CN110428395A - More material decomposition methods of monoenergetic spectrum CT image - Google Patents
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Abstract
The invention discloses a kind of more material decomposition methods of monoenergetic spectrum CT image, comprising: (1) obtains monoenergetic spectrum CT image；(2) it is directed to CT image, according to the more material resolution theories of CT image area, building includes the decomposition goal function of data fidelity term and three penalty terms, data fidelity term guarantees that the error of measured value and true value is as small as possible, in three penalty terms, first item guarantees the piecewise constant characteristic of CT images of materials using full variation, Section 2 guarantees that the sparsity of material in CT image, Section 3 guarantee the constraint that more material decomposition results meet volume fraction between 0 to 1 and all material volume fraction adduction is 1 using characteristic function item using 0 norm item；(3) initial value of objective function is sought using the matrix inversion technique assumed based on bi-material layers and objective function is solved using alternating direction multipliers method, realize the accurate decomposition of the multiple material at single energy common CT, Decomposition Accuracy and dual intensity CT are suitable.
Description
Technical field
The present invention relates to engineering in medicine technical fields, and in particular to a kind of more material decomposition methods of monoenergetic spectrum CT image.
Background technique
In CT high-end applications, such as liver fiber basis weight, Diagnosis of Breast Tumor, vertebral compression fractures diagnosis and kidney stone urine knot
In stone component detection, more material decomposition techniques show important application value.
Currently, more material decomposition mostly carry out in dual intensity CT data, one kind as disclosed in Publication No. CN108230277A
Dual-energy CT image decomposition method based on convolutional neural networks, however, dual intensity composes CT image relative to common monoenergetic spectrum CT, scanning
Hardware system is more complicated, the double bulb dual intensity CT imaging modes of the Siemens Company applied in clinic, the fast-kVp of GE company
Switching dual intensity CT imaging mode and PHILIPS Co.'s doubling plate dual intensity CT imaging mode cost are much higher than common single energy
Compose CT.The expensive price limit further high-end applications of dual intensity CT material decomposition technique.
Summary of the invention
The present invention provides a kind of more material decomposition methods of monoenergetic spectrum CT image, which can be by list
Power spectrum CT image accurately resolves into multiple material, and Decomposition Accuracy and dual intensity CT are suitable, significantly reduces more materials and decomposes institute
The hardware cost needed.
The technical solution of the present invention is as follows:
A kind of more material decomposition methods of monoenergetic spectrum CT image, comprising the following steps:
Obtain monoenergetic spectrum CT image；
The decomposition mesh of monoenergetic spectrum CT image is constructed according to the more material resolution theories of CT image area for monoenergetic spectrum CT image
Scalar functions:
Wherein,For data fidelity term, it acts as force volume fractionLinear combinationIt approaches
True CT imageFor total composite matrix,Represent Kronecker product, NpFor CT
Total number of pixels in image；It is N for sizep×NpUnit matrixIt is by substrate stockline
It declinesThe composite matrix of composition, T0It is the total quantity of sill,It is the CT image of vectorization, p represents CT image
In p-th of pixel,It is the T of vectorization0Kind sill volume fraction image, data
Fidelity termRepresent L2Square of norm operator；For penalty term,For the full variation for decomposing image, coefficient
δ is used to balance the noise and resolution ratio for decomposing image；For penalty term,For the L for decomposing image0Norm operator is
Number σ is used to adjust material sparsity weight in exploded view, and material category is fewer in the bigger expression pixel of σ；For penalty term,
It is a characteristic function, adds up to 1 and constraint of the volume fraction greater than 0 for meeting volume fraction；
The initial value of objective function is sought using the matrix inversion technique assumed based on bi-material layers, and is multiplied using alternating direction
Sub- method solves objective function, that is, realizes more materials decomposition to monoenergetic spectrum CT image.
Compared with prior art, more material decomposition methods of the invention act on common monoenergetic spectrum CT image, by setting
It counts the objective function including an item data fidelity term and three penalty terms and objective function is solved, realize in list
The accurate decomposition of multiple material under the common CT of energy, Decomposition Accuracy and dual intensity CT are suitable, decompose in fact to greatly reduce more materials
Hardware cost required for existing.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to do simply to introduce, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art, can be with root under the premise of not making the creative labor
Other accompanying drawings are obtained according to these attached drawings.
Fig. 1 is the high and low energy CT image of digital die body, and (a) is low energy (75kVp), (b) is high energy (140kVp) display
Window is [0.01 0.035] mm-1；
Fig. 2 is that digital die body uses the high and low energy CT image of the more material algorithm logarithm type matrix bodies of dual intensity CT to obtain exploded view
As a result, (a) be bone image, (b) be muscle image, (c) be fat image, (d) be air image, display window [0 1] mm-1；
Fig. 3 is the high energy using more material decomposition method logarithm type matrix bodies provided by the invention using monoenergetic spectrum CT image
The decomposition image that CT image is decomposed, (a) are bone image, (b) are muscle image, (c) are fat image, are (d) sky
Gas image, display window are [0 1] mm-1；
Fig. 4 is the low energy CT using more material decomposition method logarithm type matrix bodies provided by the invention with monoenergetic spectrum CT image
The decomposition image that image is decomposed, (a) are bone image, (b) are muscle image, (c) are fat image, (d) are air
Image, display window are [0 1] mm-1；
Use the CT image of real patient difference phase as data source, Fig. 5 (a), figure b (a) and Fig. 5 (c) as shown in Figure 5
Respectively contrast agent arterial phase, Portal venous phase and the CT of period of delay image；
Fig. 6 is the result decomposed using more material decomposition methods of monoenergetic spectrum CT image provided by the invention to Fig. 5
Figure.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention more comprehensible, with reference to the accompanying drawings and embodiments to this
Invention is described in further detail.It should be appreciated that the specific embodiments described herein are only used to explain the present invention,
And the scope of protection of the present invention is not limited.
The present invention provides a kind of more material decomposition methods of monoenergetic spectrum CT image, which can be accurate
Ground carries out more material decomposition to CT image, and Decomposition Accuracy is suitable with dual intensity CT Decomposition Accuracy.
Specifically, more material decomposition methods of monoenergetic spectrum CT image, comprising the following steps:
S101 obtains monoenergetic spectrum CT image；
S102, for monoenergetic spectrum CT image, according to the more material resolution theories of CT image area, pixel linearly declines in image
Subtract the linear combination that coefficient is counted as sill linear attenuation coefficient, it may be assumed that
Wherein, μEFor linear attenuation coefficient of the pixel under ENERGY E, μ in CT imagetEFor the linear of t kind sill
Attenuation coefficient, T0For sill total number, xtFor the volume fraction of t kind sill,xt>=0 indicates substrate
It is 1 and the constraint greater than 0 that the volume fraction of material, which meets adduction,.
S103 is N for number of pixels to solve the volume fraction of sillpAnd contain T0Single energy of a sill
CT image is composed, building includes the decomposition goal function of an item data fidelity term and three penalty terms:
Wherein,For data fidelity term, it acts as force volume fractionLinear combinationIt approaches
True CT imageFor total composite matrix,Represent Kronecker product, NpFor CT
Total number of pixels in image；It is N for sizep×NpUnit matrixIt is by substrate stockline
It declinesThe composite matrix of composition, T0It is the total quantity of sill,It is the CT image of vectorization, p represents CT image
In p-th of pixel,It is the T of vectorization0Kind sill volume fraction image, data
Fidelity termRepresent L2Square of norm operator；For penalty term,For the full variation for decomposing image, coefficient δ
For balancing the noise and resolution ratio that decompose image；For penalty term,For the L for decomposing image0Norm operator is
Number σ is used to adjust material sparsity weight in exploded view, and material category is fewer in the bigger expression pixel of σ；For penalty term,
It is a characteristic function, adds up to 1 and constraint of the volume fraction greater than 0 for meeting volume fraction.
Wherein, the first part of penalty termFor the full variation for decomposing image, guarantee that material internal pixel grey scale becomes
Change storeroom shade of gray while reduction to be maintained, to achieve the purpose that boundary keeps simultaneously noise reduction, decomposes the complete of image
VariationAre as follows:
Wherein,Gradient operator is represented, | | | |1Represent L1Norm operator,It is the t kind sill volume of vectorization
Score.
The second part of penalty termRepresent the L for decomposing image0Norm operator, by limiting material in each pixel
Number characterizes the sparsity of decomposing material,Calculation method are as follows:
Wherein,It is the volume fraction of p-th of pixel of vectorization.
The Part III of penalty termIt is characterized function, adds up to 1 and volume fraction for meeting volume fraction
Constraint greater than 0, characteristic functionCalculation method are as follows:
Wherein,
S104 seeks the initial value of objective function using the matrix inversion technique assumed based on bi-material layers.
Since decomposition goal function is a non-convex function, the solution of non-convex function needs to obtain ideal initial value, this
The initial value of objective function is sought in invention using the matrix inversion technique assumed based on bi-material layers.Detailed process is as follows:
The linear attenuation coefficient of p-th of pixel is write as:
Wherein,It is one having a size of 1 × T0Composite matrix, μpIt is p-th in CT image
The linear attenuation coefficient of pixel,For the volume fraction of p-th of pixel of vectorization, xptFor t kind substrate in p-th of pixel
The volume fraction of material；
Assuming that i.e. each pixel contains up to two kinds of materials, bi-material layers are assumed to indicate are as follows:
Wherein, I{·}Indicator function is indicated, if xtp≠ 0, then indicator function value is 1, if xtp=0, then indicator function
Value is 0；
Assume and volume fraction and under 1 constraint in bi-material layers, composite matrix A0It is written as:
Wherein, μiAnd μjBi-material layers decomposition for the linear attenuation coefficient of i-th, j kind sill, p-th of pixel is written as:
Wherein, xpiAnd xpjFor the volume fraction of i-th, j kind sill；
When solving for bi-material layers, i.e., peer-to-peer (9) solves xpiAnd xpjWhen, tentatively asked using matrix inversion technique
Solution；
When being solved for more materials, method is sought by wheel and is realized, that is, initially sets up sill library, institute is traversed in sill library
Possible bi-material layers group simultaneously solves equation (9) using the method for matrix inversion；
Meet volume fraction if there is multiple solutions and be greater than 0, then basis:
Optimal bi-material layers group is chosen from multiple solutions, and the volume fraction of corresponding bi-material layers is solved according to equation (9),
The volume fraction of remaining material is set to 0；
Meet volume fraction greater than 0 if there is no solution, then equation (9) solved and be converted into optimal way solution:
Wherein, τ*,xpi *xpj *Respectively indicate the optimal volume of every kind of material in optimal bi-material layers group and optimal bi-material layers group
Score；
Equation (11) are solved using gradient project algorithms, to obtain the volume fraction of bi-material layers.
Using the volume fraction of the above bi-material layers for solving and obtaining as the initial value of decomposition goal line number.
S105 solves decomposition goal function using alternating direction multipliers method, that is, realizes to monoenergetic spectrum CT image
More materials decompose.
After the volume fraction for obtaining bi-material layers, using the volume fraction of the bi-material layers of acquisition as the first of decomposition goal function
Initial value is brought into decomposition goal function, and solve to decomposition goal function using alternating direction multipliers method and obtained every kind of material
The volume fraction of material.
Target letter of the above-mentioned more material decomposition methods by design including an item data fidelity term and three penalty terms
Number simultaneously solves objective function, realizes the accurate decomposition of the multiple material at single energy common CT, Decomposition Accuracy and dual intensity
CT is suitable, realizes required hardware cost to greatly reduce more materials and decompose.
Embodiment
The digital die body that embodiment is reconstructed using filter back-projection algorithm is as data source, i.e., such as Fig. 1 (a) and 1 (b) institute
The high and low energy CT image of the digital die body shown is as data source, and sill image is in same width figure, in Fig. 1 (b), ROI1,
ROI2, ROI4 and ROI5 are selected sill regions, and ROI3 is the mixture region being made of sill.
Using the more material algorithm logarithm type matrix bodies of dual intensity CT it is high and low can CT image decomposed, obtain as Fig. 2 (a)~
The decomposition result of Fig. 2 (d), the Decomposition Accuracy of the more material algorithms of dual intensity CT are 87%.
More material decomposition are carried out using the high energy CT image of more material decomposition method logarithm type matrix bodies provided by the invention, point
Result such as Fig. 3 (a)~Fig. 3 (d) is solved, solution precision of the invention is 96%, the sill image decomposed with the more materials of dual intensity CT
Precision is suitable.
More material decomposition are carried out using the low energy CT image of more material decomposition method logarithm type matrix bodies provided by the invention, point
Result such as Fig. 4 (a)~Fig. 4 (d) is solved, solution precision of the invention is 93%, the sill image decomposed with the more materials of dual intensity CT
Precision is suitable.
Use the CT image of real patient difference phase as data source, Fig. 5 (a), figure b (a) and Fig. 5 (c) as shown in Figure 5
Respectively contrast agent arterial phase, Portal venous phase and the CT of period of delay image.Made using bone, muscle, contrast agent, fat and air
More material decomposition are carried out for sill.
More materials point are carried out using CT image of the more material decomposition methods provided by the invention to real patient difference phase
Solution, decomposition result is as shown in fig. 6, the present invention accurately decomposites five kinds of sills to come；Meanwhile as shown by arrows in figure, blood vessel
In contrast agent it is constantly dimmed in arterial phase, Portal venous phase and period of delay, contrast agent in kidney arterial phase, Portal venous phase and
Period of delay gradually brightens, and illustrates that contrast agent is shifted from blood vessel to kidney, meets the medicine fact.
Technical solution of the present invention and beneficial effect is described in detail in above-described specific embodiment, Ying Li
Solution is not intended to restrict the invention the foregoing is merely presently most preferred embodiment of the invention, all in principle model of the invention
Interior done any modification, supplementary, and equivalent replacement etc. are enclosed, should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of more material decomposition methods of monoenergetic spectrum CT image, comprising the following steps:
Obtain monoenergetic spectrum CT image；
The decomposition goal letter of monoenergetic spectrum CT image is constructed according to the more material resolution theories of CT image area for monoenergetic spectrum CT image
Number:
Wherein,For data fidelity term, it acts as force volume fractionLinear combinationApproaching to reality
CT imageFor total composite matrix, Represent Kronecker product, NpFor CT image
Middle total number of pixels；It is N for sizep×NpUnit matrixIt is to be declined by substrate stocklineThe composite matrix of composition,It is the CT image of vectorization, p represents p-th of pixel in CT image,It is the T of vectorization0Kind sill volume fraction image, data fidelity termRepresent L2
Square of norm operator；For penalty term,For the full variation for decomposing image, coefficient δ is used to balance exploded view
The noise and resolution ratio of picture；For penalty term,For the L for decomposing image0Norm operator, factor sigma are used to adjust decomposition
Material sparsity weight in figure, material category is fewer in the bigger expression pixel of σ；It is a characteristic function for penalty term,
1 and constraint of the volume fraction greater than 0 are added up to for meeting volume fraction；
The initial value of objective function is sought using the matrix inversion technique assumed based on bi-material layers, and uses alternating direction multipliers method
Decomposition goal function is solved, that is, realizes more materials decomposition to monoenergetic spectrum CT image.
2. more material decomposition methods of monoenergetic spectrum CT image as described in claim 1, which is characterized in that decompose the full change of image
PointAre as follows:
Wherein,Gradient operator is represented, | | | |1Represent L1Norm operator,It is the t kind sill volume fraction of vectorization.
3. more material decomposition methods of monoenergetic spectrum CT image as described in claim 1, which is characterized in thatCalculation method
For
Wherein,It is the volume fraction of p-th of pixel of vectorization.
4. more material decomposition methods of monoenergetic spectrum CT image as described in claim 1, which is characterized in that characteristic function
Calculation method are as follows:
Wherein,
5. such as more material decomposition methods of the described in any item monoenergetic spectrum CT images of Claims 1 to 4, which is characterized in that described
Include: using the initial value that objective function is sought in the matrix inversion technique assumed based on bi-material layers
The linear attenuation coefficient of p-th of pixel is write as:
Wherein,It is one having a size of 1 × T0Composite matrix, μpFor p-th of pixel in CT image
Linear attenuation coefficient,For the volume fraction of p-th of pixel of vectorization, xptFor t kind sill in p-th of pixel
Volume fraction；
Assuming that i.e. each pixel contains up to two kinds of materials, bi-material layers are assumed to indicate are as follows:
Wherein, I{·}Indicator function is indicated, if xtp≠ 0, then indicator function value is 1, if xtp=0, then indicator function value be
0；
Assume and volume fraction and under 1 constraint in bi-material layers, composite matrix A0It is written as:
Wherein, μiAnd μjBi-material layers decomposition for the linear attenuation coefficient of i-th, j kind sill, p-th of pixel is written as:
Wherein, xpiAnd xpjFor the volume fraction of i-th, j kind sill；
When solving for bi-material layers, i.e., peer-to-peer (8) solves xpiAnd xpjWhen, tentatively solved using matrix inversion technique.
6. more material decomposition methods of monoenergetic spectrum CT image as claimed in claim 5, which is characterized in that solved for more materials
When, method is sought by wheel and is realized, that is, initially sets up sill library, all possible bi-material layers group is traversed in sill library and is used
The method of matrix inversion solves equation (8)；
Meet volume fraction if there is multiple solutions and be greater than 0, then basis:
Optimal bi-material layers group is chosen from multiple solutions, and the volume fraction of corresponding bi-material layers, remaining material are solved according to equation (8)
The volume fraction of material is set to 0；
Meet volume fraction greater than 0 if there is no solution, then equation (8) solved and be converted into optimal way solution:
Wherein, τ*, xpi *xpj *Respectively indicate the optimal volume fraction of every kind of material in optimal bi-material layers group and optimal bi-material layers group；
Equation (10) are solved using gradient project algorithms, to obtain the volume fraction of bi-material layers.
7. such as more material decomposition methods of monoenergetic spectrum CT image described in claim 5 or 6, which is characterized in that obtaining double materials
After the volume fraction of material, bring into the volume fraction of the bi-material layers of acquisition as the initial value of decomposition goal function to decomposition goal
In function, and decomposition goal function is carried out using alternating direction multipliers method to solve the volume fraction for obtaining every kind of material.
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| CN113298905A (en) * | 2021-05-28 | 2021-08-24 | 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 |
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