CN105528771A - Cone beam CT cupping artifact correction method by utilizing energy function method - Google Patents

Abstract

The invention discloses a cone beam CT cupping artifact correction method by utilizing an optimized energy function method. The method directly targets to users for re-established slice images and can finish correction work without making any change to original cone beam CT equipment, can carry out cone beam CT cupping artifact correction efficiently, and meanwhile, can improve CT value uniformity of the same substance of the reconstructed image, thereby helping improved volume visualization and development of visualization technology based on threshold value in the reconstructed image. The method is applied to the technical filed of correction of the cone beam CT reconstructed images (image domain).

Description

A kind of bearing calibration using cupping artifact in the Cone-Beam CT of energy function method

Technical field

The present invention relates to technical field of medical image processing, particularly relate to the correction of pyramidal CT image cupping artifact, gray scale inhomogeneity correction technical field of medical image processing.

Background technology

Cone-Beam CT, as the medical treatment of development in recent years and industrial detection instrument, is usually used in the aspects such as image guided therapy, upper abdomen inspection, examination of mouth, industrial detection.Based on the Cone-Beam CT (CBCT) of flat panel detector compared with traditional two-dimensional ct, there is outstanding advantage, be mainly manifested in the circular scan cycle of Cone-Beam CT, the projection of hundreds of even thousands of faultage images can have been obtained, there is higher sweep velocity and radiation utilization factor, and the effective load reducing X-ray tube exports, and reduces scanning cost.Cone of influence beam CT reconstruction picture quality a lot of because have, as x-ray scattering, noise, geometric error, power spectrum, probe unit non_uniform response etc.But because the dull and stereotyped CT of cone-beam uses large-scale X-ray flat panel detector, this makes image quality be more vulnerable to the impact of X ray scattering and beam hardening compared with traditional CT.The artifact (mainly comprising cupping artifact and streak artifact) formed because of scattering and beam hardening has a strong impact on the Analysis and judgments to rebuilding image.In the cone-beam CT reconstruction image of medical grade, cupping artifact occupies very large proportion, and these artifacts affect very serious for the visual display aspect based on threshold value and the pyramidal CT image segmentation aspect based on threshold value.And the correction of cupping artifact can provide feedback reference for other artifact corrections, for other cone beam computed tomography (CT) scatterings without priori and beam hardening correction provide authorization information.Therefore the present invention is very meaningful about the correction of the cupping artifact in Cone-Beam CT.

In order to reduce the impact of cupping artifact (that is: CT value unevenness artifact), at present, the research of prior art or documents and materials mainly concentrates on the scatter correction on projected image.Early stage artifact correction is mainly reflected in hardware based correction, as X ray filter line device, collimating apparatus or metal grate, air-gap method, scanning slit technology and leads or stereotype technology etc.Recent years, artifact correction research was mainly reflected in based on monte carlo method, scattering analysis method of estimation and the scatter correction method based on partial dispersion radionetric survey.Monte Carlo simulation is effectively method in CBCT scatter correction, but calculated amount is huge.In recent years, some Monte Carlo simulation algorithms improved also are suggested, as used GPU speed technology, based on the body restoration methods etc. of model.These are based on the thought of Monte Carlo simulation, all attempt on simulation precision and calculation cost, set up a good equilibrium point.But it is too high to be confined to calculation cost all the time, and be not easy to use.

Based on the method for the Cone-Beam CT artifact correction that part ray blocks, early stage has BSA scatter removal method, is to block scattered quantum below array by measuring at ray, carrys out interpolation and goes out to arrive overall scatter distributions on detector.And then carry out the normal scan not blocking array containing ray, from the projected image of scanning, deduct scatter distributions image, just obtain the image after correction.This method will carry out twice sweep, too increases x-ray irradiation dose while adding sweep time.Occurred afterwards removablely blocking fast method, and can solve twice sweep problem.

Also research image after cone-beam CT reconstruction being carried out to artifact correction is had.This research is mainly by the anatomical structure in CT image.These class methods rely on deformable registration precision completely, and need CT view data.

The shortcoming of prior art mainly comprises:

(1) currently available technology is mainly for projection image correction, does not have the direct correction for rebuilding rear sectioning image, as patent CN104408753A.

(2) prior art great majority concentrate in the method for the artifact correction caused because of scattering, and mostly need to add hardware device, as: patent 200710019084 and 201310039298, these two patents all need to add hardware device on the Cone-Beam CT equipment of costliness, add the complicacy of operation and cause potential security risk to equipment.Particularly patent 200710019084 needs twice sweep testee, the radiant quantity of the measured object increased so undoubtedly.

In sum, in the method for prior art or documents and materials, Monte-carlo Simulation Method expends time in very much, the structure that result is limited to modulation panel self is corrected in primary ray modulator approach, based on partial dispersion radionetric survey method, need to increase exposure dose, existing method is not high to the accuracy of estimation of scatter distributions.And the present invention can solve problem above well.

Summary of the invention

The object of the invention is to solve above-mentioned the deficiencies in the prior art, proposes a kind of method that use is corrected cupping artifact in Cone-Beam CT by optimized energy function.This method is for the sectioning image after reconstruction, direct user oriented, original Cone-Beam CT equipment is not made any change, just correction work can be completed, the CT value homogeneity of the material of the same race rebuilding image can also be improved while can carrying out the cupping artifact correction of Cone-Beam CT efficiently, thus contribute to rebuilding in image, the development of perfect volume visualization and the visualization technique based on threshold value.The method is applied to cone-beam CT reconstruction image (i.e. image area) alignment technique field.

The present invention solves the technical scheme that its technical matters takes: the invention provides a kind of use in Cone-Beam CT and rebuild the optimized energy functional based method that image carries out cupping artifact correction, the method has very strong robustness, do not need multiple scanning testee, do not increase the complexity of cone-beam CT system.

Method flow:

Step 1: obtain the sectioning image after rebuilding.

Step 2: cupping artifact represents and builds energy function

$F(f_s,f_p)=F(u,c,w)=\underset{\mathrm{\Ω}}{\∫}|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}{c}_i{u}_i\left(x\right)-w^{T}G\left(x\right){|}^{2}dx,$

Wherein G (x)=(g ₁(x) ... g _m(x)) ^tfor smooth basis functions, c _ifor constant, meet as x ∈ Ω _itime, u _i(x)=1; When time, u _i(x)=0, w=(w ₁... w _m)

Step 3: fixing c and u, by solving an equation obtain the minimum value of F (u, c, w).Obtain $\hat{w}=A^{-1}v.$

Step 4: fix and use w and u upgraded, with for F (u, c, w) the minimum value solution of variable is:

${\hat{c}}_i=\frac{\underset{\mathrm{\Ω}}{\∫}\left(f\right(x)-f_s(x\left)\right)u_i\left(x\right)dx}{\underset{\mathrm{\Ω}}{\∫}{u}_i^2\left(x\right)dx},i=1,...,N$

Step 5: fix and use w and c upgraded, with u=(u ₁... u _n) ^tduring F (u, c, w) minimum value solution for variable, meet following condition:

${\hat{u}}_i=\left\{\begin{array}{c}1,i=i_{\min }\left(x\right)\\ 0,i\≠i_{\min }\left(x\right)\end{array}\right.$

Wherein, i _min(x)=argmin{f (x)-c _i-w ^tg (x) }.

Step 6: if w is stable or iterations more than 10 times, then perform step 7, otherwise get back to step 3.

Step 7: after correcting, image is $f_p=f-{\hat{f}}_s=f-w^{T}G\left(x\right).$

Further, the present invention, directly towards Cone-Beam CT slice of data, does not make any change to original Cone-Beam CT existing equipment, does not need the prior imformation of user and measured target.

Further, present invention demonstrates that cupping artifact is from reconstruction picture breakdown out, that is:

$\begin{array}{c}f=\frac{1}{4{\mathrm{\π}}^2}{\∫}_0^{2\mathrm{\π}}\frac{{d_{so}}^2}{{\left(d_{so}+r\·s\right)}^2}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\frac{d_{so}}{{\left({d_{so}}^2+t^2+z^2\right)}^{1/2}}\·\\ \left(P_{3D}\left(t,z\left(r\right),\mathrm{\φ}\right)+S_{3D}\left(t,z\left(r\right),\mathrm{\φ}\right)+n\right)\·{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left|\mathrm{\ω}\right|e^{j2\mathrm{\π}\mathrm{\ω}\left(t\left(r\right)-t\right)}d\mathrm{\ω}dtd\mathrm{\φ}\\ =f_p+f_s+f_n\end{array},$

Wherein f _prepresent true artifact-free sectioning image, f _srepresent that scattering and beam hardening cause the sectioning image of artifact, f _nrepresent the sectioning image that noise n is formed.

Beneficial effect:

1, the present invention directly corrects for the cupping artifact of the sectioning image after reconstruction, and the method calculated amount is relatively little, while can carrying out the correction of Cone-Beam CT sectioning image cupping artifact efficiently, improves the CT value homogeneity that material of the same race rebuilds image.

2, the present invention is directly towards CT section demand user, does not make any change, do not need the prior imformation of user and measured target, complete correction work well original Cone-Beam CT existing equipment.

3, the present invention can increase picture contrast, and after making correction, image can show illuminated object information originally more accurately.

4, the present invention improves well and achieves and detects based on the CT image viewing of threshold value, segmentation and focus.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is the present invention by the human skull sample axis direction view on (left side) before rebuilding image rectification (right side) afterwards.

Fig. 3 is the horizontal cross-section value of human skull's die body that the present invention measures: the longitudinal axis is image profile.

Fig. 4 is the region of interest area image schematic diagram that the present inventor's skull die body is selected.

Fig. 5 (a), Fig. 5 (b) are sample axis's direction view of CTP486 reconstruction image two difference section in CatPhan500 before and after scatter correction of the present invention.

Fig. 6 is the horizontal sectional drawing of die body measured by Fig. 5 in the present invention.

Fig. 7 is the seletion calculation area image schematic diagram of Mouse Bone.

Fig. 8 (a), Fig. 8 (b) are respectively Mouse Bone before and after scatter correction and rebuild sample axis's direction view of image.

Embodiment

Below in conjunction with Figure of description, the invention is described in further detail.

As shown in Figure 1, the invention provides a kind of bearing calibration using cupping artifact in the Cone-Beam CT of energy function method, the method comprises the steps:

Step 1: according to FDK algorithm obtain rebuild after sectioning image, and can from theoretical proof cupping artifact can from reconstruction after picture breakdown out.

Step 2: cupping artifact represents and builds energy function

$F(f_s,f_p)=F(u,c,w)=\underset{\mathrm{\Ω}}{\∫}|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}{c}_i{u}_i\left(x\right)-w^{T}G\left(x\right){|}^{2}dx,$

Wherein G (x)=(g ₁(x) ... g _m(x)) ^tfor smooth basis functions, c _ifor constant, meet as x ∈ Ω _itime, u _i(x)=1; When time, u _i(x)=0, w=(w ₁... w _m)

Step 3: fixing c and u, by solving an equation obtain the minimum value of F (u, c, w).Obtain $\hat{w}=A^{-1}v.$

Step 4: fix and use w and u upgraded, with for F (u, c, w) the minimum value solution of variable is:

${\hat{c}}_i=\frac{\underset{\mathrm{\Ω}}{\∫}\left(f\right(x)-f_s(x\left)\right)u_i\left(x\right)dx}{\underset{\mathrm{\Ω}}{\∫}{u}_i^2\left(x\right)dx},i=1,...,N$

Step 5: fix and use w and c upgraded, with u=(u ₁... u _n) ^tduring F (u, c, w) minimum value solution for variable, meet following condition:

${\hat{u}}_i=\left\{\begin{array}{c}1,i=i_{\min }\left(x\right)\\ 0,i\≠i_{\min }\left(x\right)\end{array}\right.$

Wherein, i _min(x)=argmin{f (x)-c _i-w ^tg (x) }.

Step 6: if w is stable or iterations more than 10 times, then perform step 7, otherwise get back to step 3.

Step 7: after correcting, image is $f_p=f-{\hat{f}}_s=f-w^{T}G\left(x\right).$

Cupping artifact of the present invention can from reconstruction picture breakdown out detailed process comprise:

Rebuild image in Cone-Beam CT based on FDK algorithm, rebuild image set f and can be written as following form:

$\begin{array}{c}f=\frac{1}{4{\mathrm{\π}}^2}{\∫}_0^{2\mathrm{\π}}\frac{{d_{so}}^2}{{\left(d_{so}+r\·s\right)}^2}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\frac{d_{so}}{{\left({d_{so}}^2+t^2+z^2\right)}^{1/2}}\\ \·I_{3D}\left(t,z\left(r\right),\mathrm{\φ}\right)\·{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left|\mathrm{\ω}\right|e^{j2\mathrm{\π}\mathrm{\ω}\left(t\left(r\right)-t\right)}d\mathrm{\ω}dtd\mathrm{\φ}\end{array},$ Formula 1

Wherein d _sorepresent the distance of radiographic source to turning axle, I _3D(t, z (r), φ) represents the sequence of projected image.Projected image I _3Dcan be analyzed to following form:

I _3D=P _3D+ S _3D+ n, formula 2

Wherein P _3Drepresentation theory real projection image, S _3Dthe artifact composition caused by scattering and beam hardening, n to be average be zero additive noise.Formula 1 is expressed as form:

$\begin{array}{c}f=\frac{1}{4{\mathrm{\π}}^2}{\∫}_0^{2\mathrm{\π}}\frac{{d_{so}}^2}{{\left(d_{so}+r\·s\right)}^2}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\frac{d_{so}}{{\left({d_{so}}^2+t^2+z^2\right)}^{1/2}}\·\\ \left(P_{3D}\left(t,z\left(r\right),\mathrm{\φ}\right)+S_{3D}\left(t,z\left(r\right),\mathrm{\φ}\right)+n\right)\·{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left|\mathrm{\ω}\right|e^{j2\mathrm{\π}\mathrm{\ω}\left(t\left(r\right)-t\right)}d\mathrm{\ω}dtd\mathrm{\φ}\\ =f_p+f_s+f_n\end{array},$ Formula 3

Wherein f _prepresent true artifact-free sectioning image, f _srepresent that scattering and beam hardening cause the sectioning image of artifact, f _nrepresent the sectioning image that noise n is formed.

From formula 3, rebuild image and can be expressed as three independent components additions.Wherein f _sby S _3Dobtain, and S _3Da smooth low frequency projection signal, all f _smain region (namely show as large-area Physical Zone of the same race, cupping artifact is its principal ingredient) also should be a smooth low frequency sectioning image.In order to effectively use f _sand f _pcharacter, the present invention is by f _sbe expressed as a known smooth basis functions collection g ₁... g _mlinear combination, this adapts to the smooth change character of cupping artifact.By finding linear combination in optimum coefficient w=(w ₁... w _m) estimate cupping artifact (getting M=10 in the experimental data that the present invention enumerates).The present invention is f _sx () is expressed as f _s(x)=w ^tthe vector form of G (x), wherein G (x)=(g ₁(x) ... g _m(x)) ^t.

Suppose at image area Ω _iin there is N kind tissue, then true sectioning image f _px () is in fact a constant c about x in i-th tissue _i.Each Ω _iu can be carried out with its membership function _irepresent.Under ideal conditions, u _ibe a scale-of-two membership function, meet as x ∈ Ω _itime, u _i(x)=1; When time, u _i(x)=0.As membership function u _iwith constant c _itime known, f _pfollowing form can be represented as:

$f_p=\underset{i=1}{\overset{N}{\Σ}}{c}_i{u}_i\left(x\right),$ Formula 4

Energy functional expression formula comprises:

In this model, the present invention considers how to rebuild in image f, f when acquisition makes following energy function F minimize _sand f _p:

$F(f_s,f_p)=\underset{\mathrm{\Ω}}{\∫}|f\left(x\right)-f_p\left(x\right)-f_s\left(x\right){|}^{2}dx,$ Formula 5

If obviously variable f _sand f _pwithout any constraint condition, minimizing of F is an ill-conditioning problem.In fact, f is worked as _sand f _pfor the f that satisfies condition _p=f-f _sarbitrary value time, energy F (f _s, f _p) all can obtain minimum value.Use the expression formula of true picture and cupping artifact image, energy F (f _s, f _p) following form can be represented as:

$F(f_s,f_p)=F(u,c,w)=\underset{\mathrm{\Ω}}{\∫}|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}{c}_i{u}_i\left(x\right)-w^{T}G\left(x\right){|}^{2}dx,$ Formula 6

Optimization comprises:

All variable u=(u of energy F (u, c, w) ₁... u _n), c=(c ₁... c _n) and w be all convex, this character ensure that F (u, c, w) has unique optimum solution for any variable.By F (u, c, w) minimum value solution under the different variable of interleaved computation, can reach and solve object.

First, fixing c and u, the present invention can by solving an equation obtain the minimum value of F (u, c, w).Process is as follows:

$\frac{\∂F}{\∂w}=-2\underset{\mathrm{\Ω}}{\∫}G\left(x\right)|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}\left(c_i{u}_i\right(x\left)\right)|dx+2w\underset{\mathrm{\Ω}}{\∫}G\left(x\right)G{\left(x\right)}^{T}dx=0,$ Formula 7

Above-mentioned equation can be rewritten as following form:

Aw=v, formula 8

Wherein $A=\underset{\mathrm{\Ω}}{\∫}G\left(x\right)G{\left(x\right)}^{T}dx,v=\underset{\mathrm{\Ω}}{\∫}G\left(x\right)|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}\left(c_i{u}_i\right(x\left)\right)|dx.$

Easy proof, matrix A is nonsingular matrix.Therefore, vector can be represented as:

$\hat{w}=A^{-1}v,$ Formula 9

The f upgraded _s, can be calculated by following formula and obtain:

${\hat{f}}_s={\hat{w}}^{T}G\left(x\right),$ Formula 10

Fix and use w and u upgraded, with for F (u, c, w) the minimum value solution of variable is:

${\hat{c}}_i=\frac{\underset{\mathrm{\Ω}}{\∫}\left(f\right(x)-f_s(x\left)\right)u_i\left(x\right)dx}{\underset{\mathrm{\Ω}}{\∫}{u}_i^2\left(x\right)dx},i=1,...,N$ Formula 11

Fix and use w and c upgraded, with u=(u ₁... u _n) ^tduring F (u, c, w) minimum value solution for variable, meet following condition:

${\hat{u}}_i=\left\{\begin{array}{c}1,i=i_{min}\left(x\right)\\ 0,i\≠i_{min}\left(x\right)\end{array}\right.$ Formula 12

Wherein, i _min(x)=argmin{f (x)-c _i-w ^tg (x) }.

Carry out continuous interative computation and upgrade u, c and w, obtain the stable solution of w.Great many of experiments shows that the solution of w is basicly stable after 10 iteration.After the last correction obtained, image is $f_p=f-{\hat{f}}_s=f-w^{T}G\left(x\right)$

Experiment and result

Quantitative test index definition comprises:

Definition cupping artifact τ _cup=100 (u _{m, edge}-u _{m, center})/u _{m, edge}, wherein u _{m, center}and u _{m, edge}it is the CT value (HU) of die body center and peripheral..

Root mean square contrast is expressed as $RMSC=\sqrt{\frac{1}{MN}\underset{i=0}{\overset{N-1}{\Σ}}\underset{j=0}{\overset{M-1}{\Σ}}{(I_{ij}-\stackrel{\‾}{I})}^2},$ Wherein I _ijit is the pixel value of (i, j) position in two dimensional image. all pixel average in image.

The Cone-Beam CT section cupping artifact of human skull corrects experiment and comprises:

Experimental image size is 211 × 211.As shown in Figures 2 and 3, after correcting, the CT value homogeneity of image significantly improves.Analysis result is as shown in table 1.1.89 seconds consuming time of the trimming process (CPU:i5-2450, RAM:6GB, GPU:NVIDAGeForce610M) of a section in this method.

Fig. 3 illustrates the image that horizontal cross-section corrects front and back.Therefrom can find out that the cupping artifact observing image after correcting significantly reduces.

CTP486 die body Cone-Beam CT section cupping artifact corrects experiment and comprises:

CTP486 die body is used to test.Correcting image as shown in Figure 5.CTP486 module is that the homogeneous material casting containing 2% (0-20H) water forms by CT number.Image size is 229 × 229.1.93 seconds consuming time of the trimming process (CPU:i5-2450, RAM:6GB, GPU:NVIDAGeForce610M) of a section.

Image before and after horizontal cross-section corrects as shown in Figure 6.As can be seen from Figure 6 before correcting, material slice map CT value of the same race is uneven, namely (show as cupping artifact), and after using method of the present invention, cupping artifact eliminates the subtle degree of human eye.

Table 1: the quantitative analysis of skull die body.Reconstruction image (RI_BC) before cupping artifact corrects, the reconstruction image (RI_AC) after cupping artifact corrects

Mouse Bone Cone-Beam CT section cupping artifact corrects experiment, specifically comprises:

Mouse Bone scattering data is obtained by HiscanM1000 (Micro-CT).The acquisition of rebuilding image comprises 80kVp, 360 projections of 200uA, 30ms.Fig. 8 (a) and Fig. 8 (b) Mouse Bone illustrated before and after scatter correction rebuilds sample axis's direction view of image.Image size is 339 × 339.2.7 seconds consuming time of the trimming process (CPU:i5-2450, RAM:6GB, GPU:NVIDAGeForce610M) of a section.As shown in Figure 7, cupping artifact is reduced to 9.8% by 23.8% by this method, and analysis result is as shown in table 2.

Table 2: the quantitative analysis of Mouse Bone.Reconstruction image (RI_BC) before cupping artifact corrects, the reconstruction image (RI_AC) after cupping artifact corrects.

Claims (4)

1. use in Cone-Beam CT and rebuild the optimized energy functional based method that image carries out cupping artifact correction, it is characterized in that, described method comprises the steps:

Step 1: obtain the sectioning image after rebuilding;

Step 2: cupping artifact represents and builds energy function and is:

$F(f_s,f_p)=F(u,c,w)=\underset{\mathrm{\Ω}}{\∫}{|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}{c}_i{u}_i\left(x\right)-w^{T}G\left(x\right)|}^{2}dx,$

Wherein f _prepresent true artifact-free sectioning image, f _srepresent that scattering and beam hardening cause the sectioning image of artifact, f is the reconstruction image without correcting, G (x)=(g ₁(x) ... g _m(x)) ^tfor smooth basis functions, c _ifor constant, meet as x ∈ Ω _itime, u _i(x)=1; When time, u _i(x)=0, variable u=(u ₁... u _n), c=(c ₁... c _n) and w=(w ₁... w _m) be all convex;

Step 3: fixing c and u, by solving an equation obtain the minimum value of F (u, c, w), obtain $\hat{w}=A^{-1}v,$ Wherein $A=\underset{\mathrm{\Ω}}{\∫}G\left(x\right)G{\left(x\right)}^{T}dx,$ $v=\underset{\mathrm{\Ω}}{\∫}G\left(x\right)|f\left(x\right)-\underset{i=1}{\overset{N}{\Σ}}\left(c_i{u}_i\right(x\left)\right)|dx;$

Step 4: fix and use w and u upgraded, with for F (u, c, w) the minimum value solution of variable is:

${\hat{c}}_i=\frac{\underset{\mathrm{\Ω}}{\∫}\left(f\right(x)-f_s(x\left)\right)u_i\left(x\right)dx}{\underset{\mathrm{\Ω}}{\∫}{u}_i^2\left(x\right)dx},i=1,...,N$

Step 5: fix and use w and c upgraded, with u=(u ₁... u _n) ^tduring F (u, c, w) minimum value solution for variable, meet following condition, that is:

${\hat{u}}_i=\left\{\begin{array}{cc}1,& i=i_{\min }\left(x\right)\\ 0,& i\≠i_{\min }\left(x\right)\end{array}\right.$

Wherein, i _min(x)=argmin{f (x)-c _i-w ^tg (x) };

Step 6: if w is stable or iterations more than 10 times, then perform step 7, otherwise get back to step 3;

Step 7: after correcting, image is $f_p=f-{\hat{f}}_s=f-w^{T}G\left(x\right).$

2. a kind of use in Cone-Beam CT according to claim 1 rebuilds the optimized energy functional based method that image carries out cupping artifact correction, it is characterized in that, described method is directly towards Cone-Beam CT slice of data, original Cone-Beam CT existing equipment is not made any change, do not need the prior imformation of user and measured target.

3. a kind of use in Cone-Beam CT according to claim 1 rebuilds the optimized energy functional based method that image carries out cupping artifact correction, it is characterized in that, the cupping artifact of described method is from reconstruction picture breakdown out, that is:

$\begin{array}{c}f=\frac{1}{4{\mathrm{\π}}^2}{\∫}_0^{2\mathrm{\π}}\frac{{d_{so}}^2}{{(d_{so}+r\·s)}^2}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\frac{d_{so}}{{({d_{so}}^2+t^2+z^2)}^{1/2}}\·\\ \left(P_{3D}\right(t,z\left(r\right),\mathrm{\φ})+S_{3D}(t,z\left(r\right),\mathrm{\φ})+n)\·{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left|\mathrm{\ω}\right|e^{j2\mathrm{\π}\mathrm{\ω}\left(t\right(r)-t)}d\mathrm{\ω}dtd\mathrm{\φ}\\ =f_p+f_s+f_n\end{array},$

Wherein f _prepresent true artifact-free sectioning image, f _srepresent that scattering and beam hardening cause the sectioning image of artifact, f _nrepresent the sectioning image that noise n is formed.

4. a kind of use in Cone-Beam CT according to claim 1 rebuilds the optimized energy functional based method that image carries out cupping artifact correction, it is characterized in that, described method is applied to cone-beam CT reconstruction image (i.e. image area) and corrects.