CN108416737A - Medicine CT image denoising method based on DNST - Google Patents
Medicine CT image denoising method based on DNST Download PDFInfo
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Abstract
Based on DNST medicine CT image denoising methods, include the following steps：Step 1) establishes medicine CT image model；Step 2) establishes the system framework of DNST；Step 3) carries out adaptive threshold shrink process to the shearing wave coefficient of high-frequency sub-band low frequency sub-band；To treated, coefficient carries out DNST inverse transformations to step 4).The present invention is compared by experimental analysis and newest denoising domain algorithms, is effectively applied in medicine CT denoising field；It is preferably applied by adaptive thresholding algorithm in the high-frequency sub-band and low frequency sub-band that CT figures are decomposed by DNST.A large amount of experimental data comparison is passed through, it is proposed that the medicine CT image denoising method based on DNST can preferably be conducive to the analyzing and diagnosing of doctor.
Description
Technical field
The present invention relates in Medical Image Denoising field, more particularly to medicine CT image.Design is a kind of to be suitable for medicine
CT images based on discrete inseparable shearing wave conversion (Discrete Nonseparable Shearlet
Transform, hereinafter referred to as：DNST medicine CT image denoising method).
Background technology and meaning
With the development of science and technology, in medical imaging field, the imaging techniques such as ultrasonic imaging, CT, MRI face applied to medicine
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 inspections, can shows tissue or organ 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 values of each pixel are 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..
Also electronic circuit and mechanical aspects, 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 possible.
The present invention is influenced by various physical factors for research object since CT is imaged unavoidably using medicine CT, spot
The presence of noise has seriously affected the quality of CT images, and it is poor to result in medical image quality.Speckle noise shows on the image
For relevant different fleck in spatial domain, it will cover the characteristics of image of those gray scale difference very littles.For clinic
For doctor, speckle noise causes prodigious interference to their Accurate Diagnosis, is not very abundant especially for experience
Bigger is influenced caused by doctor.Therefore, it from the angle of clinical application, needs research to CT Medical Image Denoising methods, is
Doctor makes more accurately diagnosis and provides technical support, reduces the risk of Artificial Diagnosis.
In conclusion Research of Medical CT image de-noising methods have very important significance.
Invention content
In order to overcome the shortcomings of that wavelet analysis processing high dimensional data sparse capability and discrete shearing wave frame circle effect are poor
Deficiency, the present invention provides a kind of discrete inseparable shearing wave (DNST) medicine CT image Denoising Algorithms, for solving medicine
CT image denoisings.In the prior art, Wavelet transformation can be used for image denoising well and effectively catch one-dimensional singular point, but not
It can reflect the mutation of straight line and curve.Ridgelet transform can be very good the singularity of capture line, make up the deficiency of small echo, but still
It so cannot effectively capture the singularity of curve.In recent years, the processing by discrete shearing wave algorithm to medical image so that
There is certain breakthrough to Medical Image Denoising technical field.DNST algorithms are compared to discrete shearing wave algorithm and possess better frame
Frame circle and better M8003 line, it is meant that DNST possesses better denoising effect.By discrete inseparable shearing in the present invention
Wave kit is used in medicine CT noise image, and fast, the apparent DNST of denoising medicine CT image denoising with speed has been invented
Method for acoustic, finally by the feasibility of simulating, verifying method and the effect of optimization.
Compared with prior art, creativeness and advantage of the invention：Propose a kind of medicine CT image denoising side of DNST
Method, DNST transformation overcome the deficiency of wavelet analysis processing high dimensional data sparse capability, the deficiency of discrete shearing wave frame circle.And
And the method has more resolutions, multiple dimensioned, multidirectional and time-frequency locality, being applied to CT image denoisings can preferably protect
Image edge information is protected, is provided a convenient to the diagnosis of doctor.
To make the object, technical solutions and advantages of the present invention be more clear, below just to technical scheme of the present invention make into
One step describes, and is respectively divided into following four step.
Step 1) establishes medicine CT image model
CT is to be scanned acquirement information to human body level with X-ray beam, the reconstruction image obtained after computer is handled,
It is digital imagery rather than analog imaging.But the excessive Gaussian noise that will produce under low strength transmission current conditions, meeting
So that CT projected image qualities generate serious degeneration.The noise model of foundation is handled by log-compressed to be conducive to CT images
Signal carries out noise separation.It is as follows for the universal model model of CT electric signals：
S (x, y)=r (x, y) n (x, y) (1)
Wherein, (x, y) respectively represents the transverse and longitudinal coordinate of image, and r (x, y) indicates that noise-free signal, n (x, y) indicate to be multiplied
Noise.
In order to be conducive to carry out noise separation to CT picture signals, the CT electric signals of acquisition are carried out log-compressed by the present invention
Processing.Formula (1) model being multiplied at this time will become the model being added, as follows：
Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)
Step 2) establishes the system framework of DNST
Multi-resolution decomposition is carried out to the CT images after logarithmic transformation that step 1 obtains, resolves into multiple sizes and artwork
Equal CT high frequency imagings and an equal-sized CT low-frequency image.Each CT subbands are applied to using shearing and filtering device, and
The shearing wave coefficient of subband is calculated with DNST algorithms.
We use a kind of inseparable shearing generator, its basic frequency support provides better frame
Boundary and better directional selectivity.The inseparable shearing generator ψ introduced in the present inventionnonIt is defined as follows：
In formula, trigonometric polynomial P is a two-dimensional fan-filter, and ψ is separable shearing wave producer, inseparable
From shearing wave producerIf fan-filter P meets infξ∈Ω|P(ξ)|≥C1, C1>0, wherein
It is converted according to discrete wavelet,It can be by ψnonIt is found out by following formula：
In formula, sampling matrix It is the sampling constant in conversion process.M joins for two-dimension translational
Number,It is parabola Scale Matrixes, which changes scale by specific generating function.Shear matrixChange direction by specific generating function.For calculating each scale j=0 ..., J-1 shearing wave coefficientsIn order to avoid 2j/2Each shear parameters k and scale parameter j is calculated, it is excessive so as to cause calculation amount.It will cut
Operator is cut to act onAnd it can be done such as down conversion according to shearing wave property：
By combining the separable discrete wavelet theorem of two dimension and formula (1) that can obtain：
In formula, pj(n) it is by two-dimensional sector-shaped filter P (2J-j-1ξ1,2J-j/2ξ2) Fourier coefficient；It is pj*Wj
Discretization；Pass through discrete shearing operatorWill in continuous domain digital shearing and filtering deviceDiscretization, formula
It is as follows：
Then it derives and inseparable shearing wave producer ψnonThe associated inseparable shearing wave conversion of discretization
(DNST) it defines：
In formula,N is discrete two-dimensional translation parameters, if with separable separable filter WjIt goes to replace
pj*WjIt can derive the associated separable shearing wave conversion (Discrete of separable shearing wave producer ψ
Separable Shearlet Transform)。
It is discrete it is inseparable shearing wave conversion specific algorithm process be：
S1：Input a two-dimensional CT image signal f ∈ RX*Y, scale parameter J ∈ N, a shear vector parameter k ∈ NJ, with
And choice direction filter D irectionFilter, low-pass filter QuadratureMirrorFilter.
S2：Calculate the frequency spectrum f of input signalfreq=FFT (f).
S3：Calculate the shearing wave positive-going transition coefficient shearletCoeffs (i) under different scale subband i ∈ [0, nth]
∈RX*Y*nth, according to convolution theory and Frame Theory:
S4：Export discrete inseparable shearing wave coefficient shearletCoeffs (i).
Nth represents the redundancy of entire compact schemes DNST systems in wherein the 3rd step, calculates as follows:
Nth=2* ((2*2k[0]+1))+2*((2*2k[1]+1))+...+2*((2*2k[J]+1) (11)
Experiment shows when DNST and discrete separable shearing wave (DSST) are when according to the size selection filter of support,
DNST can obtain better frame circle.In addition to this, the shearing wave generated by inseparable shearing wave producer's
One major advantage is that fan-filter P improves set direction in each size of frequency domain.It is decomposed by DNST, it will
Medicine CT image resolves into f in frequency domain1,f2,...,fnth-1Open equal-sized high frequency CT images and a low frequency CT image
fnth。
Step 3) carries out adaptive threshold shrink process to the shearing wave coefficient of high-frequency sub-band and low frequency sub-band
In medicine denoising field, the selection of threshold function table has prodigious influence to image denoising effect.Common threshold value
Algorithm has soft-threshold and hard threshold algorithm, but all effect cannot be opened up well in multiple dimensioned multidirectional shearing wave coefficient
It is existing.The present invention proposes a kind of novel adaptive threshold contraction algorithm.Pass through the high frequency CT subbands f obtained in step 2)1,
f2,...,fnth-1With low frequency CT subbands fnthShearing wave coefficient carry out adaptive threshold shrink process, the present invention proposition be more suitable for
The threshold function table of CT medical images：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter；tjAccording to specific experiment Object selection；
In the present invention, the CT figures of 512*512 are by 4 layers of decomposition, 5 σ of threshold value T ≈n, for the more decomposition subband of details, T ≈ can be used
4σnOr 3 σ of T ≈n。
To treated, coefficient carries out DNST inverse transformations to step 4)
To in previous step threshold value shrink after high-frequency sub-band and low frequency sub-band carry out DNST inverse transformations, can obtain for
It obtains being conducive to the CT images after the denoising of doctor's analysis, inventive algorithm is also demonstrated by comparative experimental data to medicine CT
The superiority of image denoising.DNST inverse process specific algorithm process introduced below：
T1:Input DNST shearing factor shearletCoeffs (i) the ∈ R that treatedX*Y*nth；
T2:If frec∈RX*YRepresent the image sequence after reconstruct；
T3:Calculate the reconstructed image sequence frequency spectrum f of shearletCoeffs (i) under each index i ∈ [0, nth]recAnd
Sum frec, according to convolution theory and Frame Theory
T4:It does inverse Fourier transform and obtains reconstructed image sequence frec:=IFFT (frec)；
The present invention has the following advantages：
1. the present invention uses discrete inseparable shearing wave variation model, become in original separable shearing wave of research
Change with the experimental data of wavelet transformation relatively in possess better medicine denoising effect.
2. discrete inseparable shearing wave transformation model possesses better frame circle and set direction in the present invention.
3. the present invention uses adaptive shearing wave coefficient threshold contraction algorithm, subband after decomposing can be handled very well and is made an uproar
Sound.
4. step of the present invention is clearly simple in structure, possess perfect theories integration.
Description of the drawings
Fig. 1 a are shearing wave ψj,0,mIn frequency domain coverage diagram, Fig. 1 b are shearing wave ψj,1,mIn frequency domain coverage diagram；
Fig. 2 is DNST shearing wave flow charts；
Fig. 3 is overall step flow chart of the present invention；
Fig. 4 is analysis of cases overall flow；
Fig. 5 a~Fig. 5 g are the comparison of various algorithms experimental result on classic map Lena (σ=40), and wherein Fig. 5 a are former
Figure, Fig. 5 b are noise patterns, and Fig. 5 c are NSST algorithm effect figures, and Fig. 5 d are SWT algorithm effect figures, and Fig. 5 e are FDCT algorithm effects
Figure, Fig. 5 f are FFST algorithm effect figures, and Fig. 5 g are inventive algorithm design sketch；
Fig. 6 a~Fig. 6 f are the comparison of various algorithms experimental result on Cranial Computed Tomography (σ=40), and wherein Fig. 6 a are CT noises
Figure, Fig. 6 b are NSST algorithm effect figures, and Fig. 6 c are SWT algorithm effect figures, and Fig. 6 d are FDCT algorithm effect figures, and Fig. 6 e are that FFST is calculated
Method design sketch, Fig. 6 f are inventive algorithm design sketch；
Fig. 7 is the comparison of various algorithms histogram on Cranial Computed Tomography (σ=40).
Specific implementation mode
Below in conjunction with attached drawing, the present invention will be further described.
The medicine CT image denoising method based on DNST of the present invention, includes the following steps：
Step 1) establishes medicine CT image model
CT is to be scanned acquirement information to human body level with X-ray beam, the reconstruction image obtained after computer is handled,
It is digital imagery rather than analog imaging；But the excessive Gaussian noise that will produce under low strength transmission current conditions, meeting
So that CT projected image qualities generate serious degeneration.The noise model of foundation is handled by log-compressed to be conducive to CT images
Signal carries out noise separation.It is as follows for the universal model model of CT electric signals：
S (x, y)=r (x, y) n (x, y) (1)
Wherein, (x, y) respectively represents the transverse and longitudinal coordinate of image, and r (x, y) indicates that noise-free signal, n (x, y) indicate to be multiplied
Noise.
In order to be conducive to carry out noise separation to CT picture signals, the CT electric signals of acquisition are carried out log-compressed by the present invention
Processing.Formula (1) model being multiplied at this time will become the model being added, as follows：
Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)
Step 2) establishes the system framework of DNST
Multi-resolution decomposition is carried out to the CT images after logarithmic transformation that step 1 obtains, resolves into multiple sizes and artwork
Equal CT high frequency imagings and an equal-sized CT low-frequency image.Each CT subbands are applied to using shearing and filtering device, and
The shearing wave coefficient of subband is calculated with DNST algorithms.
We use a kind of inseparable shearing generator, its basic frequency support provides better frame
Boundary and better directional selectivity.The inseparable shearing generator ψ introduced in the present inventionnonIt is defined as follows：
In formula, trigonometric polynomial P is a two-dimensional fan-filter, and ψ is separable shearing wave producer, inseparable
From shearing wave producerIf fan-filter P meets infξ∈Ω|P(ξ)|≥C1, C1>0, wherein
It is converted according to discrete wavelet,It can be by ψnonIt is found out by following formula：
In formula, sampling matrix It is the sampling constant in conversion process.M joins for two-dimension translational
Number,It is parabola Scale Matrixes, which changes scale by specific generating function；Shear matrixChange direction by specific generating function.For calculating each scale j=0 ..., J-1 shearing wave coefficientsIn order to avoid 2j/2Each shear parameters k and scale parameter j is calculated, it is excessive so as to cause calculation amount.It will cut
Operator is cut to act onAnd it can be done such as down conversion according to shearing wave property：
By combining the separable discrete wavelet theorem of two dimension and formula (1) that can obtain：
Then it derives and inseparable shearing wave producer ψnonThe associated inseparable shearing wave conversion of discretization
(DNST) it defines：
In formula,N is discrete two-dimensional translation parameters, if with separable separable filter WjIt goes to replace
pj*WjIt can derive the associated separable shearing wave conversion (Discrete of separable shearing wave producer ψ
Separable Shearlet Transform).As seen in figure la and lb, inseparable shearing wave algorithm has better side
Criticality and directionality.
It is discrete it is inseparable shearing wave conversion specific algorithm process be：
S1：Input a two-dimensional CT image signal f ∈ RX*Y, scale parameter J ∈ N, a shear vector parameter k ∈ NJ, with
And choice direction filter D irectionFilter, low-pass filter QuadratureMirrorFilter.
S2：Calculate the frequency spectrum f of input signalfreq=FFT (f).
S3：Calculate the shearing wave positive-going transition coefficient shearletCoeffs (i) under different scale subband i ∈ [0, nth]
∈RX*Y*nth, according to convolution theory and Frame Theory:
S4：Export discrete inseparable shearing wave coefficient shearletCoeffs (i).
Nth represents the redundancy of entire compact schemes DNST systems in wherein the 3rd step, calculates as follows:
Nth=2* ((2*2k[0]+1))+2*((2*2k[1]+1))+...+2*((2*2k[J]+1) (11)
DNST flow charts are as shown in Figure 2；Experiment shows when DNST and discrete separable shearing wave (DSST) are according to support
Size selection filter when, DNST can obtain better frame circle.In addition to this, by inseparable shearing wave producer
The shearing wave of generationA major advantage be that fan-filter P improves set direction in each size of frequency domain
Property.It is decomposed by DNST, medicine CT image is resolved into f in frequency domain1,f2,...,fnth-1Open equal-sized high frequency CT figures
Picture and a low frequency CT images fnth。
Step 3) carries out adaptive threshold shrink process to the shearing wave coefficient of high-frequency sub-band and low frequency sub-band
In medicine denoising field, the selection of threshold function table has prodigious influence to image denoising effect.Common threshold value
Algorithm has soft-threshold and hard threshold algorithm, but all effect cannot be opened up well in multiple dimensioned multidirectional shearing wave coefficient
It is existing.The present invention proposes a kind of novel adaptive threshold contraction algorithm.Pass through the high frequency CT subbands f obtained in step 2)1,
f2,...,fnth-1With low frequency CT subbands fnthShearing wave coefficient carry out adaptive threshold shrink process, the present invention proposition be more suitable for
The threshold function table of CT medical images：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter.tjAccording to specific experiment Object selection.
In the present invention, the CT figures of 512*512 are by 4 layers of decomposition, 5 σ of threshold value T ≈n, for the more decomposition subband of details, T ≈ can be used
4σnOr 3 σ of T ≈n。
To treated, coefficient carries out DNST inverse transformations to step 4)
To in previous step threshold value shrink after high-frequency sub-band and low frequency sub-band carry out DNST inverse transformations, can obtain for
It obtains being conducive to the CT images after the denoising of doctor's analysis, inventive algorithm is also demonstrated by comparative experimental data to medicine CT
The superiority of image denoising.DNST inverse process specific algorithm process introduced below：
T1:Input DNST shearing factor shearletCoeffs (i) the ∈ R that treatedX*Y*nth；
T2:If frec∈RX*YRepresent the image sequence after reconstruct；
T3:Calculate the reconstructed image sequence frequency spectrum f of shearletCoeffs (i) under each index i ∈ [0, nth]recAnd
Sum frec, according to convolution theory and Frame Theory
T4:It does inverse Fourier transform and obtains reconstructed image sequence frec:=IFFT (frec)；
Overall step flow chart of the present invention is as shown in Figure 3.
Analysis of cases
The present invention by using specific medicine CT image as object, studied on the basis of discrete shearing wave conversion respectively from
Scattered inseparable shearing wave system uses adaptive thresholding algorithm in high-frequency sub-band and low frequency sub-band, passes through simultaneously
It is compared with the prior art the superior function for presenting the present invention.
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, | | | |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 experiment of the present invention is used as input data using medicine CT noise image classics Lena figures, and it is effective right to carry out
Than experiment, analysis of cases overall flow figure such as Fig. 4.Decomposition scale is 4, and the level of shearing wave is [1,1,2,2], and algorithm is by noise
Figure is decomposed into 48 high-frequency sub-band images and 1 low frequency subband image, and size is equal with original image.It is received using adaptive threshold
Compression algorithm is effectively applied in high-frequency sub-band and low frequency sub-band, and good denoising effect can be effectively reached.Will treated son
Image with image after the inverse transformation reconstruction processing of DNST obtains denoising.By comparing NSST, (non-lower sampling is sheared for experiment
Transformation), FDCT (fast discrete curvelet transform), SWT (wavelet transformation), FFST (rapid finite shear transformation).Various algorithms are answered
Used in experiment effect figure such as Fig. 5 of figure Lena, various algorithms apply the experiment effect figure in figure Cranial Computed Tomography 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 gets over
Greatly, the requirement higher to Denoising Algorithm.On same noise variance, algorithm of the invention numerically slightly leads over NSST, very
Positive effect is more than SWT, FDCT, FFST.And there is algorithm of the invention clearer details to describe in experiment effect figure,
We can be seen that the algorithm in the present invention compares other advanced algorithms with more preferable from CT statistical data histograms Fig. 7
Denoising effect.
Table 1：Lena scheme different Denoising Algorithms different noises PSNR/dB values
| Algorithm | σ=10 | σ=20 | σ=30 | σ=40 | σ=50 |
| Inventive algorithm | 35.903 | 32.8432 | 30.9489 | 29.6564 | 28.5489 |
| NSST | 35.8483 | 32.8347 | 30.7565 | 29.4077 | 28.5219 |
| SWT | 34.1923 | 30.8132 | 28.8501 | 27.6738 | 26.6383 |
| FDCT | 33.9998 | 31.4285 | 29.6051 | 28.3746 | 27.3417 |
| FFST | 34.1686 | 31.2796 | 29.4937 | 28.3483 | 27.4132 |
Table 2：PSNR/dB value of the medicine CT figure difference Denoising Algorithm in different noises
| Algorithm | σ=10 | σ=20 | σ=30 | σ=40 | σ=50 |
| Inventive algorithm | 32.0937 | 28.5659 | 26.9113 | 25.8587 | 24.9651 |
| NSST | 31.8241 | 28.4836 | 26.9087 | 25.807 | 24.9365 |
| SWT | 30.3232 | 26.8593 | 25.2423 | 24.0277 | 23.1842 |
| FDCT | 29.7284 | 26.8415 | 25.2752 | 24.2814 | 23.5825 |
| FFST | 29.8268 | 26.6295 | 25.3201 | 24.4166 | 23.7618 |
The specific implementation mode of the present invention is described above in association with attached drawing, 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. the medicine CT image denoising method based on DNST, includes the following steps：
Step 1) establishes medicine CT image model, and log-compressed algorithm process is carried out to CT image informations；By to CT noise modes
Type estimates that the log-compressed algorithm being improved makes separation method between signal and noise, specifically：
CT is to be scanned acquirement information to human body level with X-ray beam, and the reconstruction image obtained after computer is handled, is several
Word is imaged rather than analog imaging；But the excessive Gaussian noise that will produce under low strength transmission current conditions, it can make
CT projected image qualities generate serious degeneration；The noise model of foundation is handled by log-compressed to be conducive to CT picture signals
Carry out noise separation；
Log-compressed processing is carried out to CT Noise picture signals, to reach signal and noise separation；For CT electric signals
Universal model is as follows：
S (x, y)=r (x, y) n (x, y) (1)
Wherein, (x, y) respectively represents the transverse and longitudinal coordinate of image, and r (x, y) indicates that noise-free signal, n (x, y) indicate multiplicative noise；
In order to carry out noise separation to CT picture signals, the CT electric signals of acquisition are subjected to log-compressed processing；It is multiplied at this time
Formula (1) model will become the model being added, as follows：
Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)
Step 2) establishes the system framework of DNST；By effectively carrying out inseparable discrete shearing wave conversion point to CT images
Solution, and calculate the shearing wave coefficient of CT Image Sub-Bands；It specifically includes：
Multi-resolution decomposition is carried out to the CT images after logarithmic transformation that step 1) obtains, it is equal with artwork to resolve into multiple sizes
CT high frequency imagings and an equal-sized CT low-frequency image；Each CT subbands are applied to using shearing and filtering device, are used in combination
DNST algorithms calculate the shearing wave coefficient of subband；
Using a kind of inseparable shearing generator ψnonIt is defined as follows：
In formula, trigonometric polynomial P is a two-dimensional fan-filter, and ψ is separable shearing wave producer, inseparable
Shear wave producerIf fan-filter P meets infξ∈Ω|P(ξ)|≥C1, C1>0, wherein
It is converted according to discrete wavelet,It can be by ψnonIt is found out by following formula：
In formula, sampling matrix It is the sampling constant in conversion process；M is two-dimension translational parameter,It is parabola Scale Matrixes, which changes scale by specific generating function；Shear matrixChange direction by specific generating function；For calculating each scale j=0 ..., J-1 shearing wave coefficientsIn order to avoid 2j/2Each shear parameters k and scale parameter j is calculated, it is excessive so as to cause calculation amount；It will cut
Operator is cut to act onAnd it can be done such as down conversion according to shearing wave property：
By combining the separable discrete wavelet theorem of two dimension and formula (1) that can obtain：
In formula, pj(n) it is by two-dimensional sector-shaped filter P (2J-j-1ξ1,2J-j/2ξ2) Fourier coefficient；It is pj*WjFrom
Dispersion；By discrete shearing operator by the discretization of the digital shearing and filtering device in continuous domain, formula is such as
Under：
Then it derives and inseparable shearing wave producer ψnonThe associated inseparable shearing wave conversion of discretization
(DNST) as follows：
In formula,N is discrete two-dimensional translation parameters, if with separable separable filter WjIt goes to replace pj*Wj
It can derive associated separable shearing wave conversion (the Discrete Separable of separable shearing wave producer ψ
Shearlet Transform)；
It is decomposed by DNST, medicine CT image is resolved into f in frequency domain1,f2,...,fnth-1Open equal-sized high frequency CT figures
Picture and a low frequency CT images fnth；
It is discrete it is inseparable shearing wave conversion specific algorithm process be：
S1：Input a two-dimensional CT image signalScale parameter J ∈ N, a shear vector parameter k ∈ NJ, Yi Jixuan
Select anisotropic filter DirectionFilter, low-pass filter QuadratureMirrorFilter；
S2：Calculate the frequency spectrum f of input signalfreq=FFT (f)；
S3：Calculate the shearing wave positive-going transition coefficient under different scale subband i ∈ [0, nth]Root
According to convolution theory and Frame Theory:
S4：Export discrete inseparable shearing wave coefficient shearletCoeffs (i)；
Nth represents the redundancy of entire compact schemes DNST systems in wherein S3 steps, calculates as follows:
Nth=2* ((2*2k[0]+1))+2*((2*2k[1]+1))+...+2*((2*2k[J]+1) (11)
Step 3) carries out adaptive threshold shrink process to the shearing wave coefficient of CT high-frequency sub-bands and CT low frequency sub-bands；Utilize improvement
Threshold value contraction algorithm, to CT decompose after subband shearing wave coefficients model handle；It specifically includes：
Pass through the high frequency CT subbands f obtained in step 2)1,f2,...,fnth-1With low frequency CT subbands fnthShearing wave coefficient carry out
Adaptive threshold shrink process proposes the threshold function table for being more suitable for CT medical images：
In formula, σnIt is the standard deviation of noise, tjRepresent j layers of auto-adaptive parameter；tjAccording to specific experiment Object selection；512*512
CT figure by 4 layers decomposition, T indicate threshold value；
Step 4) carries out DNST inverse transformations to the CT subband shearing wave coefficients after shrink process, obtains the CT images after denoising；It is logical
It crosses DNST inverse transformations to combine sub-band coefficients after contraction, obtains CT images after denoising；It specifically includes：
High frequency CT subbands and low frequency CT subbands after being shunk to the threshold value in previous step carry out DNST inverse transformations, obtain being terrible
CT images after to the denoising analyzed conducive to doctor；DNST inverse process specific algorithm processes：
T1：Input the shearing factor of CT subbands after DNST is handled
T2：If frec∈RX*YRepresent the image sequence after reconstruct；
T3：Calculate the reconstructed image sequence frequency spectrum f of shearletCoeffs (i) under each index i ∈ [0, nth]recAnd it sums
frec, according to convolution theory and Frame Theory
T4：It does inverse Fourier transform and obtains reconstructed image sequence frec:=IFFT (frec)。
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