reducing beam hardening effects, wherein image reconstruction is performed based on the generalized Lambert-Beer law for poly-chromatic sources.

Claims

1. Method for image reconstruction for computer tomography, in particular for reducing beam hardening and scattering artefacts, wherein image reconstruction is performed based on the generalized Lambert-Beer law for polychromatic sources with scattering term $\begin{array}{cc}I\left(p\right)={}_{e=0}^{e_{\max }}{I}_0\left(e\right)\exp \left(-{}_{t=0}^{d_{\max }}-\log \left(\left(r_p\left(t\right),e\right)\right)\mathrm{dt}\right)\mathrm{de}+S\left(p\right)& \left[\mathrm{Equation}1\right]\end{array}$ where I(p) is the intensity at pixel p, I.sub.0(e) is the energy distribution of the source, r.sub.p the ray associated with pixel p, (x,e) the energy-dependent absorption coefficient of the volume at position x, and S(p) is the amount of incident scattered intensity at pixel p, wherein the integration limits are e.sub.max, the maximum energy emitted by an source during imaging of an object and d.sub.max, the distance between the energy source and a detector used during imaging of the object.

2. Method according to claim 1, comprising the step: Solving Equation 1 by using an iterative algorithm based on differentiable Monte-Carlo simulation of photons.

3. Method according to claim 2, wherein in each iteration of the iterative algorithm, a number of n pixels is randomly selected across all projections of a number of projections.

4. Method according to claim 3, wherein for each pixel, a number of k energy samples are drawn.

5. Method according to claim 4, further comprising the step: tracing for at least one of the selected pixels, at least one of the k energy samples through a volume using the inner integral of Equation 1 thereby obtaining a transmission probability (p,e) of an energy level associated with the at least one energy sample.

6. Method according to claim 5, wherein a step of integrating all energy samples belonging to the same pixel is performed herby obtaining a transmission intensity T(p) of the primary beam.

7. Method according to claim 6, wherein the estimated scatter intensity S(p) is added to the transmission intensity T(p) resulting in the predicted intensity I(p).

8. Method according to claim 6, further comprising a step of comparing the estimated intensity I{circumflex over ()}(p) with a measured intensity I(p) at a detector element, generating a gradient from the comparison and preferably backpropagating the gradient through the Monte-Carlo photon simulation.

9. Method according to claim 6, further comprising an optimization step comprising adapting at least one parameter, a subset of parameters or all parameters of Equation 1, preferably parameters I.sub.0(e) and/or (x, e) and/or S(p).

10. System configured to perform a method according to claim 1.

11. System according to claim 10, wherein the system comprises or consists of a computer tomography device.

12. Computer program product comprising machine executable instructions causing a system executing the instructions to perform a method according to ene of claim 1.

13. Computer-readable medium comprising a computer program product according to claim 12.

14-15. (canceled)

Description

BRIEF DESCRIPTION OF THE FIGURES

[0036] Further features and effects are disclosed in the following description of the figures. In the figures,

[0037] FIG. 1a) shows a CT-image of a circuit board using conventional image reconstruction.

[0038] FIG. 1b) shows a CT-image of the same circuit board as in FIG. 1a) using image reconstruction according to the present invention.

[0039] FIG. 2a) shows a CT-image of a camera lens using conventional image reconstruction.

[0040] FIG. 2b) shows a CT-image of the same camera lens as in FIG. 2a) using image reconstruction according to the present invention.

[0041] FIG. 3 shows a flow chart of a method according to an embodiment of the invention.

[0042] FIG. 4 shows another flow chart of a method according to an embodiment of the invention.

[0043] FIG. 5a) shows a CT-image of a telephone and a computer chip using conventional image reconstruction.

[0044] FIG. 5b) shows a CT-image of the same telephone and computer chip as in FIG. 5a) using image reconstruction according to the present invention.

[0045] FIG. 6a) shows a CT-image of a high-absorption electric motor using conventional image reconstruction.

[0046] FIG. 6b) shows a CT-image of the same high-absorption electric motor as in FIG. 6a) using image reconstruction according to the present invention.

DETAILED DESCRIPTION

[0047] As can be clearly seen from the figures, the present invention achieves much clearer images with much less distortion due to beam hardening effects. The present invention demonstrates a significant reduction in beam hardening artifacts, addressing a long-standing challenge in computed tomography.

[0048] In FIG. 1, a comparison is presented between image reconstruction results of a method according to the present invention and image reconstruction results obtained using a state-of-the-art iterative reconstruction provided by the Astra Toolbox, where the latter fails to accurately reconstruct the multi-material circuit board.

[0049] Furthermore, FIG. 2 illustrates the superior image reconstruction achievable with the present invention. The lens features materials of different densities, from the rubber grip band to various metal components and the glass lenses.

[0050] With the present invention, the boundaries between these components are much more pronounced and sharper.

[0051] Further, the exemplary embodiment of the invention of FIG. 3 is described: In order to solve Equation (1), a novel iterative algorithm (as illustrated in FIG. 3) based on differentiable Monte-Carlo simulation of photons is used. This algorithm is outlined in FIG. 3 and described in the following. In the embodiment of FIG. 3, the algorithm comprises steps a) to f), but not all of these steps have to be present. The steps are explained below.

[0052] Step a) In each iteration, a number of n pixels are randomly selected across all projections. For each pixel, k energy samples are drawn from the current estimate of the source's energy distribution I0(e).

[0053] Step b) The corresponding photons are traced along rays through the volume and the absorption (x, e) is evaluated at each spatial location x using the photon's energy e.

[0054] Step c) The absorption values are integrated using the inner integral of Eq. (1). This results in the transmission probability of a photon with the energy e. For an efficient computation, the integral can be replaced by a finite sum of discretized volume samples during the reconstruction.

[0055] Step d) All photons that correspond to the same ray are integrated using the outer integral of Eq. (1) together with the energy distribution I0(e). The result is the estimated X-ray intensity at the detector pixel I{circumflex over ()}(p), which corresponds to the given ray. Similar to c), the integral is discretized to a finite sum over the k energy samples that have been drawn in a).

[0056] Step e) Finally, the estimated intensity I{circumflex over ()}(p) is compared to the measured intensity I(p) using the mean-square error (MSE) resulting in a gradient g for the pixel p.

[0057] Step f) The pixel gradient g is propagated back through the photon simulation as depicted by the dashed arrows in FIG. 3. Once the gradient reaches the parameters I0(e) and (x, e), backpropagation is finished and the parameters are optimized using gradient decent.

[0058] During the reconstruction, the steps a)-f) are preferably repeated until convergence or a maximum number of iterations is reached. In the end, the volume (x, e) is obtained, which can be used for analysis and diagnostic tasks.

[0059] A method according to the present inventions defined in claim 1 can comprise any one or more of steps a) to f) in any desirable combination.

[0060] The present invention offers a solution for eliminating beam hardening artifacts in multi-material objects, thus significantly improving image quality.

[0061] This advancement has wide-ranging applications, particularly in the fields of industrial quality assurance and measurements, where many objects consist of a combination of plastic and metal components. With reduced image artifacts, defects can now be detected more accurately, minimizing the occurrence of false positives.

[0062] Additionally, in the medical field, the present invention enables accurate diagnosis for patients with metal implants, overcoming the challenges posed by strong artifacts that previously hindered precise imaging and analysis.

[0063] FIG. 4 shows in detail an embodiment of a method according to the present invention.

[0064] The steps shown in FIG. 4 show one iteration of method in that these steps or a subset thereof are repeated until a desired image quality is achieved.

[0065] The forward simulation (downwards arrows) computes the expected image intensity for a random selection of pixels and energies. Using the measured X Ray-projections, the gradient of the loss function is evaluated and then backpropagated to the input parameters (upward arrows)

[0066] In each iteration of the iterative algorithm, a number of n pixels can be randomly selected across all projections. Preferably, for each of the selected pixels, a number of k energy samples are drawn. (See FIG. 4, Step 1.)

[0067] A method according to the present invention can further comprise the step: tracing for at least one of the selected pixels, at least one of the k energy samples through a volume using the inner integral of Equation 1 thereby obtaining a transmission probability (p,e) of the associated energy level. Preferably, the step of tracing is performed for all k energy samples and all n pixels. (See FIG. 4, Step 2.)

[0068] All energy samples belonging to the same pixel are then integrated using the transmission probability (p,e) and the energy distribution I0(e). The result is the transmission intensity T(p) of the primary beam (without scattering) (See FIG. 4, Step 3.)

[0069] As a next step, the estimated scatter intensity S(p) is added to the transmission intensity T(p) resulting in the predicted intensity I(p) at the detector pixel p. (See FIG. 4 Step 4.)

[0070] A method according to the present invention can further comprise a step of comparing the estimated intensity I(p) with a measured intensity I{circumflex over ()}(p) at the detector element, generating a gradient from the comparison and preferably backpropagating the gradient through the Monte-Carlo photon simulation. (See FIG. 4 Step 5.)

[0071] Steps 3, 4 and 5 or any desirable subset thereof can comprise a step of backpropagation to the previous step, as e.g. indicated by the upward arrows in FIG. 4.

[0072] Steps 2, 3 and 4 or any desirable subset thereof can comprise a step of updating the parameters used by the method, e.g. as indicated in FIG. 4.

[0073] A method according to the present invention can further comprise an optimization step comprising adapting at least one parameter, a subset of parameters or all parameters of Equation 1, preferably parameters I0(e) and/or (x, e) and/or S(p).

[0074] The parameters I0(e), (x, e) and S(p) can be modelled as parametric functions to reduce the complexity of equation 1 and get rid of ambiguities. Preferably these functions are differentiable and simple to compute like polynomials or piecewise linear functions.

[0075] The initialization of the parameters I0(e), (x, e) and S(p) is arbitrary. Preferably the parameters are initialised randomly in a reasonable range or to zero.

[0076] As shown in FIG. 5, top panel, a CT reconstruction using a prior art technique of a telephone with plastic housing and several metal components inside suffers from severe streaking artefacts due to the beam hardening effect.

[0077] The same holds true for FIG. 5, lower panel. In the prior art reconstruction image, horizontal stripe artefacts are visible. Furthermore, the overall image quality is significantly worse compared to the reconstruction with the present invention.

[0078] FIG. 6 shows a CT reconstruction using prior art and the present invention of a high-absorption electric motor. Due to beam hardening and scattering the prior art method creates severe artefacts and cannot estimate the correct density of the copper and steel parts.