CN103489205A - Mixed interpolation method based on cone beam X-ray FDK algorithm - Google Patents

Abstract

The invention discloses a mixed interpolation method based on a cone beam X-ray FDK algorithm. The method comprises the following steps: (1) obtaining cone beam X-ray CT projection data, (2) conducting filtering on the projection data, and (3) estimating a projection value of a projection address through the interpolation method so as to conduct FDK algorithm back projection reconstructing. According to the method, an image reconstructed in the region with the acute jumping projection data is clear in edge, the average gradient value of the image is larger than that of a bilinear interpolation method, and the edge details of the reconstructed image can be well kept. In addition, an image reconstructed in the region with the smooth change projection data is smooth, the error of mean square is smaller than that of a nearest neighbor interpolation method and the bilinear interpolation method, and meanwhile the noise can be well restrained.

Description

A kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm

Technical field

The present invention relates to the technical field of image reconstruction, particularly a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm.

Background technology

X ray CT (Computed Tomography computerized tomography) has the advantage such as penetration power is strong, harmless, three-dimensional visualization and is widely used in the fields such as industrial nondestructive testing, medical imaging diagnosis.Wherein cone-beam X-ray CT has the advantage of the aspects such as radiation utilization factor, sweep velocity, image resolution ratio, is research direction and the study hotspot of CT technology.The cone-beam CT reconstruction algorithm comprises analytical method and process of iteration.The advantage of process of iteration is to suppress noise, and shortcoming is that calculated amount is large, and speed is slow.With respect to process of iteration, it is fast that analytical method is rebuild speed, and the desired data storage space is little.Because the data volume of Cone-Beam CT is larger, the application in Cone-Beam CT is more extensive than process of iteration for analytical method.Analytical method is divided into again exact reconstruction methods and approximate reconstruction method, and wherein cone-beam FDK algorithm is the most successful approximate reconstruction algorithm.

Cone-beam FDK algorithm is a kind of filtered back projection's approximate reconstruction algorithm based on circular orbit scan proposed in 1984 by Feldkamp, Davis and Kress tri-people, is one of classical cone-beam reconstruction algorithm.For the small-angle situation, can reconstruct faultage image preferably, simultaneously because algorithm structure is simple, mechanical motion is simple, execution efficiency is high, cone-beam FDK algorithm is the main flow in practical application always.

Interpolation is a very important step in cone-beam FDK algorithm process of reconstruction, and it directly has influence on the quality of reconstructed image.In back projection's process of cone-beam FDK algorithm, discreteness due to data, the phenomenon that there will be the projection address " misalignment " of pixel, that is to say when looking for the projection value of certain projection address, sampled point can not be just aimed at, therefore generally the projection value of this projection address need to be estimated by method of interpolation.Interpolation method commonly used has arest neighbors method of interpolation, bilinear interpolation, bicubic interpolation.Consider reconstruction speed, usually adopt in practice arest neighbors method of interpolation, bilinear interpolation.The arest neighbors method of interpolation is the simplest a kind of interpolation method in image interpolation, and it gets the gray-scale value as this point apart from the projection value of subpoint nearest neighbor point.This algorithm interpolation effect is poor, can make reconstructed image obvious sawtooth occur.But it is a kind of non-linear interpolation method, there is the high-pass filtering characteristic, can retain well the edge of reconstructed image.The projection value Weighted Interpolation of two consecutive point of bilinear interpolation use subpoint is as the gray-scale value of this point.Bilinear interpolation is considered the impact of the consecutive point of subpoint on it, can effectively overcome the deficiency of arest neighbors interpolation, the interpolation effect that therefore can obtain being satisfied with, and the method has smoothing function.But bilinear interpolation is a kind of low-pass filter, can make high frequency edge details Cheng Fen Lost in image lose, cause the edge fog of image after interpolation.Occur that for bilinear interpolation the phenomenon of sawtooth appears in edge fog and arest neighbors method of interpolation, just must invent new method, to improve cone-beam X-ray CT reconstructed image quality.

Summary of the invention

The shortcoming that the object of the invention is to overcome prior art, with not enough, provides a kind of mixed interpolation method based on cone-beam X-ray FDK algorithm.

Purpose of the present invention is achieved through the following technical solutions:

A kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm comprises the following steps:

(1) obtain cone-beam X-ray CT data for projection;

(2) data for projection is carried out to filtering;

(3) projection value by method of interpolation estimated projection address carries out FDK algorithm backprojection reconstruction.

In step (1), the concrete steps of obtaining cone-beam X-ray CT data for projection are: cone-beam X-ray bundle every an angle, gathers a data for projection along the circular scan track, obtains altogether 360 sampled datas.

In step (2), when data for projection is carried out to filtering, when data for projection noiseless or noise, when less, select the R-L wave filter; When data for projection has noise, select the S-L wave filter.

Further, the R-L wave filter carries out the concrete grammar of filtering:

R-L wave filter expression formula is:

The data that step (1) collected with the R-L wave filter are carried out filtering line by line, wherein, and sampled point s=nd, sampling interval d=1.

Further, the S-L wave filter carries out the concrete grammar of filtering:

S-L wave filter expression formula is: $h_{S-L}\left(\mathrm{nd}\right)=\frac{-2}{{\mathrm{\π}}^2{d}^2({4n}^2-1)},n=0,\±1,\±2,\±3......;$

The data that step (1) collected with the S-L wave filter are carried out filtering line by line, wherein, and sampled point s=nd, sampling interval d=1.

In step (3), concrete process of reconstruction is:

(3-1) the data for projection subpoint floating-point coordinate of setting after processing after filtering is (i+u, j+v), i wherein, j is the integral part of floating-point coordinate, the fraction part that u and v are the floating-point coordinate, 0≤u, v<1, insert by arest neighbors method of interpolation and bilinearity the interpolation that interpolation calculation floating-point coordinate is (i+u, j+v) subpoint respectively, the interpolation result of the two is used respectively f ₁(i+u, j+v) and f ₂(i+u, j+v) means;

(3-2) calculate subpoint four adjacent projections point P on every side _kthe gray-scale value variance δ of (I, J) (k=1,2,3,4);

$\mathrm{\&delta;}=\sqrt{\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{[P_k(I,J)-\stackrel{\&OverBar;}{P}(I,J)]}^2}$

Wherein, $\stackrel{\&OverBar;}{P}(I,J)=\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{P}_k(I,J)$

(3-3) calculate the weighting coefficient of arest neighbors interpolation and bilinear interpolation, be respectively w ₁, w ₂;

$w_1=\frac{{1-e}^{-\mathrm{\&lambda;\&delta;}}}{2};$

w ₂=1-w ₁；

λ: constant, span is 0～10, can be adjusted according to actual requirement;

(3-4) to arest neighbors interpolation result f ₁(i+u, j+v) and bilinear interpolation be f as a result ₂(i+u, j+v) is weighted fusion, to final interpolation result f (i+u, j+v), realizes FDK algorithm backprojection reconstruction;

f(i+u,j+v)=w ₁*f ₁(i+u,j+v)+w ₂*f ₂(i+u,j+v)。

The present invention has following advantage and effect with respect to prior art:

(1) the present invention's regional reconstruction image edge clear violent in the data for projection saltus step, the average gradient value is greater than bilinear interpolation, can retain well the edge details of reconstructed image.

(2) the present invention is at data for projection smooth variation regional reconstruction image smoothing, and square error all is less than arest neighbors method of interpolation and bilinear interpolation, can suppress preferably noise simultaneously.

The accompanying drawing explanation

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

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

As shown in Figure 1, the hybrid interpolation method based on cone-beam X-ray FDK algorithm of the present invention comprises the following steps:

(1) obtain cone-beam X-ray CT data for projection;

(2) data for projection is carried out to filtering, because generally all there is noise in the data that gather in reality, so the present embodiment adopts the S-L wave filter, is specially:

Suppose the data for projection that p (x, y) processes for the filtered ripple, h (nd) is the S-L wave filter,

for the data for projection after after filtering, the data for projection filtering is:

$h\left(\mathrm{nd}\right)=\frac{-2}{{\mathrm{\&pi;}}^2{d}^2({4n}^2-1)},n=0,\&PlusMinus;1,\&PlusMinus;2,......;$

$\tilde{p}(x,y)=p(x,y)*h\left(\mathrm{nd}\right),$ In this formula, * means convolution;

(3) projection value by method of interpolation estimated projection address carries out FDK algorithm backprojection reconstruction, is specially:

(3-1) the data for projection subpoint floating-point coordinate of setting after processing after filtering is (i+u, j+v) (i wherein, j is the integral part of floating-point coordinate, u and v(0≤u, v<1) be the fraction part of floating-point coordinate), the interpolation that is (i+u, j+v) subpoint with arest neighbors method of interpolation and linear slotting interpolation calculation floating-point coordinate respectively, the interpolation result of the two is used respectively f ₁(i+u, j+v) and f ₂(i+u, j+v) means;

(3-2) calculate subpoint four adjacent projections point P on every side _kthe gray-scale value variance δ of (I, J) (k=1,2,3,4), the gray variance computing method are:

$\mathrm{\&delta;}=\sqrt{\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{[P_k(I,J)-\stackrel{\&OverBar;}{P}(I,J)]}^2};$

Wherein $\stackrel{\&OverBar;}{P}(I,J)=\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{P}_k(I,J);$

(3-3) calculate the weighting coefficient of arest neighbors interpolation and bilinear interpolation, be respectively w ₁, w ₂, the weighting coefficient computing method are:

$w_1=\frac{{1-e}^{-\mathrm{\&lambda;\&delta;}}}{2};$

w ₂=1-w ₁；

Wherein, λ is constant, and span is 0～10, can be adjusted according to actual requirement, at the present embodiment, selects λ=5 effects best.

(3-4) to arest neighbors interpolation result f ₁(i+u, j+v) and bilinear interpolation be f as a result ₂(i+u, j+v) is weighted fusion, obtains final interpolation result f (i+u, j+v), realizes FDK algorithm backprojection reconstruction, is specially:

f(i+u,j+v)=w ₁*f ₁(i+u,j+v)+w ₂*f ₂(i+u,j+v)。

Above-described embodiment is preferably embodiment of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (6)

1. the hybrid interpolation method based on cone-beam X-ray FDK algorithm, is characterized in that, comprises the following steps:

(1) obtain cone-beam X-ray CT data for projection;

(2) data for projection is carried out to filtering;

(3) projection value by method of interpolation estimated projection address carries out FDK algorithm backprojection reconstruction.

2. a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm according to claim 1, it is characterized in that, in step (1), the concrete steps of obtaining cone-beam X-ray CT data for projection are: cone-beam X-ray bundle along the circular scan track every an angle, gather a data for projection, obtain altogether 360 sampled datas.

3. a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm according to claim 1, is characterized in that, in step (2), when data for projection is carried out to filtering, when data for projection noiseless or noise, when less, selects the R-L wave filter; When data for projection has noise, select the S-L wave filter.

4. a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm according to claim 3, is characterized in that, the R-L wave filter carries out the concrete grammar of filtering:

R-L wave filter expression formula is:

The data that step (1) collected with the R-L wave filter are carried out filtering line by line, wherein, and sampled point s=nd, sampling interval d=1.

5. a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm according to claim 3, is characterized in that, the S-L wave filter carries out the concrete grammar of filtering:

S-L wave filter expression formula is: $h_{S-L}\left(\mathrm{nd}\right)=\frac{-2}{{\mathrm{\&pi;}}^2{d}^2({4n}^2-1)},n=0,\&PlusMinus;1,\&PlusMinus;2,\&PlusMinus;3......;$

The data that step (1) collected with the S-L wave filter are carried out filtering line by line, wherein, and sampled point s=nd, sampling interval d=1.

6. a kind of hybrid interpolation method based on cone-beam X-ray FDK algorithm according to claim 1, is characterized in that, in step (3), concrete process of reconstruction is:

(3-1) the data for projection subpoint floating-point coordinate of setting after processing after filtering is (i+u, j+v), i wherein, j is the integral part of floating-point coordinate, the fraction part that u and v are the floating-point coordinate, 0≤u, v<1, insert by arest neighbors method of interpolation and bilinearity the interpolation that interpolation calculation floating-point coordinate is (i+u, j+v) subpoint respectively, the interpolation result of the two is used respectively f ₁(i+u, j+v) and f ₂(i+u, j+v) means;

(3-2) calculate subpoint four adjacent projections point P on every side _kthe gray-scale value variance δ of (I, J) (k=1,2,3,4);

$\mathrm{\&delta;}=\sqrt{\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{[P_k(I,J)-\stackrel{\&OverBar;}{P}(I,J)]}^2}$

Wherein, $\stackrel{\&OverBar;}{P}(I,J)=\frac{1}{4}\underset{k=1}{\overset{4}{\mathrm{\&Sigma;}}}{P}_k(I,J)$

(3-3) calculate the weighting coefficient of arest neighbors interpolation and bilinear interpolation, be respectively w ₁, w ₂;

$w_1=\frac{{1-e}^{-\mathrm{\&lambda;\&delta;}}}{2};$

w ₂=1-w ₁；

λ: constant, span is 0～10, can be adjusted according to actual requirement;

(3-4) to arest neighbors interpolation result f ₁(i+u, j+v) and bilinear interpolation be f as a result ₂(i+u, j+v) is weighted fusion, to final interpolation result f (i+u, j+v), realizes FDK algorithm backprojection reconstruction;

f(i+u,j+v)=w ₁*f ₁(i+u,j+v)+w ₂*f ₂(i+u,j+v)。