CN102110288A - Projected chord graph repair method for CT image - Google Patents

Abstract

The invention discloses a projected chord graph repair method for a computer tomography (CT) image, and belongs to the technical field of computed tomography imaging. The method comprises the following steps of: 1, positioning unmeasured pixel coordinates; 2, determining an image space pixel family; 3, determining a sine curve family corresponding to the unmeasured chord graph coordinates; 4, determining unmeasured pixel positions and corresponding intensity values along a discrete sine line respectively; 5, constructing a structure tensor matrix of a local neighborhood using each unmeasured pixel as a center, and solving the characteristic value and the characteristic vector of the matrix; and 6, selecting a sine line most accordant with the characteristic vector with minimum characteristic value in the local neighborhood of the step 5 for each unmeasured pixel, and taking the interpolation result at the unmeasured pixel as final estimation for the intensity of the unmeasured pixel. By the method, the consistency of homogeneous regions of a chord graph can be effectively improved, and the inner edge is well reserved, so a reconstructed CT image with better quality can be obtained.

Description

A kind of projection string figure method for repairing and mending of CT image

Technical field

The present invention relates to the projection string figure method for repairing and mending of a kind of CT (CT:Computer tomography) image, belong to the computer tomography technical field.

Background technology

For the CT imaging, the X line source rotates around surveying object along circular orbit y (β) with projected angle β.F (x) distributes for waiting the linear attenuation coefficient of rebuilding object.We define image space chord map space is I and S.The circular orbit equation is

y(β)＝(Rcosβ，Rsinβ) (1)

Herein, R is that the X source is to the isocenter point distance.In the collimated beam imaging geometry, forward projection is

(ρ β) is the polar coordinates expression of f (x) to P.(ρ β) is drop shadow intensity under projected angle β to P.The image space coordinate is behind polar coordinate transform, for specific point in the reconstructed image By the β that changes, its corresponding sinusoidal trajectory in projector space is provided by (3).

In the fladellum imaging geometry, projected angle β and fan angle γ definition X-ray line.The fladellum transformation for mula is

$S(\mathrm{\β},\mathrm{\γ})={\∫}_0^{\∞}f(y\left(\mathrm{\β}\right)+t\stackrel{r}{\mathrm{\θ}})\mathrm{dt}---\left(4\right)$

Herein,

Be the roentgen-unit direction vector, by [cos (β+γ), sin (β+γ)] provide.In theory, string figure is the stack unlimited S (beta, gamma) how is arranged.Each point in the reconstructed image

Specific curvilinear path of corresponding uniquely projector space.Sinusoidal polar coordinates are expressed as

Herein, β ₀It is initial projected angle.

It is the deflection of the radial vector of each reference pixel of image space.

Be that a class S curve is through projector space unknown pixel (beta, gamma).

M, N are two points of selecting, and express the border of the image-region that needs correction.On line segment MN, x is positioned at the not reference pixel of measured zone.

With

Be three radial vectors With

Deflection.Vector

Be orthogonal to secant.r _xIt is the radius of FOV.θ _MaxBe used to the deflection scope of the sinusoidal line collection of definite discretize.

In addition,

In Δ POx,

Polar coordinates are expressed down, and fladellum is transformed to

The set of radial distance

Provide by (8).On line segment MN, along with

By

Change to

Account for

Change to N by M.Line segment MN is the part of X-ray line (beta, gamma).

When the CT imaging, tend to pseudo-shadow etc. for example occur because the picture quality that projector space lacks after causing rebuilding is not good, therefore need repair or proofread and correct projection string figure.The source of typical projector space disappearance has five kinds, and they are respectively: projected angle direction inside is blocked, the projection sparse sampling, and the outside of projected angle direction is blocked, the inside disappearance of limited angle sampling and arbitrary shape.String figure method for repairing and mending at present commonly used is linear interpolation method, estimates based on the repairing and the FOE of sample.Linear interpolation method is estimated not measurement data partly, adopts linear weighted function to be inversely proportional to the given data and the distance of measurement data not.Estimation based on sample replaces not measurement data neighborhood by choose similar neighborhood from given data.FOE estimates with markov random file image to be carried out modeling based on Bayesian statistical theory, and the construction ability functional adopts optimization method to find the solution its minimum value then.The advantage of preceding two kinds of methods is that speed is very fast.The estimated accuracy of FOE method of estimation is better than preceding two kinds.But, more than 3 kinds of methods all less than partial structurtes travel direction estimation according to string figure, therefore can't recover the inward flange of string figure preferably.Particularly block and two kinds of situations of projection sparse sampling for projected angle direction inside, the repair efficiency of existing method is undesirable, therefore can consider along the method for sinusoidal line interpolation both of these case.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiency of existing CT image string figure method for repairing and mending, a kind of projection string figure method for repairing and mending of CT image is provided, and this method can be blocked the projector space disappearance that is caused with the projection sparse sampling to detector inside and be carried out Efficient software patching.

The present invention is by the following technical solutions:

A kind of projection string figure method for repairing and mending of CT image is used for detector inside and blocks the projector space disappearance that is caused with the projection sparse sampling, it is characterized in that, may further comprise the steps:

Pixel coordinate is not measured in step 1, location;

Step 2, determine image space pixel family;

Step 3, definite corresponding to the sinusoidal curve family of not measuring string figure coordinate;

Step 4, along the discretize sinusoidal line, determine not measure location of pixels and corresponding strength value respectively;

Step 5, construct with each and do not measure the structure tensor matrix that pixel is the local neighborhood at center respectively, find the solution its eigenwert and proper vector;

Step 6, do not measure pixel, in the described local neighborhood of step 5, select the sinusoidal line that meets most with proper vector, get the interpolation result that this does not measure the pixel place, as the final estimation of this not being measured pixel intensity with minimal eigenvalue for each.

The inventive method is carried out discretize with string figure and is decomposed based on the CT image-forming principle, does not carry out the pointwise repairing to measuring string figure, and proposes the directional interpolation of new eigenwert guiding.Compared to existing technology, the present invention can keep inward flange preferably improving effectively under the consistance prerequisite of the even matter of string figure zone, thereby obtains the CT image after the reconstruction of better quality.

Description of drawings

Fig. 1 is a CT fladellum imaging geometry schematic diagram;

Fig. 2 is a string figure decomposing schematic representation;

Fig. 3 is employed original analog data and corresponding imperfect projection in the contrast test, wherein (a) and (b) are respectively original analog data 1 and 2, (c), (d) is respectively the collimated beam projection of original analog data 1 and 2, (e) for the collimated beam projection of blocking of original analog data 1, (f) be the collimated beam projection of the sparse sampling of original analog data 2, (g) image for obtaining after (e) rebuild (h) obtains image after (f) rebuild;

Result after the string figure that Fig. 4 blocks original analog data 1 for the employing distinct methods repairs and rebuilds, wherein (a) is for adopting the string figure after linear interpolation method is repaired, (b) for adopting the string figure after repairing based on the method for repairing and mending of sample, (c) for adopting the string figure after the FOE method is repaired, (d) for adopting the string figure after the inventive method is repaired, (e) be the reconstructed image of (a), (f) be the reconstructed image of (b), (g) being the reconstructed image of (c), (h) is the reconstructed image of (d);

Fig. 5 is for adopting the result after distinct methods is repaired and rebuild the string figure of original analog data 2 sparse samplings, wherein (a) is for adopting the string figure after linear interpolation method is repaired, (b) for adopting the string figure after repairing based on the method for repairing and mending of sample, (c) for adopting the string figure after the FOE method is repaired, (d) for adopting the string figure after the inventive method is repaired, (e) be the reconstructed image of (a), (f) be the reconstructed image of (b), (g) being the reconstructed image of (c), (h) is the reconstructed image of (d).

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

Accompanying drawing 1 has shown the principle of fladellum imaging.Accompanying drawing 2 is a string figure decomposing schematic representation.Adopt the inventive method to carry out string figure when repairing, carry out according to following steps:

Pixel coordinate is not measured in step 1, location;

If S is string figure current to be repaired, definition mask is the coordinate that needs the zone of repairing.S (x is that each does not measure the locations of pixels coordinate in the mask y), wherein, x ∈ [1,2 ..., P], P is the projection sum of string figure S; Y ∈ [1,2 ..., D], D is that the detector in the imaging geometry is visited unit's sum.According to formula (10), calculate S (x, y) respective projection angle and fan angular coordinate (beta, gamma).

β＝x

$\mathrm{\γ}=\frac{D+1}{2}-y$

(10)

Step 2, determine image space pixel family;

According to the fladellum image-forming principle, each unknown point in string space, corresponding to a discretize light (beta, gamma), as shown in Figure 2, discretize light (beta, gamma) meets at 2 M, N with the zone to be corrected of image space.If

For radial vector is orthogonal to the light vector

M, N are the border in image space zone to be corrected.Definition

Be corresponding border radial vector.

With

Be respectively Corresponding polar coordinates deflection.Wherein,

Definition θ _MaxFor With

The forward angle.θ _MaxBe used to the deflection scope of the sinusoidal line collection of definite discretize, the people is for providing.Consider in conjunction with repair efficiency and time complexity two aspects.The present invention is preferred

So just obtain one group of deflection and radial vector, they have defined one group of discrete pixel on line segment MN.This group discretize pixel is corresponding to same X-ray line (beta, gamma).According to the fladellum conversion, each pixel of image space, its coordinate determine sinusoidal line position, corresponding string space; Its linear attenuation coefficient is corresponding to the intensity level of string space sinusoidal line.Therefore, this group sinusoidal line meets at pixel current to be estimated (beta, gamma).If

For the radial distance set of this group discretize pixel, can try to achieve by formula (8)

Herein,

The polar coordinates that are the image space pixel are expressed.R is that the X source is to the isocenter point distance.

See the Δ POx among Fig. 2.

Step 3, definite corresponding to the sinusoidal curve family of not measuring string figure coordinate;

For the image space of determining a bit

Determine a sinusoidal line by following formula.This sinusoidal line is fixing Down, γ is about the function of β.

Then, be positioned at one group of point of the image space of same light, one group of definite sinusoidal line is formed set

It is the image space pixel

Corresponding projector space sinusoidal line.β ₀It is initial projected angle.

Step 4, along the discretize sinusoidal line, determine not measure location of pixels and corresponding strength value respectively;

When definite sinusoidal line

After, this sinusoidal line by measure portion and not measure portion form.Not measuring location of pixels is generally determined by approximating method.Because our known " transcendental form " that decomposites data is sinusoidal line.Therefore among the present invention, determine not measure location of pixels and adopt the standard sine match.Determine that not measuring intensity values of pixels is generally estimated by the one dimension interpolation.For example: linear interpolation, polynomial interpolation, image factoring, neighbor interpolation etc.Because string figure has piecewise smooth character, so the present invention adopts cubic spline interpolation to determine not measure pixel corresponding strength value.

(X, Y), each pixel is by (x for measurement data projector space coordinate set _i, y _i) expression, the process of standard sine match is equivalent to determine that one group of parameter makes formula (11) obtain the minimum value under the Euclidean distance meaning, that is,

$\underset{a,b,c,d\∈R}{\arg \min }\underset{i}{\mathrm{\Σ}}{(y_i-[a\sin (b{x}_i+c)+d\left]\right)}^2---\left(11\right)$

Wherein, a, b, c, d are the estimated parameter for the treatment of of sinusoidal line.After parameter vector is determined, determine not measure the coordinate of pixel then.The present invention utilizes Matlab numerical analysis tools case to carry out the standard sine match.

Cubic spline function is a smooth curve by a series of interpolation points, determines the process of curvilinear function group by finding the solution three moments euqation on the mathematics.Be implemented as follows:

Defined function C (x) is everywhere can be little and at each sub-range [x _k, x _K+1] on be cubic polynomial.Wherein, a=x ₀＜x ₁＜...＜x _n=b is given node.Claim that then C (x) is node a=x ₀＜x ₁＜...＜x _nCubic spline function on the=b.Definition C ₀(x) be to treat approximating function.

If cubic spline function C (x) is at each sub-range [x _k, x _K+1] on expression formula is arranged,

C(x)＝C _k(x)＝a _kx ³+b _kx ²+c _kx+d _kx∈(x _k，x _k+1)，k＝0，1，2，...，(n-1) (12)

Wherein n divides the sub-range number.Binding time complexity and interpolation consider that the present invention gets n=5.a _k, b _k, c _k, d _kBe the undetermined constant of splines in each sub-range.Then interpolation condition is:

C(x _k)＝C ₀(x _k)k＝0，1，2，...，(n-1)(13)

$\left\{\begin{array}{c}\underset{t\→0^{+}}{\lim }C(x_k+t)=\underset{t\→0^{-}}{\lim }C(x_k+t)\\ \underset{t\→0^{+}}{\lim }{C}^{\′}(x_k+t)=\underset{t\→0^{-}}{\lim }{C}^{\′}(x_k+t)\\ \underset{t\→0^{+}}{\lim }{C}^{\′\′}(x_k+t)=\underset{t\→0^{-}}{\lim }{C}^{\′\′}(x_k+t)\end{array}\right.,k=\mathrm{0,1,2},...,(n-1)---\left(14\right)$

Boundary condition is defined as:

$\left\{\begin{array}{c}{C}^{\′}\left(x_0\right)=C_0^{\′}\left(x_0\right)=0\\ C^{\′}\left(x_n\right)=C_0^{\′}\left(x_n\right)=0\end{array}\right.---\left(15\right)$

Definition C " (x _k)=M _k(k=0,1,2 ... n).Then have:

$C^{\′\′\′}\left(x\right)=\frac{M_{k+1}-M_k}{x_{k+1}-x_k},\∀x\∈[x_k,x_{k+1}]---\left(16\right)$

Under (15) such boundary condition, three curved equations arrangements are:

$\{\frac{x_k-x_{k-1}}{x_{k+1}-x_k+x_k-x_{k-1}}\begin{array}{c}2M_0+{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="110214101412.png"\; state="\{\{state\}\}">M</figure-callout>}}_1=6C_0[x_0,x_0,x_1]\\ M_{k-1}+2M_k+\frac{x_{k+1}-x_k}{x_{k+1}-x_k+x_k-x_{k-1}}{M}_{k+1}=6C_0[x_{k-1},x_k,x_{k+1}]\\ M_{n-1}+2M_n=6C_0[x_{n-1},x_n,x_n]\end{array},k=\mathrm{0,1,2},...,-(n-1)--\left(17\right)$

Find the solution this three curved equation, solve cubic polynomial coefficient corresponding to each sub-range.

Step 5, construct with each and do not measure the structure tensor matrix that pixel is the local neighborhood at center respectively, find the solution its eigenwert and proper vector;

Promptly with do not measure pixel S (x is the center y), chooses a little neighborhood, gets 7 * 21 neighborhood in this embodiment, according to formula (18) to this neighborhood structural texture tensor matrix,

$T_{i,j}=K(\&dtri;p\&dtri;p^T)=K\left(\begin{array}{cc}{p}_x{p}_x& p_x{p}_y\\ p_y{p}_x& p_y{p}_y\end{array}\right)=\left(\begin{array}{cc}{T}_{11}& T_{12}\\ T_{21}& T_{22}\end{array}\right)---\left(18\right)$

Wherein, T _{I, j}Be the structure tensor matrix, K () is the linear filtering kernel function,

Be the single order differential of structure tensor matrix, p _x, p _yBe respectively the structure tensor matrix along x, the single order partial differential of y direction.The present invention adopts the Jacobi rotary process to find the solution the eigenwert and the proper vector of this structure tensor matrix.The Jacobi rotary process is a prior art, and its specific implementation process is as follows:

According to the thinking of partitioned matrix, the structure tensor matrix of determining in (18) can be thought the real symmetric matrix of 2 * 2 piecemeal.Because any real symmetric matrix becomes diagonal form by orthogonal transformation, promptly has orthogonal matrix Q, make following formula set up:

Q ^TTQ＝diag(λ ₁，λ ₂，...，λ _n)(19)

Wherein, λ _i(i=1,2 ..., be the eigenwert of matrix n), respectively classify corresponding proper vector among the Q as.The basic thought of Jacobi rotary process is exactly by a series of orthogonal transformation, makes the quadratic sum of the matrix off-diagonal element after the conversion be tending towards 0, thereby makes this approximate matrix be called diagonal matrix.The specific implementation process is gone into down:

(a) make k=0, T ^(k)=T _{I, j}

(b) ask integer i, j is feasible, $T_{i,j}^{\left(k\right)}=\underset{1\&le;l,m\&le;n,l\&NotEqual;m}{\mathrm{<figure-callout\; id="1"\; label="max"\; filenames="110214101412.png"\; state="\{\{state\}\}">max</figure-callout>}}\left|T_{l,m}^{\left(k\right)}\right|---\left(20\right)$

(c) calculate the rotation matrix coefficient:

$a=\frac{T_{i,i}^{\left(k\right)}-T_{j,j}^{\left(k\right)}}{2T_{i,j}^{\left(k\right)}},$ $b=\mathrm{sign}\left(a\right)(\sqrt{a^2+1}-|a\left|\right),$ $c=\frac{1}{\sqrt{1+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="110214101432.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}},$ d＝bc，V ^(k)＝V _i，j(φ)(21)

(d) calculate T ^(k+1), $T_{l,m}^{(k+1)}=T_{m,l}^{(k+1)}=T_{l,m}^{\left(k\right)},l,m\&NotEqual;i,j,$ $T_{i,j}^{(k+1)}=T_{j,i}^{(k+1)}=0---\left(22\right)$

$\left\{\begin{array}{c}{T}_{i,i}^{(k+1)}=c^2{T}_{i,i}^{\left(k\right)}+d^2{T}_{j,j}^{\left(k\right)}+2\mathrm{dc}{T}_{i,j}^{\left(k\right)}\\ T_{j,j}^{(k+1)}=d^2{T}_{i,i}^{\left(k\right)}+c^2{T}_{j,j}^{\left(k\right)}-2\mathrm{dc}{T}_{i,j}^{\left(k\right)}\\ T_{i,l}^{(k+1)}=T_{l,i}^{(k+1)}=c{T}_{i,l}^{\left(k\right)}+d{T}_{j,l}^{\left(k\right)}\\ T_{j,l}^{(k+1)}=T_{l,j}^{(k+1)}=c{T}_{j,l}^{\left(k\right)}-d{T}_{i,l}^{\left(k\right)}\end{array}\right.---\left(23\right)$

(e) judge

Then Be eigenwert.Q ^T=(V ⁽⁰⁾V ⁽¹⁾... V ^(k+1)) ^Trespectively classify corresponding proper vector as.Otherwise k+1 → k returns (b), repeats said process.

Step 6, do not measure pixel, in the described local neighborhood of step 5, select the sinusoidal line that meets most with proper vector, get the interpolation result that this does not measure the pixel place, as the final estimation of this not being measured pixel intensity with minimal eigenvalue for each; This step comprises following each substep:

Step 601, choose minimal eigenvalue characteristic of correspondence vector in the step 5;

Step 602, be that true origin is set up absolute rectangular coordinate system with current pending string figure center;

Step 603, under the absolute rectangular coordinate system that step 602 is set up the structure the current feature straight line of waiting to estimate not measure pixel of process, this feature straight-line equation is under described absolute rectangular coordinate system

$y=\frac{y_e}{x_e}x+y_j-\frac{y_e}{x_e}{x}_j,$

Wherein, (x _j, y _j) be the current coordinate of waiting to estimate not measure pixel, (x _e, y _e) be the pairing proper vector of the described minimal eigenvalue of step 601;

Step 604, choose one group of pixel according to the coordinate of feature straight-line equation, this group pixel has only the center pixel to wait to estimate; Obtain described center intensity values of pixels according to bilateral intensity level by the distance inverse ratio weighted mean on this straight line, this intensity level is the current final intensity level of pixel of waiting to estimate not measure.

In step 604, be actually and should from the determined sinusoidal curve of step 3 family, select and the immediate sinusoidal line of feature straight line, in theory, we should use least square method, find out this feature straight line which bar sinusoidal line of optimal approximation under the Euclidean distance meaning.Yet, considering time complexity and actual conditions, the present invention takes a kind of approximation method.Owing to chosen less neighborhood,, can consider the thought of " with straight Dai Qu " at this less neighborhood: promptly, in less neighborhood part, the equation of all sinusoidal line can be thought straight line approx.Thereby we can choose one group of pixel according to the coordinate of feature straight-line equation, and this group pixel has only the center pixel to wait to estimate; Obtain described center intensity values of pixels according to bilateral intensity level by the distance inverse ratio weighted mean on this straight line, this intensity level is the current final intensity level of pixel of waiting to estimate not measure.

In order to verify the validity of the inventive method, adopt the inventive method and existing three kinds of string figure method for repairing and mending to compare respectively, these three kinds of existing methods are respectively linear interpolation method, based on the method for repairing and mending and the FOE method of sample.Concrete test method is as follows:

Choose simulated data 1 and 2, as shown in Figure 3, wherein (a) and (b) are respectively original analog data 1 and 2, (c), (d) is respectively the collimated beam projection of original analog data 1 and 2, (e) for the collimated beam projection of blocking of original analog data 1, (f) be the collimated beam projection of the sparse sampling of original analog data 2, (g) image for obtaining after (e) rebuild (h) obtains image after (f) rebuild.

Adopt above-mentioned 4 kinds of methods that simulated data 1,2 is repaired and rebuild respectively, result after simulated data 1 repaired and rebuild as shown in Figure 4, wherein (a) is for adopting the string figure after linear interpolation method is repaired, (b) for adopting the string figure after repairing based on the method for repairing and mending of sample, (c) for adopting the string figure after the FOE method is repaired, (d) for adopting the string figure after the inventive method is repaired, (e) be the reconstructed image of (a), (f) be the reconstructed image of (b), (g) being the reconstructed image of (c), (h) is the reconstructed image of (d); Result after simulated data 2 repaired and rebuild as shown in Figure 4, wherein (a) is for adopting the string figure after linear interpolation method is repaired, (b) for adopting the string figure after repairing based on the method for repairing and mending of sample, (c) for adopting the string figure after the FOE method is repaired, (d) for adopting the string figure after the inventive method is repaired, (e) being the reconstructed image of (a), (f) is the reconstructed image of (b), (g) being the reconstructed image of (c), (h) is the reconstructed image of (d).Can see from Fig. 3-Fig. 5, the string figure of existing method recover and reconstructed image quality relatively poor, and adopt the inventive method not only level and smooth even matter zone among the string figure, kept the edge, and also quite effective to suppressing reconstructed image puppet shadow.For the validity to the inventive method has a quantitative recognition, we weigh the quality of distinct methods with the reconstructed image mean-square error criteria.This criterion is defined as follows:

$\mathrm{MSE}=\frac{1}{N_R}\sqrt{\underset{j\&Element;R}{\mathrm{\&Sigma;}}{({\mathrm{\&mu;}}_j-{\mathrm{\&mu;}}_0)}^2}$

μ wherein ₀Expression simulation modular view data.It is just low more to rebuild square error, illustrates that then formation method is good more.By calculating, we list the reconstruction signal to noise ratio (S/N ratio) of Fig. 4 and Fig. 5 respectively in the table 1, to make comparisons.

Table 1

Obviously, can obtain lower reconstruction error, illustrate that it is superior to existing interpolation or method for repairing and mending with the inventive method.

Claims (6)

1. the projection string figure method for repairing and mending of a CT image is used for detector inside and blocks the projector space disappearance that is caused with the projection sparse sampling, it is characterized in that, may further comprise the steps:

Pixel coordinate is not measured in step 1, location;

Step 2, determine image space pixel family;

Step 3, definite corresponding to the sinusoidal curve family of not measuring string figure coordinate;

Step 4, along the discretize sinusoidal line, determine not measure location of pixels and corresponding strength value respectively;

Step 5, construct with each and do not measure the structure tensor matrix that pixel is the local neighborhood at center respectively, find the solution its eigenwert and proper vector;

Step 6, do not measure pixel, in the described local neighborhood of step 5, select the sinusoidal line that meets most with proper vector, get the interpolation result that this does not measure the pixel place, as the final estimation of this not being measured pixel intensity with minimal eigenvalue for each.

2. the projection string figure method for repairing and mending of CT image according to claim 1 is characterized in that, determines described in the step 4

Do not measure location of pixels and adopt the standard sine match, determine not measure pixel corresponding strength value and adopt cubic spline interpolation.

3. the projection string figure method for repairing and mending of CT image according to claim 1 is characterized in that, structure described in the step 5

Not measure the structure tensor matrix that pixel is the local neighborhood at center, specifically according to following formula,

In the formula,

Be the tensor product matrix, Be the linear filtering kernel function,

Be the single order differential of tensor product matrix,

, It is respectively tensor product matrix edge ,

The single order partial differential of direction.

4. the projection string figure method for repairing and mending of CT image according to claim 1 is characterized in that local neighborhood described in the step 5 is the center not measure pixel

Neighborhood.

5. the projection string figure method for repairing and mending of CT image according to claim 1 is characterized in that, the eigenwert of the matrix of structure tensor described in the step 5 and proper vector adopt the Jacobi rotary process to find the solution and obtain.

6. as the projection string figure method for repairing and mending of CT image as described in the claim 4, it is characterized in that step 6 specifically comprises following substep:

Step 601, choose minimal eigenvalue characteristic of correspondence vector in the step 5;

Step 602, be that true origin is set up absolute rectangular coordinate system with current pending string figure center;

Step 603, under the absolute rectangular coordinate system that step 602 is set up the structure the current feature straight line of waiting to estimate not measure pixel of process, this feature straight-line equation is under described absolute rectangular coordinate system

?，

Wherein,

Be the current coordinate of waiting to estimate not measure pixel,

Be the pairing proper vector of the described minimal eigenvalue of step 601;

Step 604, choose one group of pixel according to the coordinate of feature straight-line equation, this group pixel has only the center pixel to wait to estimate; Obtain described center intensity values of pixels according to bilateral intensity level by the distance inverse ratio weighted mean on this straight line, this intensity level is the current final intensity level of pixel of waiting to estimate not measure.

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