CN104408758A - Low-dose processing method of energy spectrum CT image - Google Patents
Low-dose processing method of energy spectrum CT image Download PDFInfo
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Abstract
The invention provides a low-dose processing method of an energy spectrum CT image. The low-dose processing method of the energy spectrum CT image comprises the steps of (1) acquiring low-energy CT projection data and high-energy CT projection data of the energy spectrum CT image of an imaging object under low-dose rays, and acquiring the corresponding correction parameters, system matrix, and system electronic noise variance; (2) building a mathematic model for reconstructing the energy spectrum CT image according to the statistical characteristics consistent with the low-energy CT projection data and high-energy CT projection data in step (1) and a base material decomposition model; (3) building target functions for reconstructing the energy spectrum CT image by utilizing total variation as regularization prior and on the basis of the mathematic model obtained in step (2); and (4) solving the target functions for reconstructing the energy spectrum CT image obtained in step (3) by the iterative algorithm, so as to finish the reconstruction of the energy spectrum CT image. The low-dose processing method of the energy spectrum CT image has the advantage that the energy spectrum CT image can be reconstructed with a high quality under a low-dose scanning protocol.
Description
Technical field
The present invention relates to a kind of image processing method of medical image, particularly a kind of low dosage power spectrum CT image processing method.
Background technology
X ray computer Tomography (X-ray Computed Tomography is called for short CT) is a kind of interaction principle utilizing X ray and material, material internal information is carried out to a kind of technology of imaging.CT, because of its excellent performance on time, space and density resolution, has been widely used in routine inspection and the diagnosis at different anatomic position, in human diseases control and extend in mean lifetime and achieving great achievement.
But, because being limited by the defect of conventional CT system design, still there is many deficiencies in its imaging, mainly comprises: high radiation dose, strong beam hardening and metal artifacts, low contrast tissue division degree, and only can realize anatomy imaging, cannot differentiate material composition, cannot quantitative imaging accurately.
Along with the develop rapidly of software and hardware technology, the dual intensity CT scan technology based on power spectrum integrating detector and the energy-resolved detection technology based on energy-resolved detector make power spectrum CT imaging obtain realization.Power spectrum CT can not only obtain the information of material attenuated inside coefficient, also can with crossing the information of rebuilding and obtaining material composition, and a kind of typical result is exactly the equivalent features density of material.Because power spectrum CT has better material separating capacity, be therefore with a wide range of applications: the attenuation correction, marrow components analysis etc. of bone density measurement, PET.In addition, power spectrum CT can solve many defects that conventional CT imaging exists, as reduced radiation dose, suppressing beam hardening and metal artifacts, strengthen soft tissue contrast, obtaining material composition information etc.
In high-resolution imaging situation, power spectrum CT image reconstruction problem is a nonlinear indirect problem, has the features such as non-linearity, multi-solution and high dimension, is difficult to direct solution.The research of relevant method for reconstructing starts from eighties of last century the seventies.Existing method for solving roughly can be divided into two classes: projection domain decomposition method and image area decomposition method.Projection domain decomposition method first decomposites the data for projection of substrate matter in projection domain, then utilize filtered back projection's (filtered back projection is called for short FBP) method to carry out rebuilding the density image obtaining substrate matter.The method step is simple, but is only used in the consistent scan pattern of height power spectrum geometric parameter, namely along each projection angle, all can collect high low-yield lower two kinds of data for projection.Image area decomposition method first reconstructs high energy and the low energy attenuation coefficient images of object respectively by traditional F BP method, then carry out at image area the density image that linear combination reconstructs substrate matter to reconstruction image.Image area decomposition method is a kind of approximate formation method, resolve into as time have ignored the product term of power spectrum projection, the density image of the substrate matter of rebuilding has serious artifact.But the result of these two kinds of methods is all easily subject to the impact of noise, the density image of final substrate matter can be caused so inaccurate.
Therefore, not enough for prior art, a kind of picture quality that can improve substrate matter density image is provided, the low dosage power spectrum CT image processing method that the high-quality of power spectrum CT image is rebuild under low-dose scanning agreement can be realized very necessary to overcome prior art deficiency.
Summary of the invention
The object of the invention is to avoid the deficiencies in the prior art part and provide a kind of low dosage power spectrum CT image processing method, can improve the picture quality of substrate matter density image, the high-quality that can realize power spectrum CT image under low-dose scanning agreement is rebuild.
Above-mentioned purpose of the present invention is realized by following technological means.
A kind of low dosage power spectrum CT image rebuilding method is provided, comprises the steps,
(1) obtain low-yield CT data for projection and the high-energy CT data for projection of the power spectrum CT image of imaging object under low dosage ray, and obtain corresponding correction parameter, the variance of system matrix and system electronic noise simultaneously;
(2) statistical property met according to the low-yield CT data for projection in step (1) and high-energy CT data for projection and substrate matter decomposition model, build the mathematical model being used for power spectrum CT image reconstruction;
(3) utilize the full variation of broad sense as regularization priori, the mathematical model that integrating step (2) obtains builds the objective function for power spectrum CT image reconstruction;
(4) adopt iterative algorithm to solve the objective function for power spectrum CT image reconstruction built in step (3), complete power spectrum CT image reconstruction.
Preferably, above-mentioned steps (1) is also provided with registration process step, specifically:
Whether location offsets for the low-yield CT data for projection that judgement obtains and high-energy CT data for projection, adopts the method for Registration of Measuring Data that low-yield CT data for projection and high-energy CT data for projection are carried out registration process when location offsets.
Preferably, the substrate matter decomposition model in above-mentioned steps (2) is:
Material is to the material attenuation coefficient of X-ray
the linear species attenuation coefficient of being verified by any two materials and substrate is represented:
, wherein
with
the linear species attenuation coefficient of two materials respectively,
the density of required substrate matter respectively, and
value and X-ray energy have nothing to do;
According to substrate matter decomposition model, for high-energy CT data for projection and the low-yield CT data for projection of step (1) power spectrum CT, the expression formula of corresponding material attenuation coefficient is:
, wherein
hrepresent high energy,
lrepresent low energy,
Definition material attenuation coefficient matrix
, substrate matter linear species attenuation coefficient matrix
, substrate matter density matrix
;
Line integral data for projection after low-yield CT data for projection in step (1) and high-energy CT data for projection carry out log-transformation respectively meets approximate Gaussian distribution, and the data item of the Mathematical reconstruction model set up in described step (2) is:
；
Wherein C represents power spectrum substrate matter density matrix to be reconstructed,
,
grepresent system matrix,
arepresent substrate matter linear attenuation coefficient matrix,
represent that Crow internal medicine is amassed;
pbe that in the power spectrum CT obtained in step (1), high energy projection data and low-yield data for projection carry out the data matrix after log-transformation respectively, mathematical expression is
;
,
represent that diagonal entry is
diagonal matrix,
represent respectively corresponding to high-energy and low-yield
ithe variance of probe unit.
Preferably, the detailed process that in above-mentioned steps (3), regularization priori builds is:
Use the full variation of second order broad sense as priori, the full variation definition of second order broad sense is:
；
Wherein
for non-negative weighting coefficient;
for the auxiliary parameter that the full variation of broad sense is introduced, and get
represent symmetric gradient operator, wherein
represent gradient operator,
representing matrix transpose operation.
Preferably, the objective function of the reconstruction image in above-mentioned steps (3)
for:
；
Wherein
,
representing matrix transpose operation,
regularization parameter,
for portraying the full variational regularization intensity of broad sense.
Preferably, the iterative algorithm in above-mentioned steps (4) is alternating minimization method.
Preferably, the computation process of the alternating minimization method in above-mentioned steps (4) is: introduce formula
and formula
carry out alternating iteration until convergence,
Wherein
fbe a vector value introduced, K represents iterations;
Concrete iterative process is carried out in accordance with the following steps:
(4.1) make K=0, solve according to formula Q1 according to initial value
;
(4.2) step (4.1) is obtained
substitute into formula Q2 to solve
;
(4.3) judge whether iteration ends, if iteration ends, the result obtained with step (4.2) is the density image of final substrate matter of rebuilding; Otherwise enter step (4.4);
(4.4) make K=K+1, step (4.1), (4.2) are obtained
,
substitute into formula Q1, formula Q2, reenter step (4.1).
Preferably, above-mentioned steps (4.1) adopts parabolic alternate algorithm to solve.
Preferably, above-mentioned steps (4.2) adopts Chambolle-Pock Algorithm for Solving.
Preferably, the end condition of above-mentioned steps (4.3) is: when
time, iteration ends.
Low dosage power spectrum CT image rebuilding method of the present invention, comprise the steps, (1) low-yield CT data for projection and the high-energy CT data for projection of the power spectrum CT image of imaging object under low dosage ray is obtained, and obtain corresponding correction parameter, the variance of system matrix and system electronic noise simultaneously; (2) statistical property met according to the low-yield CT data for projection in step (1) and high-energy CT data for projection and substrate matter decomposition model, build the mathematical model being used for power spectrum CT image reconstruction; (3) utilize the full variation of broad sense as regularization priori, the mathematical model that integrating step (2) obtains builds the objective function for power spectrum CT image reconstruction; (4) adopt iterative algorithm to solve the objective function for power spectrum CT image reconstruction built in step (3), complete power spectrum CT image reconstruction.The present invention to utilize in power spectrum CT the statistical distribution characteristic of height energy projection data, Momentum profiles CT imaging characteristics, and the present invention can improve the picture quality of substrate matter density image, can realize the high-quality of power spectrum CT image under low-dose scanning agreement and rebuild.
accompanying drawing explanation
The present invention is further illustrated to utilize accompanying drawing, but the content in accompanying drawing does not form any limitation of the invention.
Fig. 1 is the schematic flow sheet of low dosage power spectrum CT image rebuilding method of the present invention.
Fig. 2 is the image schematic diagram that ideal body mould does not contain artifact and noise; Wherein, Fig. 2 (a) is the image schematic diagram not containing any artifact and noise under desirable Clock body mould 80kVp; Fig. 2 (b) is the image schematic diagram that desirable Clock body mould does not contain any artifact and noise under 140kVp.
Fig. 3 is the image schematic diagram after the low dosage data acquisition FBP algorithm of Clock body mould is directly rebuild; Wherein, Fig. 3 (a) is the image schematic diagram after the low dosage data acquisition FBP algorithm of Clock body mould under 80kVp is directly rebuild; Fig. 3 (b) is the image schematic diagram of Clock body mould after 140kVp low dosage data acquisition FBP algorithm is directly rebuild respectively.
Fig. 4 is that desirable Clock body mould rebuilds the water base figure and bone base figure schematic diagram that obtain based on projection domain decomposition method; Wherein, Fig. 4 (a) is water base figure schematic diagram, and Fig. 4 (b) is bone base figure schematic diagram.
Fig. 5 is that low dosage Clock body mould rebuilds the water base figure and bone base figure schematic diagram that obtain based on projection domain decomposition method; Wherein, Fig. 5 (a) is water base figure schematic diagram, and Fig. 5 (b) is bone base figure schematic diagram.
Fig. 6 is the water base figure and bone base figure schematic diagram schematic diagram that adopt method for reconstructing of the present invention to obtain; Wherein, Fig. 6 (a) is water base figure schematic diagram, and Fig. 6 (b) is bone base figure schematic diagram.
Fig. 7 is that water base figure and bone base figure rebuild part horizontal central line sectional view, and wherein Fig. 7 (a) is that water base figure rebuilds part horizontal central line sectional view, and Fig. 7 (b) is that bone base figure rebuilds part horizontal central line sectional view.
Embodiment
The invention will be further described with the following Examples.
embodiment 1.
A kind of low dosage power spectrum CT image rebuilding method, as shown in Figure 1, comprises the steps,
(1) obtain low-yield CT data for projection and the high-energy CT data for projection of the power spectrum CT image of imaging object under low dosage ray, and obtain corresponding correction parameter, the variance of system matrix and system electronic noise simultaneously.
Step (1) is also provided with registration process step, specifically:
Whether location offsets for the low-yield CT data for projection that judgement obtains and high-energy CT data for projection, adopts the method for Registration of Measuring Data that low-yield CT data for projection and high-energy CT data for projection are carried out registration process when location offsets.
(2) statistical property met according to the low-yield CT data for projection in step (1) and high-energy CT data for projection and substrate matter decomposition model, build the mathematical model being used for power spectrum CT image reconstruction.
Substrate matter decomposition model in step (2) is:
Material is to the material attenuation coefficient of X-ray
the material attenuation coefficient of being verified by any two materials and substrate is represented:
, wherein
with
the linear species attenuation coefficient of two materials respectively,
the density of required substrate matter respectively, and
value and X-ray energy have nothing to do;
According to substrate matter decomposition model, for high-energy CT data for projection and the low-yield CT data for projection of step (1) power spectrum CT, the expression formula of corresponding material attenuation coefficient is:
, wherein
hrepresent high energy,
lrepresent low energy,
Definition material attenuation coefficient matrix
, substrate matter linear species attenuation coefficient matrix
, substrate matter density matrix
;
Line integral data for projection after low-yield CT data for projection in step (1) and high-energy CT data for projection carry out log-transformation respectively meets approximate Gaussian distribution, and the data item of the Mathematical reconstruction model set up in described step (2) is:
；
Wherein C represents power spectrum substrate matter density matrix to be reconstructed,
, G represents system matrix, and A represents substrate matter mass absorption matrix,
represent that Crow internal medicine is amassed;
pbe that in the power spectrum CT obtained in step (1), high energy projection data and low-yield data for projection carry out the data matrix after log-transformation respectively, mathematical expression is
;
,
represent that diagonal entry is
diagonal matrix,
represent respectively corresponding to high-energy and low-yield
ithe variance of probe unit.
(3) utilize the full variation of broad sense as regularization priori, the mathematical model that integrating step (2) obtains builds the objective function for power spectrum CT image reconstruction.
The detailed process that in step (3), regularization priori builds is:
Use the full variation of second order broad sense as priori, the full variation definition of second order broad sense is:
；
Wherein
for non-negative weighting coefficient;
a is the auxiliary parameter that the full variation of broad sense is introduced, and gets
represent symmetric gradient operator, wherein
represent gradient operator,
representing matrix transpose operation.
Preferably, the objective function of the reconstruction image in above-mentioned steps (3)
for:
；
Wherein
,
representing matrix transpose operation,
regularization parameter,
for portraying the full variational regularization intensity of broad sense.
(4) adopt iterative algorithm to solve the objective function for power spectrum CT image reconstruction built in step (3), complete power spectrum CT image reconstruction.
Iterative algorithm in step (4) is alternating minimization method, and computation process is: introduce formula Q1 and formula Q2 and carry out alternating iteration until convergence,
Wherein
fbe a vector value introduced, K represents iterations;
Concrete iterative process is as follows:
(4.1) make K=0, adopt parabolic alternate algorithm to solve according to initial value according to formula Q1
;
(4.2) step (4.1) is obtained
substitute into formula Q2 and adopt Chambolle-Pock Algorithm for Solving
;
(4.3) judge whether iteration ends, if iteration ends, the result obtained with step (4.2) is the density image of final substrate matter of rebuilding; Otherwise enter step (4.4);
(4.4) make K=K+1, step (4.1), (4.2) are obtained
,
substitute into formula Q1, formula Q2, reenter step (4.1).
Wherein, the end condition of step (4.3) is: when
time, iteration ends.
Low dosage power spectrum CT image rebuilding method of the present invention, utilize the statistical distribution characteristic of height energy projection data in power spectrum CT, Momentum profiles CT imaging characteristics, achieves power spectrum CT image reconstruction.While low dosage can be used to launch, still can ensure that producing high-quality power spectrum CT rebuilds image, the reconstruction image that the inventive method obtains has good robustness, better performance on all having in noise is eliminated and artifact suppresses two.
embodiment 2.
Describe the specific implementation process of the method for the invention with the Voxel Phantom data instance of Computer Simulation, as shown in Fig. 1, the implementation process of the present embodiment is as follows.
(1) utilize Clock Voxel Phantom to simulate and generate the checking assessment that low dosage power spectrum CT data for projection carries out algorithm of the present invention.In the present embodiment, simulation CT machine x-ray source is respectively to the distance of rotation center and detector: 570.00mm and 1040.00mm, the number of detection unit is 672, and size is 1.407mm, and the search angle rotated a circle is 1160 to number of samples.Clock phantom image size is 512 × 512.80kVp and the 140kVp data for projection that size is 1160 × 672 is generated respectively by CT system emulation.The variance of system electronic noise is 10.0.
(2) Data correction: utilize the systematic parameter obtained to carry out detection data correction, and carry out log-transformation.
(3) design of graphics is as reconstruction model: the statistical property that the line integral data for projection after the log-transformation obtain step 2 meets approximate Gaussian distribution carries out mathematical modeling, complete the design of the priori item of the full variation of broad sense, construct the objective function of the belt restraining for power spectrum CT image reconstruction
,
, wherein
crepresent the density image of substrate matter to be reconstructed,
,
grepresent system matrix,
arepresent substrate matter mass absorption matrix,
represent that Crow internal medicine is amassed;
prepresent the data matrix respectively after log-transformation of high energy and low energy data for projection in the power spectrum CT obtained in step 1 of the present invention, mathematical expression is
;
,
represent that diagonal entry is
diagonal matrix,
represent respectively corresponding to high-energy and low-yield under
ithe variance of probe unit.Wherein
,
representing matrix transpose operation,
it is regularization parameter.
The detailed process that above-mentioned broad sense full variational regularization priori builds is: use the full variation of second order broad sense as priori, its definition is:
; Wherein
for non-negative weighting coefficient; The full variation of broad sense introduces auxiliary parameter
v, and get
represent symmetric gradient operator, wherein
represent gradient operator.
(4) complete reconstruction: on the correlation model basis that step 3 builds, adopt alternating minimization method to carry out image reconstruction, computation process is: introduce formula Q1 and formula Q2 and carry out alternating iteration until convergence,
Wherein
fbe a vector value introduced, K represents iterations;
Concrete iterative process is as follows:
(4.1) make K=0, adopt parabolic alternate algorithm to solve according to initial value according to formula Q1
;
(4.2) step (4.1) is obtained
substitute into formula Q2 and adopt Chambolle-Pock Algorithm for Solving
;
(4.3) judge whether iteration ends, if iteration ends, the result obtained with step (4.2) is the density image of final substrate matter of rebuilding; Otherwise enter step (4.4);
(4.4) make K=K+1, step (4.1), (4.2) are obtained
,
substitute into formula Q1, formula Q2, reenter step (4.1).
Wherein, the end condition of step (4.3) is: when
time, iteration ends.
Wherein a specific embodiment subrepresentation of calculation procedure is:
；
Wherein,
, represent power spectrum substrate matter density matrix initial value to be reconstructed.
Wherein, B represents data for projection number of pixels, and S represents image pixel number.The optimization method that this formula is used is parabolic alternate algorithm.
In order to verify the effect of method for reconstructing of the present invention, the result of the present embodiment is shown as Fig. 2-Fig. 7, wherein: Fig. 2 a and Fig. 2 b is the image that desirable Clock body mould does not contain any artifact and noise under 80kVp and 140kVp respectively.Fig. 3 a and Fig. 3 b is the image that Clock body mould obtains after 80kVp and 140kVp low dosage data acquisition FBP algorithm is directly rebuild respectively, can see that the reduction due to dosage causes reconstruction image to occur serious statistical noise.Fig. 4 a and Fig. 4 b is that desirable Clock body mould rebuilds the water base figure and bone base figure that obtain based on projection domain decomposition method respectively.Fig. 5 a and Fig. 5 b is that low dosage Clock body mould rebuilds the water base figure and bone base figure that obtain based on projection domain decomposition method respectively, and equally, the noise existed in original high low energy image result in the density image of substrate matter and is also present in serious noise.Fig. 6 a and Fig. 6 b is the water base figure and bone base figure that adopt method for reconstructing of the present invention to obtain respectively, rebuilds image as can be seen from Fig. 6, and the result effect in restraint speckle and artifact utilizing the inventive method reconstruction to obtain is obvious.
Depict in Fig. 7 a and 7b and rebuild image level center line sectional view corresponding to substrate matter in Fig. 4, Fig. 5 and Fig. 6,512 pixels are contained in view of in the entire profile figure, whole display is then difficult to distinguish each method, therefore when only showing, only intercept wherein one section, for water base figure, its interval is [189,320].For bone base figure, its interval is [147,189].As seen from Figure 7, at water base figure with in bone base figure, no matter background area or target area, the inventive method reconstructed value is closer to ideal value.
The present invention utilizes the statistical distribution characteristic of height energy projection data in power spectrum CT, and Momentum profiles CT imaging characteristics, achieves power spectrum CT image reconstruction.Achieve while using low dosage to launch, still can ensure that producing high-quality power spectrum CT rebuilds image, the inventive method has good robustness, all of good performance in noise is eliminated and artifact suppresses two.
Finally should be noted that; above embodiment is only in order to illustrate technical scheme of the present invention but not limiting the scope of the invention; although be explained in detail the present invention with reference to preferred embodiment; those of ordinary skill in the art is to be understood that; can modify to technical scheme of the present invention or equivalent replacement, and not depart from essence and the scope of technical solution of the present invention.
Claims (10)
1. a low dosage power spectrum CT image rebuilding method, is characterized in that: comprise the steps,
(1) obtain low-yield CT data for projection and the high-energy CT data for projection of the power spectrum CT image of imaging object under low dosage ray, and obtain corresponding correction parameter, the variance of system matrix and system electronic noise simultaneously;
(2) statistical property met according to the low-yield CT data for projection in step (1) and high-energy CT data for projection and substrate matter decomposition model, build the mathematical model being used for power spectrum CT image reconstruction;
(3) utilize the full variation of broad sense as regularization priori, the mathematical model that integrating step (2) obtains builds the objective function for power spectrum CT image reconstruction;
(4) adopt iterative algorithm to solve the objective function for power spectrum CT image reconstruction built in step (3), complete power spectrum CT image reconstruction.
2. low dosage power spectrum CT image rebuilding method according to claim 1, is characterized in that:
Described step (1) is also provided with registration process step, specifically:
Whether location offsets for the low-yield CT data for projection that judgement obtains and high-energy CT data for projection, adopts the method for Registration of Measuring Data that low-yield CT data for projection and high-energy CT data for projection are carried out registration process when location offsets.
3. low dosage power spectrum CT image rebuilding method according to claim 2, is characterized in that:
Substrate matter decomposition model in described step (2) is:
Material is to the material attenuation coefficient of X-ray
the linear species attenuation coefficient of being verified by any two materials and substrate is represented:
, wherein
with
the linear species attenuation coefficient of two materials respectively,
the density of required substrate matter respectively, and
value and X-ray energy have nothing to do;
According to substrate matter decomposition model, for high-energy CT data for projection and the low-yield CT data for projection of step (1) power spectrum CT, the expression formula of corresponding material attenuation coefficient is:
, wherein
hrepresent high energy,
lrepresent low energy,
Definition material attenuation coefficient matrix
, substrate matter linear species attenuation coefficient matrix
, substrate matter density matrix
;
Line integral data for projection after low-yield CT data for projection in step (1) and high-energy CT data for projection carry out log-transformation respectively meets approximate Gaussian distribution, and the data item of the Mathematical reconstruction model set up in described step (2) is:
；
Wherein C represents power spectrum substrate matter density matrix to be reconstructed,
,
grepresent system matrix,
arepresent substrate matter linear attenuation coefficient matrix,
represent that Crow internal medicine is amassed;
pbe that in the power spectrum CT obtained in step (1), high energy projection data and low-yield data for projection carry out the data matrix after log-transformation respectively, mathematical expression is
;
,
represent that diagonal entry is
diagonal matrix,
represent respectively corresponding to high-energy and low-yield
ithe variance of probe unit.
4. low dosage power spectrum CT image rebuilding method according to claim 3, is characterized in that:
The detailed process that in described step (3), regularization priori builds is:
Use the full variation of second order broad sense as priori, the full variation definition of second order broad sense is:
；
Wherein
for non-negative weighting coefficient;
for the auxiliary parameter that the full variation of broad sense is introduced, and get
represent symmetric gradient operator, wherein
represent gradient operator,
representing matrix transpose operation.
5. low dosage power spectrum CT image rebuilding method according to claim 4, is characterized in that:
The objective function of the reconstruction image in described step (3)
for:
；
Wherein
,
representing matrix transpose operation,
regularization parameter,
for portraying the full variational regularization intensity of broad sense.
6. low dosage power spectrum CT image rebuilding method according to claim 5, is characterized in that: the iterative algorithm in described step (4) is alternating minimization method.
7. low dosage power spectrum CT image rebuilding method according to claim 6, is characterized in that:
The computation process of the alternating minimization method in described step (4) is: introduce formula
and formula
carry out alternating iteration until convergence,
Wherein
fbe a vector value introduced, K represents iterations;
Concrete iterative process is carried out in accordance with the following steps:
(4.1) make K=0, solve according to formula Q1 according to initial value
;
(4.2) step (4.1) is obtained
substitute into formula Q2 to solve
;
(4.3) judge whether iteration ends, if iteration ends, the result obtained with step (4.2) is the density image of final substrate matter of rebuilding; Otherwise enter step (4.4);
(4.4) make K=K+1, step (4.1), (4.2) are obtained
,
substitute into formula Q1, formula Q2, reenter step (4.1).
8. low dosage power spectrum CT image rebuilding method according to claim 7, is characterized in that: step (4.1) adopts parabolic alternate algorithm to solve.
9. low dosage power spectrum CT image rebuilding method according to claim 7, is characterized in that: step (4.2) adopts Chambolle-Pock Algorithm for Solving.
10. low dosage power spectrum CT image rebuilding method according to claim 7, is characterized in that: the end condition of step (4.3) is: when
time, iteration ends.
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