A photon counting CT ring artifact correction method based on double-domain optimization

Abstract

The present application relates to a kind of based on double-domain optimization's photon counting CT annular artifact correction method, the method includes the following steps: 1) the pre-correction of the sinogram of photon counting CT acquisition;2) to the pre-corrected sinogram, combine correction parameter fine-tuning sinogram detector direction response;3) to the fine-tuned sinogram is reconstructed, convert reconstructed CT image into HU value, and convert reconstructed CT graph into polar coordinate system;4) calculate the absolute value of the gradient of reconstructed graph along the polar radial direction under polar coordinate system, with the average value of the absolute value of the whole graph gradient minimum as the goal optimization correction coefficient in step 2, iterative calculation until convergence;5) the correction coefficient obtained by final convergence is used for the sinogram after pre-correction in step 1, image reconstruction is carried out to obtain corrected CT image.The method of the present application further corrects the problem of inconsistent detector response by optimizing the polynomial correction coefficient in double-domain, thereby removing the residual annular artifacts of photon counting CT image after pre-correction, and improving the image quality and diagnostic accuracy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of image processing, and particularly relates to a photon counting CT ring artifact correction method based on double-domain optimization. BACKGROUND

[0002] The photon counting CT detector does not need to use a physical grid to separate pixels, so the detector pixels are smaller, thereby realizing high spatial resolution and improving the contrast noise ratio, which can be used for clinical applications such as oncology, cardiology and neurology. In these applications, accurate and reliable imaging is crucial. However, due to different factors such as inconsistency of detector response, actual threshold voltage of each pixel and data acquisition error, the CT images collected and reconstructed contain high and low frequency ring artifacts. These artifacts appear as non-uniform concentric circles in the CT image, which are unrelated to the actual biological tissue structure and can seriously affect the diagnosis results of doctors.

[0003] The projection domain pre-correction based on physics can effectively correct most of the ring artifacts in the photon counting CT image. However, due to factors such as correction error and time drift of photon counting detector response, the pre-corrected CT image still has residual ring artifacts. The present application aims to remove the residual ring artifacts of the photon counting CT image after pre-correction. SUMMARY

[0004] In order to solve the problem of removing the residual ring artifacts of the photon counting CT image after pre-correction without damaging the image quality, the present application provides a photon counting CT ring artifact correction method based on double-domain optimization.

[0005] In order to achieve the above technical purpose, the technical scheme adopted by the present application is as follows: a photon counting CT ring artifact correction method based on double-domain optimization, the method comprising the following steps:

[0006] Step 1: pre-correcting the sinogram collected by the photon counting CT;

[0007] Step 2: adjusting the response of the sinogram detector direction in combination with the correction parameters for the pre-corrected sinogram;

[0008] Step 3: reconstructing the adjusted sinogram, converting the reconstructed CT image into HU value, and converting the reconstructed CT into polar coordinate system;

[0009] Step 4: calculating the absolute value of the gradient of the reconstructed image along the polar radius direction in the polar coordinate system, and optimizing the correction coefficient in step 2 with the minimum average value of the absolute value of the gradient of the whole image as the target, and iteratively calculating until convergence.

[0010] Step 5: using the correction coefficient obtained by final convergence for the sinogram pre-corrected in step 1 to perform image reconstruction to obtain the corrected CT image.

[0011] The beneficial effects of the present application are:

[0012] Compared with the physical-based projection domain annular artifact correction method, the present application takes advantage of the characteristic that the annular artifact appears as an easily identifiable and quantifiable strip artifact in the polar coordinate system, continuously optimizes the polynomial correction coefficients through the dual-domain joint of the projection domain and the image domain, applies the correction coefficients to the projection image, and then removes the residual annular artifact of the pre-corrected photon counting CT image, so that the CT image quality is higher and the tissue structure recognition is better. At the same time, the present method has a wide range of applications, does not require spectral information and training data, and can also be used for CT systems based on traditional energy integration detectors. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is a flowchart of the present application;

[0014] Figure 2 is a diagram showing the appearance of annular artifacts in different coordinate systems;

[0015] Figure 3 is a comparison diagram of annular artifact correction before and after different energy threshold values for real mouse data. DETAILED DESCRIPTION

[0016] The embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0017] Embodiment: As shown in the following, the present application is a photon counting CT annular artifact correction method based on dual-domain optimization, which comprises the following steps: Figure 1

[0018] Step 1: Pre-correcting the sinogram collected by the photon counting CT.

[0019] Step 2: Adjusting the response of the sinogram detector direction in combination with the correction parameters after pre-correcting the sinogram. The correction coefficient uses a polynomial form that does not contain a zero-order term. The first-order term in the initial correction coefficient is 1, and the remaining high-order terms are set to 0. The same adjustment parameters are used to perform polynomial correction on the pixels at the same detector position for different projection angles:

[0020]

[0021] where index i represents the projection angle direction, j represents the detector pixel direction, S i，j is the projection pixel value of the i-th row and j-th column, c p，j is the p-th order polynomial correction coefficient of the j-th column, and the adjusted sinogram S′ i，j is obtained by using the polynomial for correction.

[0022] Further, the step 3 specifically comprises the following processes:​

[0023] Step 3.1: fine-tuning the projection image S' by using the correction coefficient i，j The filtered back-projection reconstruction is performed to obtain the reconstructed image:

[0024] I μ (x, y) = R -1 (S' i，j )

[0025] where R -1 is the filtered back-projection algorithm used to reconstruct the CT image, I μ (x, y) is the reconstructed CT image.

[0026] Step 3.2: converting the reconstructed CT image into HU values:

[0027]

[0028] where μ w is the reference value of the linear attenuation coefficient of water. I HU (x, y) is represented as I HU (m, n) in a discrete image, where m is the index along the lateral direction and n is the index along the longitudinal direction.

[0029] Step 3.3: performing polar coordinate transformation on the reconstructed image to obtain a polar coordinate image:

[0030] I P (θ, r) = C2P(I HU (x, y))

[0031] where C2P(·) represents the transformation from the Cartesian coordinate system to the polar coordinate system. As Figure 2 shown, the reconstructed image I HU (x, y) is in the Cartesian coordinate system and contains ring artifacts, and the polar coordinate image I P (θ, r ) is in the polar coordinate system and contains bar artifacts corresponding to the ring artifacts. I P (θ, r) is represented as I P (k, l) in a discrete image, where k is the index along the angular direction and l is the index along the polar radial direction.

[0032] Further, the step 4 specifically includes the following processes:

[0033] Step 4.1: calculating the absolute value of the gradient of the reconstructed image along the polar radial direction in the polar coordinate system.

[0034] Step 4.2: optimizing the correction coefficient in step 2 to minimize the average value of the absolute value of the full image gradient, and iteratively calculating until convergence:

[0035]

[0036] where ||·|| denotes L2 loss, K and L are the number of pixels along the angular and radial directions of polar image I P (k, l) are the number of pixels along the angular and radial directions. The algorithm convergence criterion is that the absolute value of the gradient of the reconstructed image along the radial direction in the polar coordinate system no longer has a significant decrease, and the HU difference of the absolute value of the gradient between the two iterations within a certain range is less than 0.5 HU.

[0037] Further, the step 5 specifically includes the following processes:

[0038] Step 5.1: Use the final convergence obtained correction coefficient to the pre-corrected sinogram in step 1:

[0039]

[0040] Step 5.2: Reconstruct the corrected sinogram to obtain the corrected CT image:

[0041]

[0042] Step 5.3: Convert the reconstructed CT image to HU value:

[0043]

[0044] where μ w is the reference value of the linear attenuation coefficient of water.

[0045] The above is only the preferred embodiment of the present application, the protection scope of the present application is not limited to the above-mentioned examples, all technical solutions under the idea of the present application belong to the protection scope of the present application. It should be pointed out that for ordinary skilled in the art, some improvements and decorations without departing from the principles of the present application, should be considered as the protection scope of the present application. It should be pointed out that the above-mentioned examples, not used to limit the protection scope of the present application, the equivalent transformation or substitution made on the basis of the above technical solutions all fall within the scope of the present application claims.

Claims

1. A photon counting CT ring artifact correction method based on dual domain optimization, characterized in that, The method comprises the following steps: Step 1: pre-correcting the sinogram collected by the photon counting CT, Step 2: fine-tuning the response of the sinogram detector direction of the pre-corrected sinogram in combination with correction coefficients, Step 3: reconstructing the fine-tuned sinogram, converting the reconstructed CT image into HU values, and converting the reconstructed CT image into a polar coordinate system, Step 4: calculating the absolute value of the gradient of the reconstructed image along the polar radial direction in the polar coordinate system, optimizing the correction coefficients in step 2 with the minimum average value of the absolute value of the full image gradient as the target, and iteratively calculating until convergence, Step 5: using the correction coefficients obtained by the final convergence in step 1 to pre-correct the sinogram, and performing image reconstruction to obtain a corrected CT image; In step 2, the correction coefficients use a polynomial form that does not include a zero-order term, the first-order term in the initial correction coefficients is 1, and the remaining high-order terms are set to 0, and the same fine-tuning parameter is used to correct the pixels at the same detector position for different projection angles: wherein index i represents a projection angle direction, j represents a detector pixel direction, S i,j is a sinusogram pixel value of the ith row and jth column, c p,j is a pth order polynomial correction coefficient of the jth column, and a fine-tuned sinusogram pixel value S′ i,j is obtained by correction using a polynomial. Step 5 specifically includes the following process: Step 5.1: Final convergence of the resulting correction coefficients Sinogram S for step 1 after pre-correction i,j , Step 5.2: Final correction of the sinogram Image reconstruction is performed to obtain a corrected CT image Step 5.3: converting the reconstructed CT image into HU values: where μ w is a reference value for the linear attenuation coefficient of water, is the HU value of the final corrected CT image.

2. The photon counting CT ring artifact correction method based on double-domain optimization according to claim 1, characterized in that, Step 3 specifically includes the following process: Step 3.1: Fine-tune the projected image S' by applying a filter to S' to obtain a fine-tuned projected image S" i,j Perform filtered back-projection reconstruction to obtain a reconstructed image: I μ (x,y) = R -1 (S′ i,j ) where R -1 is a filtered back-projection algorithm for reconstructing the CT image, I μ (x,y) is the reconstructed CT image, step 3.2: converting the reconstructed CT image into HU values: where μ w is a reference value for the linear attenuation coefficient of water, I HU (x,y) corresponds to a discretized image representation I HU (m,n), where m is an index along the transverse direction and n is an index along the longitudinal direction, Step 3.3: performing polar coordinate transformation on the reconstructed image to obtain a polar coordinate image: I P (θ,r) = C2P(I HU (x,y)) where C2P(·) denotes the transformation from the Cartesian to the polar coordinate system, said reconstructed image I HU (x,y) in Cartesian coordinates and containing a ring artifact, said polar image I P (θ,r) in polar coordinates and containing a corresponding bar artifact, I P (θ,r) is represented by a discretized image I P (k,l), where k is the index along the angular direction and l is the index along the polar radial direction.

3. The photon counting CT ring artifact correction method based on double-domain optimization according to claim 1, characterized in that, Step 4 specifically includes the following process: Step 4.1: calculating the absolute value of the gradient of the reconstructed image along the polar radial direction in the polar coordinate system, Step 4.2: optimizing the correction coefficients in step 2 with the minimum average value of the absolute value of the full image gradient as the target, and iteratively calculating until convergence: where ||·|| denotes L2 loss, K and L are the number of pixels along the angular and polar direction, respectively P (k, l) along the angular and polar direction, are the optimized polynomial correction coefficients, and the convergence criterion is that the absolute value of the gradient of the reconstructed image along the polar direction in the polar coordinate system no longer has a significant decrease, and the HU difference between the absolute values of the gradients of the two iterations before and after is less than 0.5 HU within a certain range.

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