CN102274040A - Post-processing method for removing ring artifacts in CT (computed tomography) image - Google Patents

Abstract

The invention relates to a post-processing method for removing ring artifacts in a CT (computed tomography) image, and the post-processing method comprises the following steps: converting the CT image with ring artifacts from a rectangular coordinate image to a polar coordinate image; extracting the ring image in polar coordinates with a comb filter in a polar coordinate image domain; converting the ring image extracted out of the polar coordinates to a ring image in rectangular coordinates; and subtracting the ring image in the rectangular coordinates from the original CT image with the ring artifacts to obtain a ring-free image. Through frequency domain comb filtering technology, the post-processing method provided by the invention subtracts the corresponding ring artifact image from the original image, without reduction of image resolution and change of quality of the original image. The post-processing method achieves the processing effect, and meanwhile the speed meets product requirements and has space for further optimization, so that the post-processing method is fully suitable for a CT machine with higher requirements for the reconstruction speed.

Description

A kind of post-processing approach of removing ring artifact in the CT image

Technical field

The present invention relates to the Medical Image Processing technology, a kind of specifically post-processing approach of removing ring artifact in the CT image.

Background technology

The ring artifact that occurs in the CT image is inconsistent the causing of response owing to single or multiple passages in the detector in the CT machine, because it is in full accord that each channel unit of detector can not respond physically, therefore ring artifact cannot be avoided, and the intensity, the light and shade that are pseudo-shadow are different.

Fig. 1 is a certain image with ring artifact, and as seen from Figure 1, the shape of ring artifact is exactly several circles around center of rotation, and its intensity has gently to be had heavily, and brightness has brightly to be had secretly, depends on the channel position that produces error and the size of error.Ring artifact has had a strong impact on picture quality, therefore removes ring artifact and is very important.

Divide from the position of handling, existent method is divided into pre-treatment and post processing at present:

1. pre-treatment

Reach the purpose of proofreading and correct ring artifact by handling data for projection.

The shortcoming of this method:

(1), can obtain good effect for heavier ring artifact; But for lighter ring artifact, can't identify in the data for projection territory, that is to say, pre-treatment can't be removed lighter ring artifact;

(2) method of pre-treatment certainly will will change data for projection, and to any change of data for projection, all can have influence on quality of reconstructed image, and this method has very big risk, is easy to reduce the quality of image or introduce new pseudo-shadow.

(3) for many row CT (8 rows or more than 8 rows), the data volume of data for projection is very big, if adopt pre-treatment, is difficult to guarantee processing speed.

2. post processing

Technology by post processing of image removes ring artifact, and present already present method all is based on the post-processing technology in spatial domain, and there is following shortcoming in this method:

(1) the spatial domain processing is an entire image owing to what handle, can reduce the resolution of image, promptly can reduce the quality of image when getting rid of ring.

(2) for heavier ring artifact, the method for handling by the spatial domain can't be removed clean, and the result after the processing has residual.

At present or existent method is a pre-treating method above-mentioned or based on the post-processing approach in spatial domain, because two kinds of methods all have own inherent shortcoming, is difficult to guarantee the effect of decyclization.

Summary of the invention

Weak point at the ring artifact decyclization weak effect in the CT image in the prior art, the technical problem to be solved in the present invention provides a kind of resolution that does not reduce image, do not change the quality of original image, and can remove the post-processing approach of ring artifact in the removal CT image of ring artifact of any intensity.

For solving the problems of the technologies described above, the technical solution used in the present invention is:

The post-processing approach that the present invention removes ring artifact in the CT image may further comprise the steps:

The CT image that will have ring artifact is converted to polar coordinate image by the rectangular coordinate image;

At the polar diagram image field, utilize comb filter to extract polar ring image;

With the ring image that to extract polar ring image transitions be rectangular coordinate;

From original ring image, obtain acyclic image with CT figure image subtraction rectangular coordinate of ring artifact.

Describedly extract polar ring image and may further comprise the steps:

1) polar coordinate image is compressed processing, the polar coordinate image after obtaining compressing;

2) from the compression polar coordinate image, extract strong edge, obtain removing the image at strong edge;

3) image to the strong edge of above-mentioned removal carries out smoothing processing, obtains the image after the smoothing processing;

4) the polar coordinate image data after the compression deduct the view data after the smoothing processing, obtain comprising the basic ring image of ring artifact;

5) in comprising the basic ring image of ring artifact, remove straight line by comb filter, obtain compressing the ring image in the polar coordinate image;

The ring image spreading that 6) will obtain becomes and original polar coordinate image ring image of a size.

Describedly remove straight line by comb filter and may further comprise the steps:

51) all row in the basic ring of the sampling image, utilize following formula construction periodic signal y (n):

$y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{y}_i(n+\mathrm{iN})---\left(11\right)$

$y_i\left(n\right)=\left\{\begin{array}{cc}{c}_i(\mathrm{mn}+k-1)& n\∈[1,N/2]\\ -c_i(m(n-N/2)+k)-1& n\∈[N/2+1,N]\end{array}\right.---\left(12\right)$

Wherein, N is the length in the single cycle of y (n); y _i(n) i cycle of expression; I ∈ [1, M], M is the columns of compression polar coordinate image, n ∈ [1, N]; c _i(n) be column signal; K ∈ [1, m], m are the multiple of polar coordinate compression;

52) periodic signal y (n) is done the DFT conversion, obtain the periodic signal Y (k) after the DFT conversion;

53) in frequency domain, use the periodic signal Y (k) after the comb filter F (k) that pre-sets multiply by the DFT conversion, obtain frequency-region signal G (k);

54) frequency-region signal G (k) is done the IDFT conversion, obtain corresponding time-domain signal g (n);

55) recover corresponding all column signal c with time-domain signal g (n) _i(n) sampled point in.

Described polar coordinate image is compressed the circumferential direction of the compression direction of processing along polar coordinate image, get the meansigma methods of m circumferential direction data during compression.

The method of described ring image spreading is according to the inverse process of compression, will encircle image and duplicate m part along circumferential direction, and m is a compression multiple.

The described method that extracts strong edge from the compression polar coordinate image is:

21) ask the gradient of compressing each point in the polar coordinate image by following formula

With circumferential gradient

$f_{\mathrm{Deri}}^R(r,\mathrm{\θ})=f(r+1,\mathrm{\θ})-f(r-1,\mathrm{\θ})---\left(2\right)$

$f_{\mathrm{Deri}}^{\mathrm{\θ}}(r,\mathrm{\θ})=f(r,\mathrm{\θ}+1)-f(r,\mathrm{\θ}-1)---\left(3\right)$

Wherein: r is that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f.

22) add up the quadratic sum RDeriTotal of gradient and the circumferential quadratic sum of gradient θ DeriTotal:

$\mathrm{RDeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\Σ}}}\underset{\mathrm{\θ}=1}{\overset{Q}{\mathrm{\Σ}}}{\left(f_{\mathrm{Deri}}^R(r,\mathrm{\θ})\right)}^2---\left(4\right)$

$\mathrm{\θDeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\Σ}}}\underset{\mathrm{\θ}=1}{\overset{Q}{\mathrm{\Σ}}}{\left(f_{\mathrm{Deri}}^{\mathrm{\θ}}(r,\mathrm{\θ})\right)}^2---\left(5\right)$

Wherein P is sampling number radially, and Q is circumferential sampling number;

23) calculate the average RDeriMean of gradient square and the circumferential average θ DeriMean of gradient square

$\mathrm{RDeriMean}=\frac{\mathrm{RDeriTotal}}{\mathrm{PQ}}---\left(6\right)$

$\mathrm{\θDeriMean}=\frac{\mathrm{\θDeriTotal}}{\mathrm{PQ}}---\left(7\right)$

Wherein: (wherein P is for radially sampling number, Q are circumferential sampling number), RDeriTotal is the gradient summation of radial direction, θ DeriTotal is the gradient summation of circumferential direction.

24), promptly multiply by one less than 1 coefficient S cale respectively to the average RDeriMean of gradient radially square, circumferentially the average θ DeriMean of gradient square adjusts:

RDeriMean＝RDeriMean×Scale (8)

θDeriMean＝θDeriMean×Scale (9)

25) according to the average RDeriMean of the gradient of (multiply by coefficient S cale after value) after adjusting square, the circumferential average θ DeriMean of gradient square, judge whether it is strong edge for each point, result f _Edge(r, θ) expression;

$f_{\mathrm{Edge}}(r,\mathrm{\&theta;})=\left\{\begin{array}{cc}0& f(r,\mathrm{\&theta;})<\mathrm{RDeriMean\; or\; f}(r,\mathrm{\&theta;})<\mathrm{\&theta;DeriMean}\\ 1& \mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein: (r represents that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f to f for r, the θ) value of expression compression polar coordinate image.

The image at the strong edge of described removal carries out smoothing processing: along the radial direction of the image of removing strong edge, the continuum of non-strong marginal point is carried out 53 times smoothly; Level and smooth number of times requires to reach fully smoothly to fall straight line.

The present invention has following beneficial effect and advantage:

1. the present invention has only deducted corresponding ring artifact image by the technology of frequency domain comb filtering from original image, does not reduce the resolution of image, does not change the quality of original image.

2. because the present invention adopts the method for frequency domain processing, can remove the ring artifact of any intensity.

3. the inventive method is when reaching treatment effect, and speed has guaranteed the requirement of product, and the space also have to continue optimized of speed, goes for fully rebuilding the better CT machine of rate request.

4. the present invention is a kind of post processing of image technology, does not rely on the hardware parameter of machine, is suitable for follow-up product (the later product of 16 rows) fully.

Description of drawings

Fig. 1 one has the CT image under the rectangular coordinate system of ring artifact;

Fig. 2 one has the CT image under the polar coordinate system of ring artifact;

Fig. 3 is Fig. 2 result images after compression;

Fig. 4 is the result images at Fig. 3 strong edge of removal after compression;

Fig. 5 is the result images of Fig. 4 after smoothing processing;

Fig. 6 deducts the result images after the view data of Fig. 5 for the view data of Fig. 4;

Fig. 7 is to the result images behind Fig. 6 comb filtering;

Fig. 8 deducts the ring image that obtains after the view data of Fig. 7 for the view data of Fig. 6;

Fig. 9 deducts the result images of the view data of Fig. 8 for the view data of Fig. 3;

Figure 10 expands to the size of original polar coordinate image for Fig. 8;

Figure 11 is the rectangular coordinate ring image after Figure 10 conversion;

Figure 12 is for removing ring artifact image afterwards;

Figure 13 is the inventive method flow chart.

The specific embodiment

The post processing that the present invention removes ring artifact in the CT image is to have on the image (as shown in Figure 1) of ring artifact one to carry out, for the ease of analyzing, now with the image f (x in the original rectangular coordinate system of band, y) be decomposed into acyclic rectangular coordinate image g (x, y) and the rectangular coordinate image h (x of ring arranged, y) sum, promptly

f(x，y)＝g(x，y)+h(x，y) (1)

The purpose of decyclization be for obtain g (x, y), according to formula (1) can obtain acyclic rectangular coordinate image g (x, y); Perhaps directly obtain g (x, y); Perhaps obtain earlier ring rectangular coordinate image h (x, y), then the image f from the original rectangular coordinate system of band (x, deduct in y) ring rectangular coordinate image h (x, y), and then obtain acyclic rectangular coordinate image g (x, y).In order to keep the resolution of image, make the resolution unanimity before and after handling, reasonable method be by the rectangular coordinate image h that obtains ring (x, y) so that obtain acyclic rectangular coordinate image g (x, y).

So how obtain ring rectangular coordinate image h (x, y).Observe Fig. 1, because the ring artifact of rectangular coordinate is to be the circle in the center of circle around center of rotation, if be the center of circle with the center of rotation so, rectangular coordinate is converted to polar coordinate, the ring artifact of rectangular coordinate just shows as straight line at polar coordinate so, as shown in Figure 2.

So now problem is converted to and in polar coordinate image, extracts the pseudo-shadow of straight line.And extract collinear reasonable method is to adopt comb filter.

Set forth the basic ideas of decyclization above, the key step that the present invention removes the post-processing approach of ring artifact in the CT image following (as shown in figure 13):

The rectangular coordinate image that will have ring artifact is converted to polar coordinate image;

At the polar diagram image field, utilize comb filter to extract polar ring image;

With above-mentioned polar ring image transitions ring image that is rectangular coordinate;

From have the original rectangular coordinate image of ring artifact f (x, y) deduct rectangular coordinate ring image h (x, y), obtain acyclic rectangular coordinate image g (x, y).

Elaborate each step below in conjunction with accompanying drawing.

(1) the rectangular coordinate image that will have a ring is converted to polar coordinate image

As shown in Figure 2, be the polar coordinate image after the conversion, with Fig. 1 contrast, the shape of visible ring artifact is in the different manifestations of rectangular coordinate image and polar coordinate image.

(2), utilize comb filter to extract polar ring image in the polar coordinate image zone

Extract the ring image in the polar coordinate image after above-mentioned conversion, may further comprise the steps:

1) polar coordinate image is compressed processing, the polar coordinate image after obtaining compressing;

According to back projection's principle, the intensity of the ring artifact that same error path produces is basically identical, shows as the intensity basically identical of straight line (ring artifact) on polar coordinate image.According to these characteristics, polar coordinate image to be compressed, the direction of compression is along the circumferential direction of polar coordinate image, and the method for compression is get m circumferential direction data average.The benefit of the maximum that compression brings is to make operand be kept to original 1/m (m is a compression multiple), makes the ring artifact intensity more consistent (straight line intensity is more even, more helps follow-up sampling) after overcompression simultaneously.As shown in Figure 3, provided Fig. 2 compressed 10 times after image.

2) from the compression polar coordinate image, extract strong edge, obtain removing the image at strong edge

Need below to extract strong edge from the compression polar coordinate image, the purpose of extracting strong edge is the smooth operation for next step.

(r θ) represents polar coordinate image after the compression with f.

Extract the process at strong edge:

21) ask the gradient of compressing each point in the polar coordinate image by following formula

With circumferential gradient

$f_{\mathrm{Deri}}^R(r,\mathrm{\&theta;})=f(r+1,\mathrm{\&theta;})-f(r-1,\mathrm{\&theta;})---\left(2\right)$

$f_{\mathrm{Deri}}^{\mathrm{\&theta;}}(r,\mathrm{\&theta;})=f(r,\mathrm{\&theta;}+1)-f(r,\mathrm{\&theta;}-1)---\left(3\right)$

Wherein: r represents that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f;

22) add up the quadratic sum RDeriTotal of gradient and the circumferential quadratic sum of gradient θ DeriTotal

$\mathrm{RDeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{\mathrm{\&theta;}=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(f_{\mathrm{Deri}}^R(r,\mathrm{\&theta;})\right)}^2---\left(4\right)$

$\mathrm{\&theta;DeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{\mathrm{\&theta;}=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(f_{\mathrm{Deri}}^{\mathrm{\&theta;}}(r,\mathrm{\&theta;})\right)}^2---\left(5\right)$

Wherein P is for radially sampling number, Q are circumferential sampling number;

23) respectively RDeriMean, θ DeriMean be multiply by one less than 1 coefficient S cale

RDeriMean＝RDeriMean×Scale (8)

θDeriMean＝θDeriMean×Scale (9)

26) according to the RDeriMean, the θ DeriMean that (multiply by coefficient S cale value afterwards) after adjusting, judge whether it is strong edge for each point, result f _Edge(r, θ) expression.

$f_{\mathrm{Edge}}(r,\mathrm{\&theta;})=\left\{\begin{array}{cc}0& f(r,\mathrm{\&theta;})<\mathrm{RDeriMean\; or\; f}(r,\mathrm{\&theta;})<\mathrm{\&theta;DeriMean}\\ 1& \mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein: (r represents that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f to f for r, the θ) value of expression compression polar coordinate image.

As shown in Figure 4, provided according to f _Edge(r, θ) result at the strong edge of removal.

3) image at the strong edge of described removal carries out smoothing processing and is: along the radial direction of the image of removing strong edge, to the continuum of non-strong marginal point carry out 53 times level and smooth; Level and smooth number of times requires to reach fully smoothly to fall straight line.

According to 2) the definite strong edge labelling f of step _Edge(r, θ), (r θ) carries out smoothly level and smooth result f to image f _Smooth(r, θ) expression.As shown in Figure 5, provided level and smooth result.

4) (r θ) deducts image f after the smoothing processing to the polar coordinate image f after the compression _Smooth(r θ) just can obtain comprising the basic ring image f of ring artifact _BasicRing(r, θ), as shown in Figure 6.As can be seen, encircle image substantially and not only comprised ring, but also will comprise other information.

5) describedly remove straight line by comb filter and may further comprise the steps:

51) all row in the basic ring of the sampling image, utilize following formula construction periodic signal y (n):

$y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{y}_i(n+\mathrm{iN})---\left(11\right)$

$y_i\left(n\right)=\left\{\begin{array}{cc}{c}_i(\mathrm{mn}+k-1)& n\&Element;[1,N/2]\\ -c_i(m(n-N/2)+k)-1& n\&Element;[N/2+1,N]\end{array}\right.---\left(12\right)$

Wherein, N is the length in the single cycle of y (n); y _i(n) i cycle of expression; I ∈ [1, M], M is the columns of compression polar coordinate image; N ∈ [1, N]; c _i(n) be column signal; K ∈ [1, m], m are the multiple of polar coordinate compression;

52) periodic signal y (n) is done DFT (discrete Fourier transform) conversion, obtain the periodic signal Y (k) after the DFT conversion;

53) in frequency domain, use the periodic signal Y (k) after the comb filter F (k) that pre-sets multiply by the DFT conversion, obtain frequency-region signal G (k)

54) frequency-region signal G (k) is done IDFT (discrete fourier inverse transformation) conversion, obtain its corresponding time-domain signal g (n);

55) recover corresponding all column signal c with time-domain signal g (n) _i(n) sampled point in.

Observe Fig. 6, for every row of image, have only the position that has ring, this row is only straight line, just can constitute periodically positive negative pulse stuffing signal by sampling, and then be filtered by comb filter; And other row because the value of each point of row is all different, are not straight lines, can't pass through periodically positive negative pulse stuffing signal of sampling structure, can not filtered by comb filter.

It is as follows to remove collinear process with comb filter:

Suppose that Fig. 6 has the M row, counting of every row is mN/2, and wherein N is an even number, every column signal c _i(n) expression, i ∈ [1, M] wherein, m are the multiple of polar coordinate compression.

Existing periodic signal y (n), the length in the single cycle of y (n) is T, i cycle used y _i(n) expression is suc as formula (11)

$y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{y}_i(n+\mathrm{iT})---\left(11\right)$

N ∈ [1, T] wherein.

By c _i(n) process of structure y (n) is as follows:

To i column signal c _i(n) once, obtain N/2 point, use y as i the cycle of y (n) with these some structures every m point sampling _i(n), suc as formula (12)

$y_i\left(n\right)=\left\{\begin{array}{cc}{c}_i(\mathrm{mn}+k-1)& n\&Element;[1,N/2]\\ -c_i(m(n-N/2)+k)-1& n\&Element;[N/2+1,N]\end{array}\right.---\left(12\right)$

Wherein k ∈ [1, m] is controlling the initial point position that every row are sampled.

During now with k=1 is example, and the process of a comb filtering is described:

A. all row of sampling utilize formula (11), formula (12) structure periodic signal y (n).

B. periodic signal y (n) is done the DFT conversion, obtain Y (k).

C. in frequency domain, multiply by Y (k), obtain G (k) with the comb filter F (k) that pre-sets.

D. G (k) is done the IDFT conversion, obtain g (n).

E. use g (n) to recover corresponding all row c _i(n) sampled point in

c _i(mn)＝(g _i(n+iN)-g _i(n+iN+N/2))/2 (13)

K=2, process above repeating.

……

K=m, process above repeating.

Travel through all k value (each point to image is all sampled), image has been carried out m sampling, carried out comb filtering m time.

In the whole process, only sample collinear position, the y that is constituted (n) signal just comprises the positive negative pulse stuffing signal, just can be filtered by comb filtering; For non-directional position,, therefore be retained owing to can't constitute the positive negative pulse stuffing signal.

Utilize comb filtering can remove image f _{BasicRingWithLine}Ring in (r θ), result f _{BasicRingWithoutLine}(r, θ) expression.From f _{BasicRingWithLine}(r deducts f in θ) _{BasicRingWithoutLine}(r θ) obtains encircling image f _Line(r, θ), the result of comb filtering as shown in Figure 7.

If f _Line(r θ) comprises the information of ring fully, and (r deducts f in θ) from f so _Line(r, the result who θ) obtains will be the images that does not contain ring artifact.Fig. 9 has provided f, and (r θ) deducts f _Line(r, result θ) have removed ring artifact as can be seen really, have verified and have utilized comb filter to remove collinear correctness.

6) 5) the ring f that extracts in the step _Line(r is that (r, the ring that extracts in θ) need expand to it and original polar coordinate image ring image of a size ring image f after the expansion from compression polar coordinate image f θ) _ExLine(r, θ) expression.The method of expansion: according to the inverse process of compression, with f _Line(r θ) duplicates m part (m is a compression multiple) along circumferential direction.Fig. 8 deducts the ring image that obtains after the view data of Fig. 7 for the view data of Fig. 6, and this ring image is the straight line that comb filtering proposes; Figure 10 expands to the size of original polar coordinate image for Fig. 8.

(3) the ring image that is rectangular coordinate with above-mentioned polar ring image transitions

Result after the conversion as shown in figure 11.

(4) in image area,, obtain acyclic image from original ring image with rectangular plots image subtraction (corresponding pixel value is subtracted each other) rectangular coordinate of ring artifact.

The ring image of the rectangular coordinate above original rectangular plots image subtraction has promptly obtained removing the rectangular coordinate ring image of ring artifact.Figure 12 has provided the contrast before and after handling.

Claims (7)

1. post-processing approach of removing ring artifact in the CT image is characterized in that may further comprise the steps:

The CT image that will have ring artifact is converted to polar coordinate image by the rectangular coordinate image;

At the polar diagram image field, utilize comb filter to extract polar ring image;

With the ring image that to extract polar ring image transitions be rectangular coordinate;

From original ring image, obtain acyclic image with CT figure image subtraction rectangular coordinate of ring artifact.

2. by the post-processing approach of ring artifact in the described removal of the claim 1 CT image, it is characterized in that:

Describedly extract polar ring image and may further comprise the steps:

1) polar coordinate image is compressed processing, the polar coordinate image after obtaining compressing;

2) from the compression polar coordinate image, extract strong edge, obtain removing the image at strong edge;

3) image to the strong edge of above-mentioned removal carries out smoothing processing, obtains the image after the smoothing processing;

4) the polar coordinate image data after the compression deduct the view data after the smoothing processing, obtain comprising the basic ring image of ring artifact;

5) in comprising the basic ring image of ring artifact, remove straight line by comb filter, obtain compressing the ring image in the polar coordinate image;

The ring image spreading that 6) will obtain becomes and original polar coordinate image ring image of a size.

3. by the post-processing approach of ring artifact in the described removal of the claim 2 CT image, it is characterized in that:

Describedly remove straight line by comb filter and may further comprise the steps:

51) all row in the basic ring of the sampling image, utilize following formula construction periodic signal y (n):

$y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{y}_i(n+\mathrm{iN})---\left(11\right)$

$y_i\left(n\right)=\left\{\begin{array}{cc}{c}_i(\mathrm{mn}+k-1)& n\&Element;[1,N/2]\\ -c_i(m(n-N/2)+k)-1& n\&Element;[N/2+1,N]\end{array}\right.---\left(12\right)$

Wherein, N is the length in the single cycle of y (n); y _i(n) i cycle of expression; I ∈ [1, M], M is the columns of compression polar coordinate image, n ∈ [1, N]; c _i(n) be column signal; K ∈ [1, m], m are the multiple of polar coordinate compression;

52) periodic signal y (n) is done the DFT conversion, obtain the periodic signal Y (k) after the DFT conversion;

53) in frequency domain, use the periodic signal Y (k) after the comb filter F (k) that pre-sets multiply by the DFT conversion, obtain frequency-region signal G (k);

54) frequency-region signal G (k) is done the IDFT conversion, obtain corresponding time-domain signal g (n);

55) recover corresponding all column signal c with time-domain signal g (n) _i(n) sampled point in.

4. by the post-processing approach of ring artifact in the described removal of the claim 2 CT image, it is characterized in that:

Described polar coordinate image is compressed the circumferential direction of the compression direction of processing along polar coordinate image, get the meansigma methods of m circumferential direction data during compression.

5. by the post-processing approach of ring artifact in the described removal of the claim 2 CT image, it is characterized in that:

The method of described ring image spreading is according to the inverse process of compression, will encircle image and duplicate m part along circumferential direction, and m is a compression multiple.

6. by the post-processing approach of ring artifact in the described removal of the claim 2 CT image, it is characterized in that:

The described method that extracts strong edge from the compression polar coordinate image is:

21) ask the gradient of compressing each point in the polar coordinate image by following formula

With circumferential gradient

$f_{\mathrm{Deri}}^R(r,\mathrm{\&theta;})=f(r+1,\mathrm{\&theta;})-f(r-1,\mathrm{\&theta;})---\left(2\right)$

$f_{\mathrm{Deri}}^{\mathrm{\&theta;}}(r,\mathrm{\&theta;})=f(r,\mathrm{\&theta;}+1)-f(r,\mathrm{\&theta;}-1)---\left(3\right)$

Wherein: r is that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f.

22) add up the quadratic sum RDeriTotal of gradient and the circumferential quadratic sum of gradient θ DeriTotal:

$\mathrm{RDeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{\mathrm{\&theta;}=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(f_{\mathrm{Deri}}^R(r,\mathrm{\&theta;})\right)}^2---\left(4\right)$

$\mathrm{\&theta;DeriTotal}=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{\mathrm{\&theta;}=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left(f_{\mathrm{Deri}}^{\mathrm{\&theta;}}(r,\mathrm{\&theta;})\right)}^2---\left(5\right)$

Wherein P is sampling number radially, and Q is circumferential sampling number;

23) calculate the average RDeriMean of gradient square and the circumferential average θ DeriMean of gradient square

$\mathrm{RDeriMean}=\frac{\mathrm{RDeriTotal}}{\mathrm{PQ}}---\left(6\right)$

$\mathrm{\&theta;DeriMean}=\frac{\mathrm{\&theta;DeriTotal}}{\mathrm{PQ}}---\left(7\right)$

Wherein: (wherein P is for radially sampling number, Q are circumferential sampling number), RDeriTotal is the gradient summation of radial direction, θ DeriTotal is the gradient summation of circumferential direction.

24), promptly multiply by one less than 1 coefficient S cale respectively to the average RDeriMean of gradient radially square, circumferentially the average θ DeriMean of gradient square adjusts:

RDeriMean＝RDeriMean×Scale (8)

θDeriMean＝θDeriMean×Scale (9)

25) according to the average RDeriMean of the gradient of (multiply by coefficient S cale after value) after adjusting square, the circumferential average θ DeriMean of gradient square, judge whether it is strong edge for each point, result f _Edge(r, θ) expression;

$f_{\mathrm{Edge}}(r,\mathrm{\&theta;})=\left\{\begin{array}{cc}0& f(r,\mathrm{\&theta;})<\mathrm{RDeriMean\; or\; f}(r,\mathrm{\&theta;})<\mathrm{\&theta;DeriMean}\\ 1& \mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein: (r represents that (r, radially index θ), θ represent polar coordinate image f (r, circumferential index θ) to polar coordinate image f to f for r, the θ) value of expression compression polar coordinate image.

7. by the described post-processing approach of removing ring artifact in the CT image of claim 2, it is characterized in that: the image at the strong edge of described removal carries out smoothing processing and is: along the radial direction of the image of removing strong edge, the continuum of non-strong marginal point is carried out 53 times smoothly; Level and smooth number of times requires to reach fully smoothly to fall straight line.

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