A noise suppression method for multi-material decomposition in energy-spectral CT based on basis transformation and selective filtering

Abstract

This invention discloses a noise suppression method for multi-material decomposition in energy-spectral CT based on basis transformation and selective filtering, comprising the following steps: normalizing the noise level of the energy-spectral CT image; performing singular value decomposition on the product matrix of the inverse of the material decomposition matrix and the noise level matrix of the energy-spectral CT image to obtain a basis transformation matrix; applying the basis transformation matrix to the noise-normalized energy-spectral CT image to obtain low-noise sub-images and high-noise sub-images; calculating weighted terms based on the differences in values ​​of the low-noise sub-images and spatial distances, and performing denoising filtering on the high-noise sub-images to obtain denoised high-noise sub-images; performing basis transformation inversion to transform the low-noise sub-images and denoised high-noise sub-images into energy-spectral CT images, and then performing material decomposition to form a noise-suppressed material basis image. Compared with existing technologies, this invention can better preserve the details in the basis image during noise suppression, has less bias in the material basis image values, and is closer to the gold standard image overall, while also having faster computation speed and lower hardware resource requirements.

Description

Technical Field

[0001] This invention belongs to the field of energy spectrum CT material decomposition noise suppression technology, specifically relating to an energy spectrum CT multi-material decomposition noise suppression method based on basis transformation and selective filtering. Background Technology

[0002] In the medical field and scientific research, spectral CT uses two or more X-rays of different energies to scan and image objects, allowing for the calculation of material composition ratios based on physical principles, thus enabling more advanced diagnostic techniques. However, in spectral CT, the large condition number of the material decomposition matrix leads to noise amplification, resulting in high noise levels in the obtained material-based images. This limitation restricts the clinical application of spectral CT.

[0003] Existing methods for noise suppression in energy dispersive spectroscopy (EDS) mainly include general methods derived from digital image processing, such as 3D block matched filtering (BM3D) and regularization. These methods fail to consider the underlying physical characteristics of the noise in EDS, resulting in limited effectiveness. Therefore, a new approach is urgently needed to address these technical problems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for suppressing noise in energy spectrum CT material decomposition based on basis transformation and selective filtering, which addresses the shortcomings of the prior art.

[0005] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for suppressing noise from energy-spectral CT material decomposition based on basis transformation and selective filtering, characterized by comprising the following steps:

[0007] Step S1: Normalize the noise level of the spectral CT image; normalize the noise level of the spectral CT image before performing the basis transformation, and divide the linear attenuation coefficients measured in the spectral CT image by their respective standard deviations.

[0008] Step S2: Perform singular value decomposition (SVD) on the product matrix of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image to obtain the basis transformation matrix; the basis transformation matrix is ​​obtained by performing singular value decomposition on the product matrix of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image.

[0009] Step S3: Apply the basis transformation matrix to the noise-level-normalized energy spectrum CT image to obtain a low-noise sub-image and several high-noise sub-images; the result of the basis transformation is a low-noise sub-image and several high-noise sub-images.

[0010] Step S4: Calculate a weighted term based on the differences in values ​​of the low-noise subgraphs and the spatial distance, and perform denoising filtering on the high-noise subgraphs to obtain a series of denoised high-noise subgraphs; the denoising filtering of the high-noise subgraphs is based on calculating a weighted term based on the differences in values ​​of the low-noise subgraphs and the spatial distance.

[0011] Step S5: Basis transformation inversion, transforming the low-noise sub-image and the denoised high-noise sub-image back into an energy spectrum CT image, and then performing material decomposition to form a noise-suppressed material basis image.

[0012] To optimize the above technical solution, the specific measures also include:

[0013] Further, step 1 refers to dividing the linear attenuation coefficients measured in the energy-spectral CT images by their respective standard deviations:

[0014]

[0015] in Let be a vector of linear decay coefficients at different energies. for The vector is formed by the standard deviations of each of the , and the length of the vector is the number of energies m used in the energy spectrum CT scan.

[0016] Furthermore, the product of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image in step 2 refers to:

[0017]

[0018] Where M + =(M T M) -1 M T It is the pseudo-inverse of the material decomposition matrix M. It is a matrix composed of vectors representing the linear decay coefficients of n base materials at m energies. It is a vector of length m, representing the linear decay coefficient of the k-th base material at the j-th energy. Usually, m ≥ n is required to make the material decomposition equation undetermined.

[0019] Furthermore, the basis transformation matrix in step 2 is calculated as follows:

[0020] U∑V T =SVD(A)

[0021] Where SVD represents singular value decomposition, and U and V T A is a unitary matrix, and ∑ is a diagonal matrix with eigenvalues ​​of A as its elements.

[0022] Furthermore, in step 3, applying the basis transformation matrix to the noise-level-normalized energy spectrum CT image refers to:

[0023]

[0024] in It is the material decomposition coefficient. This results in one low-noise subgraph and n-1 high-noise subgraphs.

[0025] Furthermore, the weighted filtering operation in step 4 is specifically as follows:

[0026]

[0027] Among them I bi ,i≥2 represents a specific image among n-1 high-noise sub-images, x and y represent the coordinates on the image, and w represents the weighting coefficient, which is calculated as follows:

[0028]

[0029] Where w d Distance-weighted terms:

[0030]

[0031] Where η is the scale parameter controlling the smoothness of the filter, a is the pixel size of the image, Th(·) is a 0-1 hard thresholding function, with a value of 1 when the condition is true and 0 otherwise, and D is the distance threshold; Weighting terms for low-noise subplot values:

[0032]

[0033] Where λ is a scale parameter controlling the smoothness of the filter, σ b1 isI b1 The standard deviation of X is the threshold value.

[0034] Furthermore, the material decomposition step in step 5 specifically involves: [decomposing material into form I]. b1 and I′ bi Reassembled pixel by pixel into vectors Inversion basis transformation yields the noise-suppressed material basis image.

[0035] The beneficial effects of this invention are:

[0036] Compared with existing technologies, this invention solves the problem of inconsistent noise levels in CT images acquired at different energies through a noise level normalization step, avoiding the impact on the basis transformation step. By setting a hard distance threshold in the selective filtering step, the filter becomes finite in length, resulting in faster overall computation speed and lower hardware resource requirements, providing a feasible solution for rapid image processing in practical applications. Furthermore, the noise suppression results achieved by this method better preserve details in the material-based image, and the noise-suppressed image more accurately reflects the characteristics of the original image. Simultaneously, compared to previous technologies, the bias in the material-based image values ​​is less, and it is closer to the gold standard image overall. In summary, this invention effectively suppresses material decomposition noise in spectral CT, contributing to enhancing the clinical application value of spectral CT. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the present invention;

[0038] Figure 2 These are schematic diagrams illustrating the intermediate results of the method of the present invention;

[0039] Figure 3 , Figure 4 The diagram shows the processing results of the method of the present invention on resolution evaluation phantoms, simulated energy spectrum CT data, and real energy spectrum CT data. Detailed Implementation

[0040] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0041] Example 1: As Figure 1 As shown, this invention is a method for suppressing noise in energy-spectral CT material decomposition based on basis transformation and selective filtering, comprising the following steps:

[0042] Step S1: Normalize the noise level of the energy spectrum CT image;

[0043] Specifically, the linear attenuation coefficients measured in the energy spectrum CT images are divided by their respective standard deviations:

[0044]

[0045] in Let be a vector of linear decay coefficients at different energies. Let m be a vector formed by the standard deviations of each element, and let m be the number of energies used in the spectral CT scan.

[0046] Step S2: Perform singular value decomposition (SVD) on the product matrix of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image to obtain the basis transformation matrix;

[0047] Specifically, the product of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image refers to:

[0048]

[0049] Where M + =(M T M) -1 M T It is the pseudo-inverse of the material decomposition matrix M. It is a matrix composed of vectors representing the linear decay coefficients of n basic materials at m energies. Let be a vector of length m, representing the linear decay coefficient of the k-th basis material at the j-th energy. Typically, m ≥ n is required to ensure that the material decomposition equation is undetermined. The basis transformation matrix is ​​calculated as follows:

[0050] U∑V T =SVD(A)

[0051] Where SVD represents singular value decomposition, and U and V T A is a unitary matrix, and ∑ is a diagonal matrix with eigenvalues ​​of A as its elements.

[0052] Step S3: Apply the basis transformation matrix to the noise level-normalized energy spectrum CT map to obtain a low-noise sub-map and several high-noise sub-maps;

[0053] Specifically, applying the basis transformation matrix to the noise-level-normalized energy spectrum CT image refers to:

[0054]

[0055] in It is the material decomposition coefficient. This results in one low-noise subgraph and n-1 high-noise subgraphs.

[0056] Step S4: Calculate the weighting term based on the difference in values ​​of the low-noise subgraphs and the spatial distance, and perform denoising filtering on the high-noise subgraphs to obtain a series of denoised high-noise subgraphs;

[0057] Specifically, this involves a weighted filtering operation:

[0058]

[0059] Among them I bi ,i≥2 represents a specific image among n-1 high-noise sub-images, x and y represent the coordinates on the image, and w represents the weighting coefficient, which is calculated as follows:

[0060]

[0061] Where wd Distance-weighted terms:

[0062]

[0063] Where η is the scale parameter that controls the smoothness of the filter, a is the pixel size of the image, Th(·) is a 0-1 hard thresholding function, which is 1 when the condition is true and 0 otherwise, and D is the distance threshold.

[0064] in Weighting terms for low-noise subplot values:

[0065]

[0066] Where λ is a scale parameter controlling the smoothness of the filter, σ b1 isI b1 The standard deviation of X is the threshold value.

[0067] Step S5: Basis transformation inversion, transforming the low-noise sub-image and the denoised high-noise sub-image back into an energy spectrum CT image, and then performing material decomposition to form a noise-suppressed material basis image.

[0068] Specifically, I b1 and I′ bi Reassembled pixel by pixel into vectors Inversion basis transformation yields the noise-suppressed material basis image.

[0069] like Figure 3 , 4 The figure shows the processing results of the method of the present invention on resolution evaluation phantoms, simulated spectral CT data, and real spectral CT data. As clearly seen in the figure, the noise suppression results obtained by this method better preserve the details in the material-based image. The noise-suppressed image more accurately reflects the characteristics of the original image, while exhibiting less bias in the material-based image values. Overall, it is closer to the gold standard image, has faster processing speed, lower hardware resource requirements, and also considers the issue of inconsistent noise levels in CT images acquired at different energies. Therefore, the present invention can effectively suppress material decomposition noise in spectral CT, contributing to enhancing the clinical application value of spectral CT.

[0070] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for suppressing noise from multi-material decomposition in energy-spectral CT based on basis transformation and selective filtering, characterized in that, The method includes the following steps: Step 1: Normalize the noise level of the energy spectrum CT images; Step 2: Perform singular value decomposition (SVD) on the product matrix of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image to obtain the basis transformation matrix; Step 3: Apply the basis transformation matrix to the noise level-normalized energy spectrum CT map to obtain a low-noise sub-map and several high-noise sub-maps; Step 4: Calculate the weighting term based on the difference in values ​​of the low-noise subgraphs and the spatial distance, and perform denoising filtering on the high-noise subgraphs to obtain a series of denoised high-noise subgraphs; Step 5: Basis transformation inversion, transforming the low-noise sub-image and the denoised high-noise sub-image back into the energy spectrum CT image, and then performing material decomposition to form the noise-suppressed material basis image; Step 1 involves dividing the linear attenuation coefficients measured in the energy spectrum CT images by their respective standard deviations. in Let be a vector of linear decay coefficients at different energies. for A vector formed by the standard deviations of each, the length of which is the number of energies used in the energy spectrum CT scan. ; In step 2, the product of the inverse of the material decomposition matrix and the noise level matrix of the energy spectrum CT image refers to: in It is a material decomposition matrix The pseudo-inverse matrix, yes Seed base material in A matrix composed of vectors representing the linear decay coefficients at various energies. It is a length of The vector represents the first... Seed material in the first The linear decay coefficient at this energy level is required to be... To ensure that the material decomposition equation is undetermined, The basis transformation matrix in step 2 is calculated as follows: in This represents singular value decomposition. and It is a unitary matrix. Therefore The eigenvalues ​​are diagonal matrices of elements; Step 3, applying the basis transformation matrix to the noise-level-normalized energy spectrum CT image, refers to: in It is the material decomposition coefficient. Construct a low-noise subgraph and Zhang Gao noise subgraph; The weighted filtering operation in step 4 is as follows: in express One of the high-noise subgraphs, , Represents coordinates on the image. This represents the weighting coefficient, and the specific calculation method is as follows: in Distance-weighted terms: in It is a scale parameter that controls the smoothness of the filter. It is the pixel size of the image. yes The hard threshold function has a value of 1 when the condition is true and 0 otherwise. It is the distance threshold; where Weighting terms for low-noise subplot values: in It is a scale parameter that controls the smoothness of the filter. yes standard deviation It is a threshold value.

2. The method for suppressing noise from multi-material decomposition in energy-spectral CT based on basis transformation and selective filtering according to claim 1, characterized in that, The specific steps of the material decomposition process in step 5 are as follows: ... and Reassembled pixel by pixel into vectors The inversion basis transformation yields the noise-suppressed material basis image. .

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