CN108846813A - The medicine CT image denoising method of frame and NSST is decomposed based on MFDF - Google Patents
The medicine CT image denoising method of frame and NSST is decomposed based on MFDF Download PDFInfo
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Abstract
The medicine CT image denoising method that frame and NSST are decomposed based on MFDF, is included the following steps：Step 1) establishes medicine CT image model；Step 2) calculates the gradient and local derviation value of image；Step 3) passes through MFDF frame for CT picture breakdown；Step 4) carries out MFDF component Jrec1, Jrec3 after non-lower sampling shearing wave is denoised to J1, and J3 respectively.Step 5) carries out MFDF inverse transformation to the MFDF component after denoising.The present invention is compared by experimental analysis and other algorithms in denoising field, is effectively applied and is denoised field in medicine CT；Three components are obtained by MFDF framework decomposition CT image, are preferably applied in the high-frequency sub-band and low frequency sub-band that each component is decomposed by NSST by improving thresholding algorithm.Pass through a large amount of experimental data comparison, proposed the medicine CT image denoising method for decomposing frame and non-lower sampling shearing wave conversion based on MFDF, is capable of the analyzing and diagnosing of better helpful doctor.
Description
Technical field
The present invention relates to a kind of medicine CT image denoising methods
Background technique and meaning
With the development of science and technology, the imaging techniques such as ultrasonic imaging, CT, MRI face applied to medicine in medical imaging field
In bed diagnosis.CT scan, also referred to as computed tomography, using the combination x-ray of computer disposal many measure from
The specific region sweep object in the cross section that different angle generates allows user to see the inside of object and do not cut down.By
It is axial imaging in CT imaging technique inspection, tissue or organ can be shown by image reconstruction, arbitrary orientation, it is aobvious to lesion
Show more fully, prevents from omitting；With high density resolution ratio, the small lesions for having density to change can also be shown, it can be with
Specify the property of lesion；In addition, there are CT the advantages such as noninvasive, imaging is fast to have become a kind of be widely used and highly safe doctor
Treat diagnostic techniques.
The CT value of each pixel is irregular in the image of non-uniform object, and image is in graininess, influences density resolution, this
Phenomenon claims the noise of CT.In terms of there is detector in its source, such as detector sensitivity, pixel size, thickness and x-ray amount etc..
There are also electronic circuit and mechanical aspects, and method for reconstructing and ray at random etc. can also cause noise.The quality of noise and image at
Inverse ratio, therefore it is to be understood that the mechanism that noise generates, is inhibited as far as possible.
In the past twenty years, people have studied in large quantities keep image main feature (edge, texture, color,
Contrast etc.) while removal picture noise the problem of, the present invention using medicine CT be research object, due to CT imaging not from
To the influence of various physical factors, the presence of speckle noise has seriously affected the quality of CT image, has resulted in medical image quality
It is poor.Speckle noise shows as relevant different fleck in spatial domain on the image, it will cover those gray scale differences
The characteristics of image of other very little.And traditional filtering method often destroys the original characteristics of image structure of CT image.For clinic
For doctor, speckle noise causes very big interference to their Accurate Diagnosis, even filtered picture, as
The image structure information that filtering destroys influences their judgement, is not influence caused by doctor very abundant especially for experience
It is bigger.Therefore, from the angle of clinical application, need to study the denoising side that image structure information is kept to CT medical image
Method makes more accurately diagnosis for doctor and provides technical support, reduces the risk of Artificial Diagnosis.
In conclusion Research of Medical CT medical image keeps the denoising method of image structure information to have very important meaning
Justice.
Summary of the invention
In order to overcome the shortcomings of traditional filtering method on retaining image structure information, and in order to overcome at wavelet analysis
The deficiency for managing high dimensional data sparse capability decomposes frame based on MFDF the present invention provides one kind and non-lower sampling shears wave conversion
(non-subsampled shearlet transform) medicine CT image Denoising Algorithm, for solving medicine CT image denoising.
In the prior art, the filtering method of many classics has played great effect in terms of image filtering, still
These methods often destroy the original structural information such as image border of image, and Wavelet transformation can be gone for image well
It makes an uproar and effectively catches one-dimensional singular point, but cannot reflect the mutation of straight line and curve.Ridgelet transform can be very good capture line
Singularity, make up the deficiency of small echo, but still cannot effectively capture the singularity of curve.In recent years, by discrete
Processing of the shearing wave algorithm to medical image, so that there is certain breakthrough to Medical Image Denoising technical field.It will in the present invention
MFDF decomposes frame combination shearing wave kit and uses in medicine CT noise image, invented have speed is fast, denoise it will be evident that
Retain the stronger medicine CT image of image structure information and denoise method for acoustic, finally by simulating, verifying method feasibility with it is excellent
The effect of change.
It is an advantage of the invention that：It proposes a kind of based on MFDF decomposition frame and non-lower sampling shearing wave conversion (non-
Subsampled shearlet transform) medicine CT image Denoising Algorithm MFDF decomposes frame and overcomes traditional denoising side
Method retains the deficiency of image structural capacity, and non-lower sampling shearing wave conversion overcomes wavelet analysis processing high dimensional data sparse capability
Deficiency, and have translation invariance.And the method has more resolutions, multiple dimensioned, multidirectional and time-frequency locality, by it
Image edge information can be preferably protected applied to CT image denoising, is provided convenience to the diagnosis of doctor.
To be more clear the object, technical solutions and advantages of the present invention, below just to technical solution of the present invention make into
The description of one step, the medicine CT image denoising method of frame and NSST is decomposed based on MFDF, steps are as follows：
Step 1) establishes new medicine CT image model.
The CT iconic model finally obtained consists of two parts：Tissue reflects signal (useful signal) and noise itself
(being made of multiplicative noise and additive noise two parts), the model of CT electric signal is as follows：
fpre(i, j)=gpre(i,j)npre(i,j)+wpre(i,j) (1)
Wherein (i, j) respectively represents the transverse and longitudinal coordinate of image, gpre(i, j) indicates noise-free signal, npre(i, j) is indicated
Multiplicative noise, wpre(i, j) indicates additive noise.
Influence due to additive noise to CT image is extremely limited, we ignore additive noise, and carry out logarithm to model
Compression processing, in order to remove the noise of CT image.
Formula (1) model being multiplied at this time will become the model being added, as follows：
log(fpre(i, j))=log (gpre(i,j))+log(npre(i,j)) (2)
Step 2) calculates the gradient and local derviation value of image.
MFDF framework decomposition of the invention needs to use each point of image for the local derviation of x, y and the gradient of each point.
Image I is located at the local derviation I that (x, y) point corresponds to xxLocal derviation I for I (x+1, y)-I (x, y), corresponding to yyFor I (x,
y+1)-I(x,y)。
The gradient value calculation formula that image I is located at (x, y) point is as follows：
Step 3) passes through MFDF frame for CT picture breakdown.
MFDF decomposition is carried out to the CT image after logarithmic transformation that step 1 obtains, we will construct one by image ladder
Degree and the element in matrix P, the P matrix of local derviation composition are derived from the calculating of step 2, in the P matrix that each pair of point is answered in image
Each point is defined as follows：
Wherein IxThe local derviation for x, I are put at (x, y) for image IyThe local derviation for y is put at (x, y) for image I, ▽ I is
For image I in the gradient of (x, y) point, μ is smoothing parameter, is set as 0.001 in the present invention.
Three component J1 in each point that image obtains after MFDF framework decomposition, J2, J3 are exported by following formula：
Wherein P-1For the inverse matrix of P, in IxWith IyIt is all zero point, P is set as unit matrix, after image traversal operates
Obtained J1 contains the edge and texture of image, and J2 is always zero, J3 approximate with original image, and has subtracted the ladder in original image
The norm of degree.
Step 4) carries out the MFDF component Jrec1 after non-lower sampling shearing wave is denoised to J1, and J3 respectively,
Jrec3。
When dimension is n=2, the cutting system function with discrete parameter is as follows：
SAB(φ)={ φj,l,k=| det A |j/2φ(BlAjx-k)；j,l∈Z,k∈Z2}
(6)
Wherein φ ∈ L2(R2), A and B are the invertible matrix of 2*2, | det B |=1, j are scale parameters, and l is directioin parameter,
K is spatial position.For j >=0, -2j≤l≤2j-1,k∈Z2, the Fourier transformation of d=0,1 shearing wave can use compact schemes frame
Frame indicates：
Wherein (2 V-2jIt ξ) is scaling function,Be localization trapezoidal to upper window function, AdIt is anisotropic extension square
Battle array, BdIt is shearing matrix, the shearing wave conversion of function f can be calculated with equation (8).
Its corresponding high-frequency sub-band and low is calculated by above formula in two components J1, J3 obtaining through MFDF framework decomposition
Frequency subband, then threshold value shrink process is carried out to the shearing wave coefficient of each component high-frequency sub-band and low frequency sub-band.Carrying out medicine figure
When as denoising, the selection of threshold function table has very big influence to image denoising effect.Common thresholding algorithm have soft-threshold and
Hard threshold algorithm, threshold function table of the present invention are as follows：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter；tjObject selection according to specific experiments；This
What invention obtained after decomposing for MFDF chooses more suitable threshold function table parameter σ comprising detail view and comprising approximate diagramn.At this
In invention, the CT figure of 512*512 is by decomposing, for including detail view, threshold parameter σn1It is selected as σn/ 200, for including approximation
The image of figure, threshold parameter σn1It is selected as σn/1.1。
To treated, coefficient carries out NSST inverse transformation, may finally obtain J1, the image Jrec1 after the denoising of J3 component,
Jrec3。
Step 5) carries out MFDF inverse transformation to the MFDF component after denoising.
Jrec1 obtained in previous step, Jrec3 are done into MFDF inverse transformation together with null component J2, transformation for mula is such as
Under：
Wherein Jrec1, Jrec3 are the components denoised by non-lower sampling shearing wave, equally, by going back for each pixel
Final image I can be obtained in original.
The present invention has the following advantages that：
1. the present invention decomposes frame and non-lower sampling shearing wave variation model using MFDF, by the details such as the edge of image with
The approximate information of image is separately handled, and in conjunction with the shearing wave conversion of non-lower sampling, shears wave conversion in original research non-lower sampling
With the experimental data of wavelet transformation relatively in possess better medicine denoising effect and picture structure retention.
2. non-lower sampling shearing wave transformation model possesses better directional sensitivity in the present invention.
3. the present invention uses targeted shearing wave coefficient threshold contraction algorithm, can preferably handle after MFDF is decomposed
The obtained noise on different components.
4. structure of the invention is succinct, and has used more novel theory.
Detailed description of the invention
Fig. 1 a is original image, and Fig. 1 b and Fig. 1 c are respectively the J1 of the Lena figure after MFDF is decomposed, J3 component map；
Fig. 2 is non-lower sampling shearing wave shift process figure；
Fig. 3 is overall step flow chart of the present invention；
Fig. 4 is analysis of cases overall flow；
Fig. 5 a~5e is various algorithms in classic map Lena (σn=40) comparison of experimental result on, wherein Fig. 5 a is former
Figure, Fig. 5 b are noise patterns, and Fig. 5 c is NSST algorithm effect figure, and Fig. 5 d is FFST algorithm effect figure, and Fig. 5 e is inventive algorithm effect
Fruit figure；
Fig. 6 a~Fig. 6 e is various algorithms in Cranial Computed Tomography (σn=40) comparison of experimental result on, wherein Fig. 6 a is CT noise
Figure, Fig. 6 b are CT original images, and Fig. 6 c is NSST algorithm effect figure, and Fig. 6 d is FFST algorithm effect figure, and Fig. 6 e is inventive algorithm effect
Fruit figure；
Specific embodiment
The present invention will be further described below with reference to the accompanying drawings.
It is of the invention frame to be decomposed based on MFDF and non-lower sampling shears wave conversion medicine CT image denoising method, including with
Lower step：
Step 1) establishes new medicine CT image model
The CT iconic model finally obtained consists of two parts：Tissue reflects signal (useful signal) and noise itself
(being made of multiplicative noise and additive noise two parts), the model of CT electric signal is as follows：
fpre(i, j)=gpre(i,j)npre(i,j)+wpre(i,j) (1)
Wherein (i, j) respectively represents the transverse and longitudinal coordinate of image, gpre(i, j) indicates noise-free signal, npre(i, j) is indicated
Multiplicative noise, wpre(i, j) indicates additive noise.
Influence due to additive noise to CT image is extremely limited, we ignore additive noise, and carry out logarithm to model
Compression processing, in order to remove the noise of CT image.
Formula (1) model being multiplied at this time will become the model being added, as follows：
log(fpre(i, j))=log (gpre(i,j))+log(npre(i,j)) (2)
Step 2) calculates the gradient and local derviation value of image.
MFDF framework decomposition of the invention needs to use each point of image for the local derviation of x, y and the gradient of each point.
Image I is located at the local derviation I that (x, y) point corresponds to xxLocal derviation I for I (x+1, y)-I (x, y), corresponding to yyFor I (x,
y+1)-I(x,y)。
The gradient value calculation formula that image I is located at (x, y) point is as follows：
Step 3) passes through MFDF frame for CT picture breakdown
MFDF decomposition is carried out to the CT image after logarithmic transformation that step 1 obtains, we will construct one by image ladder
Degree and the element in matrix P, the P matrix of local derviation composition are derived from the calculating of step 2, in the P matrix that each pair of point is answered in image
Each point is defined as follows：
Wherein IxThe local derviation for x, I are put at (x, y) for image IyThe local derviation for y is put at (x, y) for image I,For
For image I in the gradient of (x, y) point, μ is smoothing parameter, is set as 0.001 in the present invention.
Three component J1 in each point that image obtains after MFDF framework decomposition, J2, J3 are exported by following formula：
Wherein P-1For the inverse matrix of P, in IxWith IyIt is all zero point, P is set as unit matrix, after image traversal operates
Obtained J1 contains the edge and texture of image, and J2 is always zero, J3 approximate with original image, and has subtracted the ladder in original image
The norm of degree.Fig. 1 a~Fig. 1 c illustrates the image of each component after MFDF framework decomposition.
Step 4) carries out the MFDF component Jrec1 after non-lower sampling shearing wave is denoised to J1, and J3 respectively,
For Jrec3 when dimension is n=2, the cutting system function with discrete parameter is as follows：
SAB(φ)={ φj,l,k=| det A |j/2φ(BlAjx-k)；j,l∈Z,k∈Z2}
(6)
Wherein φ ∈ L2(R2), A and B are the invertible matrix of 2*2, | det B |=1, j are scale parameters, and l is directioin parameter,
K is spatial position.For j >=0, -2j≤l≤2j-1,k∈Z2, the Fourier transformation of d=0,1 shearing wave can use compact schemes frame
Frame indicates：
Wherein (2 V-2jIt ξ) is scaling function,Be localization trapezoidal to upper window function, AdIt is anisotropic extension square
Battle array, BdIt is shearing matrix, the shearing wave conversion of function f can be calculated with equation (8).
Its corresponding high-frequency sub-band and low is calculated by above formula in two components J1, J3 obtaining through MFDF framework decomposition
Frequency subband, then threshold value shrink process is carried out to the shearing wave coefficient of each component high-frequency sub-band and low frequency sub-band.Carrying out medicine figure
When as denoising, the selection of threshold function table has very big influence to image denoising effect.Common thresholding algorithm have soft-threshold and
Hard threshold algorithm, threshold function table of the present invention are as follows：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter；tjObject selection according to specific experiments；This
What invention obtained after decomposing for MFDF chooses more suitable threshold function table parameter σ comprising detail view and comprising approximate diagramn.At this
In invention, the CT figure of 512*512 is by decomposing, for including detail view, threshold parameter σn1It is selected as σn/ 200, for including approximation
The image of figure, threshold parameter σn1It is selected as σn/1.1。
To treated, coefficient carries out NSST inverse transformation, may finally obtain J1, the image Jrec1 after the denoising of J3 component,
Jrec3.Shearing wave shift process figure is as shown in Fig. 2.
Step 5) carries out MFDF inverse transformation to the MFDF component after denoising
Jrec1 obtained in previous step, Jrec3 are done into MFDF inverse transformation together with null component J2, transformation for mula is such as
Under：
Wherein Jrec1, Jrec3 are the components denoised by non-lower sampling shearing wave, equally, by going back for each pixel
Final image I can be obtained in original.
Overall step flow chart of the present invention is as shown in Figure 3.
Analysis of cases
The present invention decomposes the combination of frame and NSST by MFDF by using specific medicine CT image as object,
Improved thresholding algorithm is used in NSST medium-high frequency subband and low frequency sub-band, while presenting this hair by being compared with the prior art
Bright superior function.The flow chart of analysis of cases is as shown in Figure 4.
The present invention cashes the quality after image reconstruction using Y-PSNR (PSNR), and PSNR is defined as follows：
Wherein N indicates the number of pixels in image, | | g | |FIndicate not Robbie Nice norm, 255 be that pixel can be in ash
The maximum value obtained in degree image.PSNR numerical value is bigger, and denoising effect is better.
The hardware parameter of experiment of the invention is CPU：Intel Core i5-4210U double-core dominant frequency 1.70GHz 2.40GHz, operation
Memory：3.67GB.Software uses the MATLAB2014a run under 64 bit manipulation system of Microsoft windows7.This experiment
Input data is used as using medicine CT noise image and classics Lena figure, effective comparative experiments can be carried out, analysis of cases is whole
Body flow chart such as Fig. 4.It is effectively applied using improved threshold value contraction algorithm in high-frequency sub-band and low frequency sub-band, can effectively be reached
To good denoising effect.Experiment by comparison NSST (non-lower sampling shear transformation), FFST (rapid finite shear transformation) and
Context of methods.Various algorithms apply experiment effect figure such as Fig. 5 in figure Lena, and various algorithms apply the experiment effect in figure lung CT
Fruit figure is as shown in Figure 6.
It can be seen that in table 1,2, can be seen that noise variance from the experimental data of classical image Lena and medicine CT image and get over
Greatly, higher to the requirement of Denoising Algorithm.On same noise variance, algorithm of the invention numerically slightly leads over NSST, very
Positive effect is greater than FFST, and with the increase of noise variance, the leading superiority of this algorithm more reduces, in experiment effect figure originally
There is the algorithm of invention clearer details to describe.
Table 1：Lena schemes different Denoising Algorithms in the PSNR/dB value of different noises
Table 2：PSNR/dB value of the medicine CT figure difference Denoising Algorithm in different noises
| Algorithm | σn=10 | σn=20 | σn=30 | σn=40 | σn=50 |
| Inventive algorithm | 34.2222 | 29.5020 | 26.5183 | 24.8193 | 23.7477 |
| NSST | 33.7465 | 29.0505 | 26.3989 | 24.7752 | 23.7290 |
| FFST | 31.3273 | 27.6832 | 25.3151 | 23.1483 | 22.2328 |
A specific embodiment of the invention is described in conjunction with attached drawing above, but these explanations cannot be understood to limit
The scope of the present invention, protection scope of the present invention are limited by appended claims, any in the claims in the present invention base
Change on plinth is all protection scope of the present invention.
Claims (1)
1. decomposing the medicine CT image denoising method of frame and non-lower sampling shearing wave conversion based on MFDF, steps are as follows:
Step 1) establishes medicine CT image model；
Obtained CT iconic model consists of two parts：Tissue reflects signal=and noise itself, tissue reflection letter
It number is useful signal, noise itself is made of multiplicative noise and additive noise two parts, and the model of CT electric signal is as follows：
fpre(i, j)=gpre(i,j)npre(i,j)+wpre(i,j) (1)
Wherein (i, j) respectively represents the transverse and longitudinal coordinate of image, gpre(i, j) indicates noise-free signal, npre(i, j) indicates to be multiplied
Noise, wpre(i, j) indicates additive noise；
Influence due to additive noise to CT image is extremely limited, we ignore additive noise, and carry out log-compressed to model
Processing, in order to remove the noise of CT image；
Formula (1) model being multiplied at this time will become the model being added, as follows：
log(fpre(i, j))=log (gpre(i,j))+log(npre(i,j)) (2)
Step 2) calculates the gradient and local derviation value of image；
MFDF framework decomposition needs to use each point of image for the local derviation of x, y and the gradient of each point；
Image I is located at the local derviation I that (x, y) point corresponds to xxLocal derviation I for I (x+1, y)-I (x, y), corresponding to yyFor I (x, y+
1)-I(x,y)；
The gradient value calculation formula that image I is located at (x, y) point is as follows：
Step 3) passes through MFDF frame for CT picture breakdown；
MFDF decomposition is carried out to the CT image after logarithmic transformation that step 1 obtains, constructs one by image gradient and local derviation group
At matrix P, P matrix in element be derived from the calculating of step 2, each point definition in the P matrix that each pair of point is answered in image
It is as follows：
Wherein IxThe local derviation for x, I are put at (x, y) for image IyThe local derviation for y is put at (x, y) for image I,For image I
In the gradient of (x, y) point, μ is smoothing parameter, is set as 0.001；
Three component J1 in each point that image obtains after MFDF framework decomposition, J2, J3 are exported by following formula：
Wherein P-1For the inverse matrix of P, in IxWith IyIt is all zero point, P is set as unit matrix, obtains after image traversal operates
J1 contain the edge and texture of image, J2 is always zero, J3 approximate with original image, and has subtracted gradient in original image
Norm；
Step 4) carries out MFDF component Jrec1, Jrec3 after non-lower sampling shearing wave is denoised to J1, and J3 respectively
When dimension is n=2, the cutting system function with discrete parameter is as follows：
SAB(φ)={ φj,l,k=| det A |j/2φ(BlAjx-k)；j,l∈Z,k∈Z2}
(6)
Wherein φ ∈ L2(R2), A and B are the invertible matrix of 2*2, | det B |=1, j are scale parameters, and l is directioin parameter, and k is
Spatial position；For j >=0, -2j≤l≤2j-1,k∈Z2, the Fourier transformation of d=0,1 shearing wave can use compact schemes frame
To indicate：
Wherein (2 V-2jIt ξ) is scaling function,Be localization trapezoidal to upper window function, AdIt is anisotropic extended matrix,
BdIt is shearing matrix, the shearing wave conversion of function f can be calculated with equation (8)；
Its corresponding high-frequency sub-band and low frequency is calculated by above formula in two components J1, J3 obtaining through MFDF framework decomposition
Band, then threshold value shrink process is carried out to the shearing wave coefficient of each component high-frequency sub-band and low frequency sub-band；It is gone carrying out medical image
When making an uproar, the selection of threshold function table has very big influence to image denoising effect；Common thresholding algorithm has soft-threshold and hard threshold
Value-based algorithm, threshold function table are as follows：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter；tjObject selection according to specific experiments；For
What MFDF was obtained after decomposing chooses more suitable threshold function table parameter σ comprising detail view and comprising approximate diagramn；The CT of 512*512
Figure is by decomposing, for including detail view, threshold parameter σn1It is selected as σn/ 200, for the image comprising approximate figure, threshold value ginseng
Number σn1It is selected as σn/1.1；
To treated, coefficient carries out NSST inverse transformation, may finally obtain J1, the image Jrec1 after the denoising of J3 component,
Jrec3；
Step 5) carries out MFDF inverse transformation to the MFDF component after denoising；
Jrec1 obtained in previous step, Jrec3 are done into MFDF inverse transformation together with null component J2, transformation for mula is as follows：
Wherein Jrec1, Jrec3 are the components denoised by non-lower sampling shearing wave, equally, by the reduction of each pixel,
Final image I can be obtained.
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