CN110428395B - Multi-material decomposition method of single-energy spectrum CT image - Google Patents

Multi-material decomposition method of single-energy spectrum CT image Download PDF

Info

Publication number
CN110428395B
CN110428395B CN201910537340.0A CN201910537340A CN110428395B CN 110428395 B CN110428395 B CN 110428395B CN 201910537340 A CN201910537340 A CN 201910537340A CN 110428395 B CN110428395 B CN 110428395B
Authority
CN
China
Prior art keywords
image
decomposition
volume fraction
spectrum
energy
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910537340.0A
Other languages
Chinese (zh)
Other versions
CN110428395A (en
Inventor
牛田野
薛一
胡溪
江阳康
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang University ZJU
Original Assignee
Zhejiang University ZJU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang University ZJU filed Critical Zhejiang University ZJU
Priority to CN201910537340.0A priority Critical patent/CN110428395B/en
Publication of CN110428395A publication Critical patent/CN110428395A/en
Application granted granted Critical
Publication of CN110428395B publication Critical patent/CN110428395B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0012—Biomedical image inspection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00—Image generation
    • G06T2211/40—Computed tomography
    • G06T2211/416—Exact reconstruction

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Medical Informatics (AREA)
  • General Health & Medical Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
  • Radiology & Medical Imaging (AREA)
  • Quality & Reliability (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Image Processing (AREA)
  • Apparatus For Radiation Diagnosis (AREA)

Abstract

The invention discloses a multi-material decomposition method of a single-energy-spectrum CT image, which comprises the following steps: (1) acquiring a single-energy-spectrum CT image; (2) aiming at a CT image, according to a CT image domain multi-material decomposition theory, a decomposition target function comprising a data fidelity term and three punishment terms is constructed, wherein the data fidelity term ensures that errors of a measured value and a true value are as small as possible, the first term in the three punishment terms ensures the piecewise constant characteristic of the CT material image by using a total variation component, the second term ensures the sparsity of materials in the CT image by using a 0 norm term, and the third term ensures that a multi-material decomposition result meets the constraint that the volume fraction is between 0 and 1 and the sum of all material volume fractions is 1 by using a characteristic function term; (3) the initial value of the objective function is obtained by adopting a matrix inversion method based on the dual-material hypothesis, the objective function is solved by adopting an alternative direction multiplier method, the accurate decomposition of various materials under the single-energy common CT is realized, and the decomposition accuracy is equivalent to that of the dual-energy CT.

Description

Multi-material decomposition method of single-energy spectrum CT image
Technical Field
The invention relates to the technical field of medical engineering, in particular to a multi-material decomposition method of a single-energy-spectrum CT image.
Background
In high-end applications of CT, such as liver fiber quantification, breast tumor diagnosis, spinal compression fracture diagnosis and kidney stone and urinary stone component detection, the multi-material decomposition technology shows important application value.
At present, multi-material decomposition is mostly performed on dual-energy CT data, for example, a dual-energy CT image decomposition method based on a convolutional neural network disclosed in publication No. CN108230277A, however, a dual-energy CT image is more complex than a common single-energy CT, a scanning hardware system is more complex, and the cost of a dual-bulb dual-energy CT imaging mode of siemens company, a fast-kVp switching dual-energy CT imaging mode of GE company, and a dual-layer panel dual-energy CT imaging mode of philips company, which are clinically applied, is much higher than that of the common single-energy CT. The expensive price limits further high-end applications of dual-energy CT material decomposition technology.
Disclosure of Invention
The invention provides a multi-material decomposition method of a single-energy-spectrum CT image, which can accurately decompose the single-energy-spectrum CT image into various materials with decomposition precision equivalent to that of dual-energy CT and greatly reduce the hardware cost required by multi-material decomposition.
The technical scheme of the invention is as follows:
a multi-material decomposition method of a single-energy spectrum CT image comprises the following steps:
acquiring a single-energy-spectrum CT image;
aiming at the single-energy-spectrum CT image, according to the multi-material decomposition theory of the CT image domain, a decomposition target function of the single-energy-spectrum CT image is constructed:
Figure BDA0002101585590000021
wherein the content of the first and second substances,
Figure BDA0002101585590000022
is a data fidelity term that acts to force a volume fraction
Figure BDA0002101585590000023
Linear combination of
Figure BDA0002101585590000024
Approximation to true CT image
Figure BDA0002101585590000025
To be the total composite matrix, the matrix is,
Figure BDA0002101585590000026
represents the kronecker product, NpThe total number of pixels in the CT image is obtained;
Figure BDA0002101585590000027
is of size Np×NpThe identity matrix of (2).
Figure BDA0002101585590000028
Is made of base material
Figure BDA0002101585590000029
Composed synthesis matrix, T0Is the total amount of base material that is,
Figure BDA00021015855900000210
is a vectorized CT image, p represents the p-th pixel point in the CT image,
Figure BDA00021015855900000211
is vectorized T0Volume fraction image of seed-based material, data fidelity item
Figure BDA00021015855900000212
Represents L2The square of the norm operator;
Figure BDA00021015855900000213
in order to be a penalty term,
Figure BDA00021015855900000214
to decompose the total variation of the image, the coefficient δ is used to balance the noise and resolution of the decomposed image;
Figure BDA00021015855900000215
in order to be a penalty term,
Figure BDA00021015855900000216
for decomposing L of the image0A norm operator, wherein the coefficient sigma is used for adjusting the material sparsity weight in the exploded view, and the larger sigma represents the less material types in the pixel;
Figure BDA00021015855900000217
the penalty term is a characteristic function which is used for meeting the constraint that the volume fraction is added to be 1 and the volume fraction is larger than 0;
the initial value of the objective function is solved by adopting a matrix inversion method based on the bi-material hypothesis, and the objective function is solved by adopting an alternative direction multiplier method, namely the multi-material decomposition of the single-energy-spectrum CT image is realized.
Compared with the prior art, the multi-material decomposition method acts on a common single-energy-spectrum CT image, and by designing an objective function including one data fidelity term and three punishment terms and solving the objective function, the accurate decomposition of various materials under the single-energy common CT is realized, the decomposition precision is equivalent to that of the dual-energy CT, and the hardware cost required by the multi-material decomposition is greatly reduced.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 shows high and low energy CT images of a digital phantom (a) at low energy (75kVp) and (b) at high energy (140kVp) with a window of [ 0.010.035 ]]mm-1；
FIG. 2 is a decomposition image result of the digital phantom obtained by using dual-energy CT multi-material algorithm to the high-energy and low-energy CT images of the digital phantom, (a) is a bone image, (b) is a muscle image, (c) is a fat image, (d) is an air image, and a display window [ 01 ]]mm-1；
FIG. 3 is a decomposition image obtained by decomposing a high-energy CT image of a digital phantom by using the multi-material decomposition method using a single-energy-spectrum CT image according to the present invention, (a) is a bone image, (b) is a muscle image, (c) is a fat image, and (d) is an air image, and the display window is [ 01 ]]mm-1；
FIG. 4 is a decomposition image obtained by decomposing a low-energy CT image of a digital phantom by using a multi-material decomposition method of a single-energy-spectrum CT image according to the present invention, (a) is a bone image, (b) is a muscle image, (c) is a fat image, and (d) is an air image, and the display window is [ 01 ]]mm-1；
Using CT images of different phases of a real patient as a data source as shown in fig. 5, fig. 5(a), fig. b (a) and fig. 5(c) are CT images of an arterial phase, a portal venous phase and a delayed phase of a contrast agent, respectively;
FIG. 6 is a result diagram of the decomposition of FIG. 5 by the multi-material decomposition method of the single-spectrum CT image according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a multi-material decomposition method of a single-energy-spectrum CT image, which can accurately perform multi-material decomposition on the CT image, and the decomposition precision is equivalent to that of dual-energy CT decomposition.
Specifically, the multi-material decomposition method of the single-energy spectrum CT image comprises the following steps:
s101, acquiring a single-energy-spectrum CT image;
s102, aiming at the single-energy-spectrum CT image, according to the multi-material decomposition theory of the CT image domain, the linear attenuation coefficient of a pixel point in the image is regarded as the linear combination of the linear attenuation coefficients of the basis materials, namely:
Figure BDA0002101585590000041
wherein, muEIs the linear attenuation coefficient mu of the pixel point in the CT image under the energy EtELinear attenuation coefficient of T-th base material, T0Is the total number of base materials, xtIs the volume fraction of the t-th base material,
Figure BDA0002101585590000042
xt≧ 0 indicates that the volume fraction of the base material satisfies the constraint of adding 1 and being greater than 0.
S103, aiming at the pixel number N, in order to solve the volume fraction of the base materialpAnd contains T0The single-energy spectrum CT image of each base material is constructed to include one data fidelity item and three punishment itemsDecomposition objective function of (2):
Figure BDA0002101585590000043
wherein the content of the first and second substances,
Figure BDA0002101585590000044
is a data fidelity term that acts to force a volume fraction
Figure BDA0002101585590000045
Linear combination of
Figure BDA0002101585590000046
Approximation to true CT image
Figure BDA0002101585590000047
To be the total composite matrix, the matrix is,
Figure BDA0002101585590000048
represents the kronecker product, NpThe total number of pixels in the CT image is obtained;
Figure BDA0002101585590000049
is of size Np×NpThe identity matrix of (2).
Figure BDA00021015855900000410
Is made of base material
Figure BDA00021015855900000411
Composed synthesis matrix, T0Is the total amount of base material that is,
Figure BDA0002101585590000051
is a vectorized CT image, p represents the p-th pixel point in the CT image,
Figure BDA0002101585590000052
is vectorized T0Volume fraction image of seed-based material, data fidelity item
Figure BDA0002101585590000053
Represents L2The square of the norm operator;
Figure BDA0002101585590000054
in order to be a penalty term,
Figure BDA0002101585590000055
to decompose the total variation of the image, the coefficient δ is used to balance the noise and resolution of the decomposed image;
Figure BDA0002101585590000056
in order to be a penalty term,
Figure BDA0002101585590000057
for decomposing L of the image0A norm operator, wherein the coefficient sigma is used for adjusting the material sparsity weight in the exploded view, and the larger sigma represents the less material types in the pixel;
Figure BDA0002101585590000058
for the penalty term, a feature function is used to satisfy the constraint that the volume fraction is added to 1 and the volume fraction is greater than 0.
Wherein a first part of the penalty term
Figure BDA0002101585590000059
In order to decompose the total variation of the image, the gray gradient among materials is maintained while the gray change of pixels in the materials is reduced, thereby achieving the purposes of boundary maintenance and noise reduction and decomposing the total variation of the image
Figure BDA00021015855900000510
Comprises the following steps:
Figure BDA00021015855900000511
wherein the content of the first and second substances,
Figure BDA00021015855900000512
represents a gradient operator, | · | | luminance1Represents L1The norm operator is used for calculating the norm of the vector,
Figure BDA00021015855900000513
is the vectorized volume fraction of the t-th base material.
Second part of penalty term
Figure BDA00021015855900000514
L representing a decomposed image0The norm operator represents the sparsity of decomposed materials by limiting the number of materials in each pixel point,
Figure BDA00021015855900000515
the calculation method comprises the following steps:
Figure BDA00021015855900000516
wherein the content of the first and second substances,
Figure BDA00021015855900000517
is the volume fraction of the p-th pixel of the vectorization.
Third part of penalty term
Figure BDA00021015855900000518
Is a characteristic function for satisfying the constraints of volume fraction adding to 1 and volume fraction greater than 0
Figure BDA00021015855900000519
The calculation method comprises the following steps:
Figure BDA00021015855900000520
wherein the content of the first and second substances,
Figure BDA00021015855900000521
and S104, solving an initial value of the objective function by adopting a matrix inversion method based on the bi-material assumption.
Because the decomposition target function is a non-convex function, the solution of the non-convex function needs to obtain an ideal initial value, and the initial value of the target function is obtained by adopting a matrix inversion method based on bi-material hypothesis. The specific process is as follows:
the linear attenuation coefficient for the p-th pixel is written as:
Figure BDA0002101585590000061
wherein the content of the first and second substances,
Figure BDA0002101585590000062
is a size of 1 XT0Of the synthetic matrix, mupFor the linear attenuation coefficient of the p-th pixel in the CT image,
Figure BDA0002101585590000063
volume fraction, x, of the p-th pixel for vectorizationptIs the volume fraction of the t-th base material in the p-th pixel;
assuming that each pixel contains at most two materials, the bi-material assumption is expressed as:
Figure BDA0002101585590000064
wherein, I{·}Represents an indicator function if xtpNot equal to 0, indicating a function value of 1, if xtpIf 0, the function value is indicated to be 0;
the matrix A is synthesized under the two-material assumption and the constraint that the sum of volume fractions is 10Write as:
Figure BDA0002101585590000065
wherein, muiAnd mujIs linear of ith, j base materialAttenuation coefficient, the bimaterial decomposition of the p-th pixel is written as:
Figure BDA0002101585590000066
wherein x ispiAnd xpjIs the volume fraction of the ith, jth base material;
when solving for bimaterials, i.e. solving equation (9) for xpiAnd xpjThen, a matrix inversion method is preliminarily adopted for solving;
when solving for multiple materials, the method is realized through a round searching method, namely, a base material library is established firstly, all possible double-material groups are traversed in the base material library, and an equation (9) is solved by using a matrix inversion method;
if there are multiple solutions that satisfy a volume fraction greater than 0, then according to:
Figure BDA0002101585590000071
selecting an optimal bimaterial group from the multiple solutions, solving the volume fraction of the corresponding bimaterial according to equation (9), and setting the volume fractions of the rest materials as 0;
if no solution exists and the volume fraction is larger than 0, the solution of equation (9) is converted into an optimized solution:
Figure BDA0002101585590000072
wherein, tau*,xpi *xpj *Respectively representing the optimal bimaterial group and the optimal volume fraction of each material in the optimal bimaterial group;
equation (11) is solved using a gradient projection algorithm to obtain the volume fraction of the bimaterial.
The volume fraction of the bimaterial obtained by the above solution is taken as the initial value of the number of decomposition target lines.
And S105, solving the decomposition objective function by adopting an alternating direction multiplier method, namely realizing multi-material decomposition of the single-energy-spectrum CT image.
After the volume fraction of the bimaterial is obtained, the obtained volume fraction of the bimaterial is taken as an initial value of a decomposition objective function and is brought into the decomposition objective function, and the decomposition objective function is solved by adopting an alternating direction multiplier method to obtain the volume fraction of each material.
According to the multi-material decomposition method, the target function including one data fidelity item and three punishment items is designed and solved, so that the accurate decomposition of various materials under the single-energy common CT is realized, the decomposition precision is equivalent to that of the dual-energy CT, and the hardware cost required by the multi-material decomposition is greatly reduced.
Examples
Embodiments use a digital phantom reconstructed by a filtered back-projection algorithm as a data source, i.e., high and low energy CT images of the digital phantom as shown in fig. 1(a) and 1(b) as data sources, the basis material images in the same figure, wherein ROI1, ROI2, ROI4 and ROI5 are selected basis material regions, and ROI3 is a mixture region composed of basis materials.
The dual-energy CT multi-material algorithm is adopted to decompose the high-energy and low-energy CT images of the digital phantom, so that the decomposition results shown in the figures 2(a) to 2(d) are obtained, and the decomposition precision of the dual-energy CT multi-material algorithm is 87%.
The multi-material decomposition method provided by the invention is adopted to carry out multi-material decomposition on the high-energy CT image of the digital phantom, the decomposition results are shown in figures 3(a) to 3(d), the resolution precision of the method is 96 percent and is equivalent to the precision of the base material image decomposed by the dual-energy CT multi-material.
The multi-material decomposition method provided by the invention is adopted to carry out multi-material decomposition on the low-energy CT image of the digital phantom, the decomposition results are shown in fig. 4(a) to 4(d), the resolution precision of the method is 93 percent, and the method is equivalent to the precision of the base material image decomposed by the dual-energy CT multi-material.
As shown in fig. 5, CT images of different phases of a real patient are used as data sources, and fig. 5(a), b (a) and 5(c) are CT images of an arterial phase, a portal venous phase and a delay phase of a contrast agent, respectively. Bone, muscle, contrast agent, fat and air are used as base materials for multi-material decomposition.
The multi-material decomposition method provided by the invention is adopted to carry out multi-material decomposition on CT images of real patients in different time phases, the decomposition result is shown in figure 6, and the method can accurately decompose five base materials; meanwhile, as shown by arrows in the figure, the contrast agent in the blood vessel becomes dark continuously in the arterial phase, the portal venous phase and the delay phase, and the contrast agent in the kidney becomes light gradually in the arterial phase, the portal venous phase and the delay phase, which indicates that the contrast agent is transferred from the blood vessel to the kidney, and accords with the medical fact.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (7)

1. A multi-material decomposition method of a single-energy spectrum CT image comprises the following steps:
acquiring a single-energy-spectrum CT image;
aiming at the single-energy-spectrum CT image, according to the multi-material decomposition theory of the CT image domain, a decomposition target function of the single-energy-spectrum CT image is constructed:
Figure FDA0003157413770000011
wherein the content of the first and second substances,
Figure FDA0003157413770000012
is a data fidelity term that acts to force a volume fraction
Figure FDA0003157413770000013
Linear combination of
Figure FDA0003157413770000014
Approximation to true CT image
Figure FDA0003157413770000015
Figure FDA0003157413770000016
To be the total composite matrix, the matrix is,
Figure FDA0003157413770000017
Figure FDA0003157413770000018
represents the kronecker product, NpThe total number of pixels in the CT image is obtained;
Figure FDA0003157413770000019
is of size Np×NpThe unit matrix of (a) is,
Figure FDA00031574137700000110
is made of base material
Figure FDA00031574137700000111
The composite matrix is composed of a plurality of composite matrixes,
Figure FDA00031574137700000112
is a vectorized CT image, p represents the p-th pixel point in the CT image,
Figure FDA00031574137700000113
is vectorized T0Volume fraction image of seed-based material, data fidelity item
Figure FDA00031574137700000114
Represents L2The square of the norm operator;
Figure FDA00031574137700000115
in order to be a penalty term,
Figure FDA00031574137700000116
to decompose the total variation of the image, the coefficient δ is used to balance the noise and resolution of the decomposed image;
Figure FDA00031574137700000117
in order to be a penalty term,
Figure FDA00031574137700000118
for decomposing L of the image0A norm operator, wherein the coefficient sigma is used for adjusting the material sparsity weight in the exploded view, and the larger sigma represents the less material types in the pixel;
Figure FDA00031574137700000119
the penalty term is a characteristic function which is used for meeting the constraint that the volume fraction is added to be 1 and the volume fraction is larger than 0;
solving an initial value of the objective function by adopting a matrix inversion method based on bi-material hypothesis, and solving the decomposed objective function by adopting an alternative direction multiplier method, namely realizing multi-material decomposition of the single-energy-spectrum CT image;
characteristic function
Figure FDA00031574137700000120
The calculation method comprises the following steps:
Figure FDA0003157413770000021
wherein the content of the first and second substances,
Figure FDA0003157413770000022
xptis the volume fraction of the t-th base material in the p-th pixel.
2. The method of multi-material decomposition of single-spectrum CT images as claimed in claim 1, wherein the full variation of the decomposed image
Figure FDA0003157413770000023
Comprises the following steps:
Figure FDA0003157413770000024
wherein the content of the first and second substances,
Figure FDA0003157413770000025
represents the gradient operator, | · |1Represents L1The norm operator is used for calculating the norm of the vector,
Figure FDA0003157413770000026
is the vectorized volume fraction of the t-th base material.
3. The method of multi-material decomposition of single-spectrum CT images of claim 1,
Figure FDA0003157413770000027
is calculated by
Figure FDA0003157413770000028
Wherein the content of the first and second substances,
Figure FDA0003157413770000029
is the volume fraction of the p-th pixel of the vectorization.
4. The method of multi-material decomposition of single-spectrum CT images according to any of claims 1 to 3, wherein the using a matrix inversion method based on bi-material assumption to find the initial value of the objective function comprises:
the linear attenuation coefficient for the p-th pixel is written as:
Figure FDA00031574137700000210
wherein the content of the first and second substances,
Figure FDA00031574137700000213
for the linear attenuation coefficient of the p-th pixel in the CT image,
Figure FDA00031574137700000211
volume fraction, x, of the p-th pixel for vectorizationptIs the volume fraction of the t-th base material in the p-th pixel;
assuming that each pixel contains at most two materials, the bi-material assumption is expressed as:
Figure FDA00031574137700000212
wherein, I{·}Represents an indicator function if xptNot equal to 0, indicating a function value of 1, if xptIf 0, the function value is indicated to be 0;
the matrix A is synthesized under the two-material assumption and the constraint that the sum of volume fractions is 10Write as:
Figure FDA0003157413770000031
wherein, muiAnd mujFor the linear attenuation coefficient of the ith and j-th base materials, the bi-material decomposition of the p-th pixel point is written as:
Figure FDA0003157413770000032
wherein x ispiAnd xpjIs the volume fraction of the ith, jth base material;
when solving for bimaterials, i.e. solving equation (8) for xpiAnd xpjAnd then, solving by adopting a matrix inversion method preliminarily.
5. The method of multi-material decomposition of single-spectrum CT images as claimed in claim 4, wherein for multi-material solution, it is implemented by round-robin, i.e. first building a base material library, traversing all possible bi-material groups in the base material library and solving equation (8) using matrix inversion;
if there are multiple solutions that satisfy a volume fraction greater than 0, then according to:
Figure FDA0003157413770000033
selecting an optimal bimaterial group from the multiple solutions, solving the volume fraction of the corresponding bimaterial according to equation (8), and setting the volume fractions of the rest materials as 0;
if no solution exists and the volume fraction is larger than 0, the solution of equation (8) is converted into an optimized solution:
Figure FDA0003157413770000034
wherein, tau*，xpi *xpj *Respectively representing the optimal bimaterial group and the optimal volume fraction of each material in the optimal bimaterial group;
equation (10) is solved using a gradient projection algorithm to obtain the volume fraction of the bimaterial.
6. The method of multi-material decomposition of single-spectrum CT images according to claim 4, wherein after obtaining the volume fraction of the bimaterials, the obtained volume fraction of the bimaterials is taken as an initial value of the decomposition objective function into the decomposition objective function, and the decomposition objective function is solved by using an alternating direction multiplier method to obtain the volume fraction of each material.
7. The method of multi-material decomposition of single-spectrum CT images according to claim 5, wherein after obtaining the volume fraction of the bimaterials, the obtained volume fraction of the bimaterials is taken as an initial value of the decomposition objective function into the decomposition objective function, and the decomposition objective function is solved by using an alternating direction multiplier method to obtain the volume fraction of each material.
CN201910537340.0A 2019-06-20 2019-06-20 Multi-material decomposition method of single-energy spectrum CT image Active CN110428395B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910537340.0A CN110428395B (en) 2019-06-20 2019-06-20 Multi-material decomposition method of single-energy spectrum CT image

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910537340.0A CN110428395B (en) 2019-06-20 2019-06-20 Multi-material decomposition method of single-energy spectrum CT image

Publications (2)

Publication Number Publication Date
CN110428395A CN110428395A (en) 2019-11-08
CN110428395B true CN110428395B (en) 2021-10-08

Family

ID=68408784

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910537340.0A Active CN110428395B (en) 2019-06-20 2019-06-20 Multi-material decomposition method of single-energy spectrum CT image

Country Status (1)

Country Link
CN (1) CN110428395B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111079863B (en) * 2019-12-31 2023-05-19 重庆青信科技有限公司 System for identifying focus tissue by utilizing spectral curve statistical fingerprint
CN113298905B (en) * 2021-05-28 2022-12-16 同济大学 Multi-energy spectrum CT reconstruction method based on base material decomposition and computer readable medium
CN113706419A (en) * 2021-09-13 2021-11-26 上海联影医疗科技股份有限公司 Image processing method and system

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104346820A (en) * 2013-07-26 2015-02-11 清华大学 X-ray dual-energy CT reconstruction method
CN109903355A (en) * 2019-03-04 2019-06-18 四川大学 Power spectrum CT method for reconstructing based on empty spectrum dual domain tensor self similarity

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105512487A (en) * 2015-12-15 2016-04-20 浙江大学 Image domain statistical decomposition method for dual-energy CT (computed tomography) multi-materials
WO2017205379A2 (en) * 2016-05-23 2017-11-30 Rensselaer Polytechnic Institute Image reconstruction method for computed tomography
EP3691529B1 (en) * 2017-10-06 2022-07-06 Mayo Foundation for Medical Education and Research System and method for basis material decomposition with a general physical constraint for multi-energy computed tomography
CN108230277B (en) * 2018-02-09 2020-09-11 中国人民解放军战略支援部队信息工程大学 Dual-energy CT image decomposition method based on convolutional neural network

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104346820A (en) * 2013-07-26 2015-02-11 清华大学 X-ray dual-energy CT reconstruction method
CN109903355A (en) * 2019-03-04 2019-06-18 四川大学 Power spectrum CT method for reconstructing based on empty spectrum dual domain tensor self similarity

Also Published As

Publication number Publication date
CN110428395A (en) 2019-11-08

Similar Documents

Publication Publication Date Title
CN110428395B (en) Multi-material decomposition method of single-energy spectrum CT image
Kuchenbecker et al. Dual energy CT: how well can pseudo‐monochromatic imaging reduce metal artifacts?
Yuan et al. Half2Half: deep neural network based CT image denoising without independent reference data
Lee et al. CT image conversion among different reconstruction kernels without a sinogram by using a convolutional neural network
US9824468B2 (en) Dictionary learning based image reconstruction
Zha et al. Naf: Neural attenuation fields for sparse-view cbct reconstruction
Berger et al. Motion compensation for cone-beam CT using Fourier consistency conditions
Byl et al. Photon‐counting normalized metal artifact reduction (NMAR) in diagnostic CT
Lu et al. A diffusion-based truncated projection artifact reduction method for iterative digital breast tomosynthesis reconstruction
Lee et al. Development of a deep neural network for generating synthetic dual-energy chest x-ray images with single x-ray exposure
Cuadros et al. Compressive spectral X-ray tomography based on spatial and spectral coded illumination
Zhang et al. Nonlinear reconstruction of coded spectral X-ray CT based on material decomposition
Rahim et al. Total variant based average sparsity model with reweighted analysis for compressive sensing of computed tomography
Bal et al. Uniqueness criteria in multi-energy CT
Zhou et al. The synthesis of high-energy CT images from low-energy CT images using an improved cycle generative adversarial network
He et al. Noise suppression–guided image filtering for low-SNR CT reconstruction
Lu et al. Image reconstruction by an alternating minimisation
Tilley et al. A general CT reconstruction algorithm for model-based material decomposition
Zhang et al. Reconstruction of limited-angle dual-energy CT using mutual learning and cross-estimation (mlce)
Scarparo et al. Evaluation of denoising digital breast tomosynthesis data in both projection and image domains and a study of noise model on digital breast tomosynthesis image domain
CN113592968B (en) Method and device for reducing metal artifacts in tomographic images
Bal et al. An inversion algorithm for P-functions with applications to multi-energy CT
Duan et al. Image quality guided iterative reconstruction for low-dose CT based on CT image statistics
Kudo et al. Metal artifact reduction in CT using fault-tolerant image reconstruction
Ge et al. Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant