CN106127711A - Shearlet conversion and quick two-sided filter image de-noising method - Google Patents

Abstract

The invention discloses a kind of shearlet conversion and quick two-sided filter image de-noising method, comprise the following steps: 1) utilize the envelope signal of noise imaging system acquisition noise image, set up medical ultrasonic image model；2) to described step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes pyramid filter group to carry out multiple dimensioned multi-direction decomposition, and 3) to described step 2) the two-dimensional discrete shearlet conversion coefficient of each sub-band images medium-high frequency part that obtains carries out threshold method shrink process；4) quick two-sided filter is utilized to step 2) the shearlet coefficient of medium and low frequency part does Filtering Processing；5) to through step 3) and step 4) process after all coefficients make shearlet inversion process, obtain the medical ultrasonic image after denoising.In the present invention, the introducing of quick two-sided filter can not only well improve the performance of denoising and substantially increase the efficiency of process.

Description

Shearlet conversion and quick two-sided filter image de-noising method

Technical field

The present invention relates to a kind of shearlet conversion and quick two-sided filter image de-noising method.Belong to medical ultrasonic figure As denoising field, a kind of medical science based on shearlet conversion with quick two-sided filter being applicable to medical ultrasonic image Ultrasonic Image Denoising method.

Background technology

At medical imaging field, the imaging technique such as ultra sonic imaging, CT, MRI has been applied in medical clinic applications.Ultrasonic examine Disconnected application as a kind of diagnostic techniques in medical diagnosis is to start, the most closely from coming out of gray scale ultrasound in 1972 In the past few years, ultrasonic diagnosis is used extensively in medical clinic applications, especially fetus growth situation and diagnosis in observing anemia of pregnant woman's body In the clinical practices such as abdomen organ's pathological changes, the use of ultrasonic imaging technique is even more important.

But, in the clinical practice of supersonic imaging apparatus, the speckle noise in ultrasonoscopy has had a strong impact on ultrasonic figure The quality of picture.In order to solve this difficult problem, people have developed Image Denoising Technology.The process of image denoising is according to known fall The original true picture of the noisy Image estimation of matter, obtains the best approximation under certain meaning of original image.Picture noise be one random Process, noise component(s) gray value is a random component, can be divided into according to the statistical nature of its probability density: Gauss makes an uproar Sound, salt-pepper noise, poisson noise, rayleigh noise etc..Feature, the statistical nature of noise and spectrum distribution rule according to real image Rule, has developed various different Medical Image Denoising method.

Medical ultrasound image denoising often mainly filters noise frequency composition by the method for filtering, improves the noise of image Ratio, thus improve picture quality.The distribution of signal is primarily present in low frequency part theoretically. and the distribution of noise is mainly deposited Being HFS, filtering noise contribution is exactly the HFS filtering signal.But for picture signal, image thin If joint signal exists in HFS. after filtering HFS, say the details the most just destroying image to varying degrees, And in clinical diagnosis, the details of medical image plays critical effect often, and therefore Medical Image Denoising is necessary for doing Retain again image detail to while reducing picture noise, under not reducing image spatial resolution premise, eliminate or maximum Limit ground suppression speckle noise.

Image sparse represents and is widely used in signal with image procossing in recent years, and the de-noising for transform domain carries Supply thinking.Wavelet analysis is signal and the sparse of image is laid a good foundation, and the zero dimension approached that wavelet transformation can be optimum is strange Different characteristic, but its premium properties is difficult to be generalized to two dimensional image and higher data space.

Multi-scale geometric analysis theory overcomes wavelet analysis and processes the deficiency of high dimensional data sparse capability.Due to MCA side Method has many resolutions, multiple dimensioned, multidirectional and time-frequency locality, is applied to Image Denoising by Use and can produce good effect.

Summary of the invention

Present invention aim at providing a kind of shearlet conversion and quick two-sided filter image de-noising method, this The defect that the bright one side wavelet transformation to using in the past exists, is processing higher-dimension problem only with level, vertical, diagonal angle etc. three The restriction in individual direction, it is proposed that there is the shearlet conversion of decomposition multiple dimensioned, multi-direction, improve denoising effect；The opposing party Face, owing to the present invention utilizes quick two-sided filter that low frequency part carried out filtration treatment, therefore for speckle that granule is bigger Spot noise (being present in low frequency part) has the strongest rejection ability equally.So quick the drawing of two-sided filter in the present invention Enter and can not only well improve the performance of denoising and substantially increase the efficiency of process.It is simultaneous for the spy of medical ultrasonic image Point, the method for this combination can not only well suppress speckle noise, can also retain the thin of focus edge in image etc. simultaneously Joint part, can preferably help doctor to carry out illness analysis.

The present invention in order to achieve the above object, the technical scheme is that

A kind of shearlet conversion and quick two-sided filter image de-noising method, comprise the following steps:

1) utilize the envelope signal of noise imaging system acquisition noise image, by logarithmic transformation, set up medical ultrasonic figure As model；Two-dimensional discrete shearlet coefficient, described two-dimensional discrete is obtained after two-dimensional discrete shearlet converts Shearlet coefficient includes noise-free picture two-dimensional discrete shearlet coefficient and the discrete shearlet of speckle noise two-dimensional image Coefficient；

2) to described step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes pyramid filter group Carry out multiple dimensioned multi-direction decomposition, obtain k+1 and the equal-sized sub-band images of medical ultrasonic image model, described subband Image includes a low frequency part and K HFS, utilizes step 1) the two-dimensional discrete shearlet coefficient that obtains releases height The two-dimensional discrete shearlet conversion coefficient of frequency part；

3) to described step 2) the two-dimensional discrete shearlet conversion of each sub-band images medium-high frequency part of obtaining Coefficient carries out threshold method shrink process；

4) quick two-sided filter is utilized to step 2) the shearlet coefficient of medium and low frequency part does Filtering Processing；

5) to through step 3) and step 4) process after all coefficients make shearlet inversion process, obtain the doctor after denoising Learn ultrasonoscopy.

Described step 1) particularly as follows: the factor that described ultrasonic image-forming system can affect acoustic power to those is made Appropriate dynamic compensation, the envelope signal of wherein said ultrasonic image-forming system collection includes the reflection of significant in-vivo tissue Signal and noise signal；Wherein said noise signal is divided into multiplicative noise and additive noise, and described multiplicative noise is with ultrasonic The principle of image formation is relevant, is mainly derived from random scattered signal, and described additive noise is system noise, main source Noise in sensor；Shown in the universal model model such as formula (1) of described envelope signal:

S (x, y)=r (x, y) n (x, y) (1)

Wherein said (x, y) the transverse and longitudinal coordinate of difference representative image, r (x, y) expression noise-free signal, n (x, y) expression Multiplicative noise；

Then the envelope signal collected described ultrasonic image-forming system carries out logarithmic compression process, to adapt to ultrasonic one-tenth As the Dynamic Announce scope of system display screen, i.e. by described formula (1) being become the model being added, as shown in formula (2):

Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)

Now, (s (x, y)) is medical ultrasonic image model to the signal log obtained；

Owing to wavelet transformation is linear transformation, shearlet conversion is the wavelet transformation expansion at higher-dimension, because of by institute Formula (2) model stated obtains shown in model such as formula (3) after two-dimensional discrete shearlet converts:

$\begin{array}{ccc}{S}_{l,k}^j=R_{l,k}^j+N_{l,k}^j& j=1,2,...,J.& (l,k)\∈Z^2\end{array}---\left(3\right)$

WhereinWithRepresent respectively containing the shearlet coefficient of noise image, noise-free picture The shearlet coefficient of shearlet coefficient and speckle noise；Wherein subscript j is the Decomposition order of shearlet conversion, subscript (l k) is the coordinate in transform domain.

Described step 2) particularly as follows: first to step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes Pyramid filter group carries out multiple dimensioned two-dimensional discrete shearlet and decomposes, and image, through k level sampling pyramid, obtains k+1 Sub-band images equal-sized with medical ultrasonic image model；Shearing and filtering device group is used to enter each scale subbands image obtained Line direction decomposes；The conversion coefficient R without noise cancellation signal after two-dimensional discrete shearlet decomposes_l ^j, k meets normal state against Gaussian mode Type (NIG), mainly by a dead wind area and a Gauss distribution with different average, its probability distribution such as formula (4) institute Show:

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}}{\mathrm{\π}q\left(r\right)}\exp \left(f\right(r\left)\right)\·K_1\left(\mathrm{\α}q\right(r\left)\right)---\left(4\right)$

In formula, $f\left(r\right)=\mathrm{\δ}\sqrt{{\mathrm{\α}}^2-{\mathrm{\β}}^2}+\mathrm{\β}(r-\mathrm{\μ}),q\left(r\right)=\sqrt{{\mathrm{\δ}}^2+(r^2-{\mathrm{\μ}}^2)},$ K₁() be index be the of 1 The Bessel function of two class corrections；Parameter r, α, β, μ, δ are respectively noise-free picture two-dimensional discrete shearlet conversion coefficient, spy Levy the factor, the deflection factor, shift factor and scale factor, when the deflection factor is zero, be distributed as symmetrical；For decomposing Rear image coefficient is the most symmetrical, it is assumed that parameter beta in NIG, and μ is zero, then the probability density function for NIG be reduced to as Shown in formula (5):

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}\exp \left(\mathrm{\α}\mathrm{\δ}\right)}{\mathrm{\π}}\frac{K_1\left(\mathrm{\α}\sqrt{r^2+{\mathrm{\δ}}^2}\right)}{\sqrt{r^2+{\mathrm{\δ}}^2}}---\left(5\right)$

The shearlet coefficient of the speckle noise described in Tong ShiObedience zero-mean gaussian is distributed, as shown in formula (6):

$P_n\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{2{\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula_nFor the standard deviation of noise in transform domain, parameter n is speckle noise image.

Described step 3) particularly as follows: in shearlet conversion denoising, the selection of threshold function table can directly influence Whole image denoising result.When threshold value selects less, a part can be taken as useful signal more than the noise coefficient of this threshold value Remaining, still there is much noise in the image after this results in denoising；When threshold value selects bigger, can by a lot of coefficients very The zero setting as noise of little useful information, the image after this will make denoising becomes the most smooth, loses a lot of detailed information.Cause This selects appropriate threshold function table extremely important.

Classical contraction method has Soft thresholding and hard threshold method, but in Soft thresholding, bigger shearlet system Number is always reduced by threshold value, and the mathematic expectaion of the signal after therefore shrinking is different from before contraction, so the image phase after Chu Liing To smooth.The shortcoming of hard threshold method be the shearlet coefficient near null value territory by unexpected zero setting, result in data Discontinuity, and this makes the variance of signal bigger, and these conversion affect bigger for the details in image.But in reality In the application of border, when particularly noise level is the highest, the image after hard threshold method processes can produce concussion, shadow around discontinuity point Ring the denoising effect of image.

Donoho et al. proposes a kind of typical Research on threshold selection, and demonstrates this threshold value and noise theoretically Standard deviation be directly proportional, change threshold function table and be also called uniform threshold function, its formula is as follows

$T={\mathrm{\σ}}_n\sqrt{2logM}---\left(7\right)$

Wherein, M is i.e. the overall number of correspondent transform territory internal conversion coefficient, σ_nIt it is the standard deviation of noise.In this threshold value In function, threshold value T is affected relatively big by the number of conversion coefficient, and i.e. when M is excessive, bigger threshold value may smooth out those and be The useful information that number is less.

On the basis of formula (7), the present invention proposes the threshold function table of a kind of applicable ultrasonoscopy, formula such as formula (8) Shown in:

$T_j=t_j{\mathrm{\σ}}_n\sqrt{2logM}---\left(8\right)$

Wherein, σ_nIt is the standard deviation of noise, t_jRepresent the auto-adaptive parameter of j layer.This is kind of the side that common threshold value is improved Method, t_jChoose according to experiment determine, shearlet decompose after, different layers decompose conversion coefficient have different Distribution, thus t_jSelect selection based on j layer.In the present invention, decompose 5 layers, for 512x512 image, according to (7) (8) Formula, threshold value T ≈ 5 σ_n, can reduce risks owing to reducing threshold value, improve denoising effect, fine dimension is taken T ≈ 4 σ_n, remaining Take T ≈ 3 σ_n。

In shearlet conversion denoising method, first select a given threshold value, then according to certain rule is right Shearlet coefficient shrinks, and just completes the denoising to shearlet coefficient.I.e. giving a threshold value, all absolute values are little Coefficient in this threshold value is taken as noise, then it is made zero setting and processes；Absolute value is more than the shearlet coefficient of threshold value Reduce by certain method, the new value after then being reduced.

Described step 4) particularly as follows: utilize quick two-sided filter that the shearlet coefficient in low frequency part is filtered Process.

Two-sided filter is when processing picture noise, and on the one hand it has the strongest noise removal capability, has the most smooth Effect；On the other hand can retain image edge details, this is particular importance in medical ultrasonic image is applied.But due to bilateral Filtering is nonlinear, it is impossible to realize linearity convolutional calculation, and bilateral filtering is the most time-consuming, it is difficult to for real-time system.With The resolution image is increasing, which greatly limits the application space of bilateral filtering, the most quickly realizes double Limit filters, and the minimizing calculating time has great significance in actual applications.

Quickly two-sided filter is known as again increasing d type two-sided filter, plus input on the basis of original two-dimensional coordinate The pixel value composition three dimensions of image, structure three-dimensional Gaussian kernel function carries out linear convolution calculating with 3-D view function, connects Get off just can utilize fast Fourier transform to calculate and replace traditional node-by-node algorithm, thus improve the speed of computing.

AssumeThe three-dimensional image matrix that representing input images I obtains after increasing dimension,Represent three-dimensional weight matrix, then the structure of quick two-sided filter is as shown in Equation 9:

$BI(x,y)=\frac{IY(x,y)}{EY(x,y)}=\frac{\mathrm{int}erp(G\⊗IX,\frac{x}{s_s},\frac{y}{s_s},\frac{I(x,y)}{s_r})}{\mathrm{int}erp(G\⊗EX,\frac{x}{s_s},\frac{y}{s_s},\frac{I(x,y)}{s_r})}---\left(9\right)$

In formula, (x, y) is the coordinate of input image pixels point,Representing the linear convolution of matrix, interp is interpolation letter Number, major function is rightWithInterpolation arithmetic is carried out to obtain in coordinate three dimensionsOn value, then result is assigned to IY (x, y) and EY (x, y).G is the spatial neighbor degree factor after linearisation G_sWith gray scale similarity factor G_rProduct, i.e. gaussian kernel function.Amount of calculation can be accordingly increased after increasing dimension, so should Method uses the mode of down-sampling to improve computational efficiency, wherein s_sRepresent spatial domain sample rate, s_rRepresent the sampling of pixel codomain Rate, this is just divided into several space sizes three-dimensional matrice is its s_s×s_s×s_rLittle three dimensions.Increase number in dimension matrix Reduce as well as the raising of sample rate according to the size of amount, so the data participating in convolutional calculation after down-sampling can be big Big minimizing, thus reach to reduce the purpose of operation time.

First by three-dimensional matrice IX and EX distribution and three-dimensional height from formula (9) it can be seen that in quick two-sided filter This kernel function carries out linear convolution operation, obtain after then the two filter result being carried out linear interpolation two-dimensional matrix IY and EY, obtains the image BI after denoising after finally IY being carried out division arithmetic to EY.Down-sampling, convolution meter is used in three dimensions The computings such as calculation and interpolation can quickly realize numerical solution.For noisy image, utilize two-sided filter and quick two-sided filter Carry out filtration treatment respectively.Two-sided filter and quick two-sided filter do not have the biggest difference on denoising effect, make an uproar in removal Marginal information can be effectively maintained while sound, but at time-consuming aspect, the latter performs better than than the former and is well positioned to meet The real-time system requirement to rapidity.

Described step 5) particularly as follows: after threshold value shrink process and the process of quick two-sided filter can be obtained by denoising The whole coefficient of shearlet, in order to obtain the ultrasonoscopy after denoising, need that shearlet coefficient is carried out shearlet inverse Conversion, such that it is able to obtain the image after the denoising that beneficially doctor analyzes, also demonstrating the present invention by experiment can expire really Foot is for the requirement of medical ultrasound image denoising.

The invention has the beneficial effects as follows: shearlet of the present invention conversion have multiresolution, directivity, locality, respectively to The opposite sex, is the expression that image is the most sparse, and is widely used in image processing field.When processing one-dimensional problem, The denoising effect of small echo is preferable, it is possible to meet general product demand, but for higher-dimension problem, just with wavelet transformation Denoising method is bad to the inhibition of speckle noise in medical ultrasonic image.But, merely with the denoising of shearlet conversion Algorithm is not fine to the inhibition of speckle noise in medical ultrasonic image, this is because shearlet filters for high-frequency domain Noise denoising effect preferable, and speckle noise equally exists in lower frequency region.Quickly two-sided filter, it is made an uproar at process image During sound, on the one hand having the strongest noise removal capability, on the other hand can keep image edge details, i.e. quickly two-sided filter exists Process image lower frequency region signal preferable.Therefore the present invention utilize shearlet conversion replace wavelet transformation to process high frequency problem, Shearlet conversion presents the direction characteristic different from traditional wavelet, and the rarefaction representation of image is made shearlet There is more preferable localization property and the strongest directional sensitivity, the most more preferable slickness and multiresolution analysis ability, simultaneously Its good Decay Rate can obtain the more preferable wave filter of filtering performance.For two-sided filter, process low frequency problem.Specifically Thinking is as follows: the principle converted according to shearlet and ultrasonoscopy and the statistical property of speckle noise, uses new threshold value Method, carries out multiple dimensioned and multi-direction decomposition, produces high-frequency sub-band and low frequency sub-band, can be more effectively by shearlet conversion Remove the speckle noise of HFS；Then the quick two-sided filter by proposing removes low-frequency noise.

The defect that the one aspect of the present invention wavelet transformation to using in the past exists, process higher-dimension problem only with level, Vertically, the restriction in three directions such as diagonal angle, it is proposed that there is the shearlet conversion of decomposition multiple dimensioned, multi-direction, improve Make an uproar effect；On the other hand, owing to the present invention utilizes quick two-sided filter that low frequency part carried out filtration treatment, therefore for The speckle noise (being present in low frequency part) that granule is bigger has the strongest rejection ability equally.So it is the most double in the present invention The introducing of limit wave filter can not only well improve the performance of denoising and substantially increase the efficiency of process.It is simultaneous for medical science The feature of ultrasonoscopy, the method for this combination can not only well suppress speckle noise, can also retain in image sick simultaneously The detail section of range edge etc., can preferably help doctor to carry out illness analysis.

Accompanying drawing explanation

Fig. 1 is the flow chart of steps of the present invention；

Fig. 2 is the experiment schematic diagram in embodiment 1；

Fig. 3 is the experiment simulation noise-free picture in embodiment 1；

Fig. 4 is the experiment simulation noise image in embodiment 1；

Fig. 5 is the ridgelet transform figure of the denoising effect of emulating image in embodiment 1；

Fig. 6 is the warp wavelet figure of the denoising effect of emulating image in embodiment 1；

Fig. 7 is the profile wave convert figure of the denoising effect of emulating image in embodiment 1；

The wavelet transformation of the denoising effect of emulating image and bilateral figure in Fig. 8 embodiment 1；

The shearlet Transformation Graphs of the denoising effect of emulating image in Fig. 9 embodiment 1；

Figure 10 is the shearlet conversion of the denoising effect of emulating image in embodiment 1 and quick bilateral figure；

Figure 11 is liver clinical ultrasound image in embodiment 1；

Figure 12 is the ridgelet transform figure going dry effect of liver clinical ultrasound image in embodiment 1；

Figure 13 is the warp wavelet figure going dry effect of liver clinical ultrasound image in embodiment 1；

Figure 14 is the profile wave convert figure going dry effect of liver clinical ultrasound image in embodiment 1；

Figure 15 is the wavelet transformation going dry effect of liver clinical ultrasound image in embodiment 1 and bilateral figure；

Figure 16 is the shearlet Transformation Graphs going dry effect of liver clinical ultrasound image in embodiment 1；

Figure 17 is the shearlet conversion going dry effect of liver clinical ultrasound image in embodiment 1 and quick bilateral figure；

Table 1 is the denoising performance comparison sheet of six big algorithms in embodiment 1.

Detailed description of the invention

Embodiment 1

As it is shown in figure 1, a kind of shearlet conversion of the present embodiment and quick two-sided filter image de-noising method, such as figure Shown in 1, comprise the following steps:

1) utilize the envelope signal of noise imaging system acquisition noise image, by logarithmic transformation, set up medical ultrasonic figure As model；Two-dimensional discrete shearlet coefficient, described two-dimensional discrete is obtained after two-dimensional discrete shearlet converts Shearlet coefficient includes noise-free picture two-dimensional discrete shearlet coefficient and the discrete shearlet of speckle noise two-dimensional image Coefficient；

2) to described step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes pyramid filter group Carry out multiple dimensioned multi-direction decomposition, obtain k+1 and the equal-sized sub-band images of medical ultrasonic image model, described subband Image includes a low frequency part and K HFS, utilizes step 1) the two-dimensional discrete shearlet coefficient that obtains releases height The two-dimensional discrete shearlet conversion coefficient of frequency part；

3) to described step 2) the two-dimensional discrete shearlet conversion of each sub-band images medium-high frequency part of obtaining Coefficient carries out threshold method shrink process；

4) quick two-sided filter is utilized to step 2) the shearlet coefficient of medium and low frequency part does Filtering Processing；

5) to through step 3) and step 4) process after all coefficients make shearlet inversion process, obtain the doctor after denoising Learn ultrasonoscopy.

Described step 1) particularly as follows: the factor that described ultrasonic image-forming system can affect acoustic power to those is made Appropriate dynamic compensation, the envelope signal of wherein said ultrasonic image-forming system collection includes the reflection of significant in-vivo tissue Signal and noise signal；Wherein said noise signal is divided into multiplicative noise and additive noise, and described multiplicative noise is with ultrasonic The principle of image formation is relevant, is mainly derived from random scattered signal, and described additive noise is system noise, main source Noise in sensor；Shown in the universal model model such as formula (1) of described envelope signal:

S (x, y)=r (x, y) n (x, y) (1)

Wherein said (x, y) the transverse and longitudinal coordinate of difference representative image, r (x, y) expression noise-free signal, n (x, y) expression Multiplicative noise；

Then the envelope signal collected described ultrasonic image-forming system carries out logarithmic compression process, to adapt to ultrasonic one-tenth As the Dynamic Announce scope of system display screen, i.e. by described formula (1) being become the model being added, as shown in formula (2):

Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)

Now, (s (x, y)) is medical ultrasonic image model to the signal log obtained；

Owing to wavelet transformation is linear transformation, shearlet conversion is the wavelet transformation expansion at higher-dimension, because of by institute Formula (2) model stated obtains shown in model such as formula (3) after two-dimensional discrete shearlet converts:

$\begin{array}{ccc}{S}_{l,k}^j=R_{l,k}^j+N_{l,k}^j& j=1,2,...,J.& (l,k)\∈Z^2\end{array}---\left(3\right)$

WhereinWithRepresent respectively containing the shearlet coefficient of noise image, noise-free picture The shearlet coefficient of shearlet coefficient and speckle noise；Wherein subscript j is the Decomposition order of shearlet conversion, subscript (l k) is the coordinate in transform domain.

Described step 2) particularly as follows: first to step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes Pyramid filter group carries out multiple dimensioned two-dimensional discrete shearlet and decomposes, and image, through k level sampling pyramid, obtains k+1 Sub-band images equal-sized with medical ultrasonic image model；Shearing and filtering device group is used to enter each scale subbands image obtained Line direction decomposes；The conversion coefficient without noise cancellation signal after two-dimensional discrete shearlet decomposesMeet normal state against Gaussian mode Type (NIG), mainly by a dead wind area and a Gauss distribution with different average, its probability distribution such as formula (4) institute Show:

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}}{\mathrm{\π}q\left(r\right)}\exp \left(f\right(r\left)\right)\·K_1\left(\mathrm{\α}q\right(r\left)\right)---\left(4\right)$

In formula,K₁() be index be the of 1 The Bessel function of two class corrections；Parameter r, α, β, μ, δ are respectively noise-free picture two-dimensional discrete shearlet conversion coefficient, spy Levy the factor, the deflection factor, shift factor and scale factor, when the deflection factor is zero, be distributed as symmetrical；For decomposing Rear image coefficient is the most symmetrical, it is assumed that parameter beta in NIG, and μ is zero, then the probability density function for NIG be reduced to as Shown in formula (5):

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}\exp \left(\mathrm{\α}\mathrm{\δ}\right)}{\mathrm{\π}}\frac{K_1\left(\mathrm{\α}\sqrt{r^2+{\mathrm{\δ}}^2}\right)}{\sqrt{r^2+{\mathrm{\δ}}^2}}---\left(5\right)$

The shearlet coefficient of the speckle noise described in Tong ShiObedience zero-mean gaussian is distributed, as shown in formula (6):

$P_n\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{2{\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula_nFor the standard deviation of noise in transform domain, parameter n is speckle noise image.

Described step 3) particularly as follows: in shearlet conversion denoising, the selection of threshold function table can directly influence Whole image denoising result.When threshold value selects less, a part can be taken as useful signal more than the noise coefficient of this threshold value Remaining, still there is much noise in the image after this results in denoising；When threshold value selects bigger, can by a lot of coefficients very The zero setting as noise of little useful information, the image after this will make denoising becomes the most smooth, loses a lot of detailed information.Cause This selects appropriate threshold function table extremely important.

Classical contraction method has Soft thresholding and hard threshold method, but in Soft thresholding, bigger shearlet system Number is always reduced by threshold value, and the mathematic expectaion of the signal after therefore shrinking is different from before contraction, so the image phase after Chu Liing To smooth.The shortcoming of hard threshold method be the shearlet coefficient near null value territory by unexpected zero setting, result in data Discontinuity, and this makes the variance of signal bigger, and these conversion affect bigger for the details in image.But in reality In the application of border, when particularly noise level is the highest, the image after hard threshold method processes can produce concussion, shadow around discontinuity point Ring the denoising effect of image.

Donoho et al. proposes a kind of typical Research on threshold selection, and demonstrates this threshold value and noise theoretically Standard deviation be directly proportional, change threshold function table and be also called uniform threshold function, its formula is as follows

$T={\mathrm{\σ}}_n\sqrt{2logM}---\left(7\right)$

Wherein, M is i.e. the overall number of correspondent transform territory internal conversion coefficient, σ_nIt it is the standard deviation of noise.In this threshold value In function, threshold value T is affected relatively big by the number of conversion coefficient, and i.e. when M is excessive, bigger threshold value may smooth out those and be The useful information that number is less.

On the basis of formula (7), the present invention proposes the threshold function table of a kind of applicable ultrasonoscopy, formula such as formula (8) Shown in:

$T_j=t_j{\mathrm{\σ}}_n\sqrt{2logM}---\left(8\right)$

Wherein, σ_nIt is the standard deviation of noise, t_jRepresent the auto-adaptive parameter of j layer.This is kind of the side that common threshold value is improved Method, t_jChoose according to experiment determine, shearlet decompose after, different layers decompose conversion coefficient have different Distribution, thus t_jSelect selection based on j layer.In the present invention, decompose 5 layers, for 512x512 image, according to (7) (8) Formula, threshold value T ≈ 5 σ_n, can reduce risks owing to reducing threshold value, improve denoising effect, fine dimension is taken T ≈ 4 σ_n, remaining Take T ≈ 3 σ_n。

In shearlet conversion denoising method, first select a given threshold value, then according to certain rule is right Shearlet coefficient shrinks, and just completes the denoising to shearlet coefficient.I.e. giving a threshold value, all absolute values are little Coefficient in this threshold value is taken as noise, then it is made zero setting and processes；Absolute value is more than the shearlet coefficient of threshold value Reduce by certain method, the new value after then being reduced.

Described step 4) particularly as follows: utilize quick two-sided filter that the shearlet coefficient in low frequency part is filtered Process.

Two-sided filter is when processing picture noise, and on the one hand it has the strongest noise removal capability, has the most smooth Effect；On the other hand can retain image edge details, this is particular importance in medical ultrasonic image is applied.But due to bilateral Filtering is nonlinear, it is impossible to realize linearity convolutional calculation, and bilateral filtering is the most time-consuming, it is difficult to for real-time system.With The resolution image is increasing, which greatly limits the application space of bilateral filtering, the most quickly realizes double Limit filters, and the minimizing calculating time has great significance in actual applications.

Quickly two-sided filter is known as again increasing d type two-sided filter, plus input on the basis of original two-dimensional coordinate The pixel value composition three dimensions of image, structure three-dimensional Gaussian kernel function carries out linear convolution calculating with 3-D view function, connects Get off just can utilize fast Fourier transform to calculate and replace traditional node-by-node algorithm, thus improve the speed of computing.

AssumeThe three-dimensional image matrix that representing input images I obtains after increasing dimension,Represent three-dimensional weight matrix, then the structure of quick two-sided filter is as shown in Equation 9:

$BI(x,y)=\frac{IY(x,y)}{EY(x,y)}=\frac{\mathrm{int}erp(G\⊗IX,\frac{x}{s_s},\frac{y}{s_s},\frac{I(x,y)}{s_r})}{\mathrm{int}erp(G\⊗EX,\frac{x}{s_s},\frac{y}{s_s},\frac{I(x,y)}{s_r})}---\left(9\right)$

In formula, (x, y) is the coordinate of input image pixels point,Representing the linear convolution of matrix, interp is interpolation letter Number, major function is rightWithInterpolation arithmetic is carried out to obtain in coordinate three dimensionsOn value, then result is assigned to IY (x, y) and EY (x, y).G is the spatial neighbor degree factor after linearisation G_sWith gray scale similarity factor G_rProduct, i.e. gaussian kernel function.Amount of calculation can be accordingly increased after increasing dimension, so should Method uses the mode of down-sampling to improve computational efficiency, wherein s_sRepresent spatial domain sample rate, s_rRepresent the sampling of pixel codomain Rate, this is just divided into several space sizes three-dimensional matrice is its s_s×s_s×s_rLittle three dimensions.Increase number in dimension matrix Reduce as well as the raising of sample rate according to the size of amount, so the data participating in convolutional calculation after down-sampling can be big Big minimizing, thus reach to reduce the purpose of operation time.

First by three-dimensional matrice IX and EX distribution and three-dimensional height from formula (9) it can be seen that in quick two-sided filter This kernel function carries out linear convolution operation, obtain after then the two filter result being carried out linear interpolation two-dimensional matrix IY and EY, obtains the image BI after denoising after finally IY being carried out division arithmetic to EY.Down-sampling, convolution meter is used in three dimensions The computings such as calculation and interpolation can quickly realize numerical solution.For noisy image, utilize two-sided filter and quick two-sided filter Carry out filtration treatment respectively.Two-sided filter and quick two-sided filter do not have the biggest difference on denoising effect, make an uproar in removal Marginal information can be effectively maintained while sound, but at time-consuming aspect, the latter performs better than than the former and is well positioned to meet The real-time system requirement to rapidity.

Described step 5) particularly as follows: after threshold value shrink process and the process of quick two-sided filter can be obtained by denoising The whole coefficient of shearlet, in order to obtain the ultrasonoscopy after denoising, need that shearlet coefficient is carried out shearlet inverse Conversion, such that it is able to obtain the image after the denoising that beneficially doctor analyzes, also demonstrating the present invention by experiment can expire really Foot is for the requirement of medical ultrasound image denoising.

Experimental verification

In order to evaluate the denoising method that the present invention proposes objectively, with Y-PSNR (PSNR), structural similarity (SSIM), FoM (Pratt ' s Figure of Merit) and running time T ime are as image quality evaluation standard.Peak value is believed Make an uproar than computing formula such as formula (10) shown in:

$PSNR(X,\hat{X})=10lg\left(\frac{{255}^2}{MSE}\right)---\left(10\right)$

In formula,For the estimated value of signal X, MSE is calculated as shown in formula (11) by formula below:

Here M, N represent length and the width of 2D signal X respectively.

Structural similarity can quantify two width images difference structurally, and formula defines as shown in formula (12):

$SSIM(X,\hat{X})=\frac{(2{\mathrm{\μ}}_X{\mathrm{\μ}}_{\hat{X}}+c_1)(2{\mathrm{\σ}}_{X,\hat{X}}+c_2)}{({\mathrm{\μ}}_X^2+{\mathrm{\μ}}_{\hat{X}}^2+c_1)({\mathrm{\σ}}_X^2+{\mathrm{\σ}}_{\hat{X}}^2+c_2)}---\left(12\right)$

In formula, μ_X、WithIt is reference picture and average and the variance estimating image respectively.Be X and Covariance, c₁And c₂For constant.Work as c₁And c₂When being all chosen as positive number, the span of SSIM is [01], and wherein 1 is best As a result, represent that the structure of two width figures is identical.

FoM can compare the rim detection quality of denoising image objectively, and formula defines as shown in formula (13):

$FoM(X,\hat{X})=\frac{1}{max(N_X,N_{\hat{X}})}\underset{i=1}{\overset{N_X}{\Σ}}\frac{1}{1+{\mathrm{\αd}}_i^2}---\left(13\right)$

In formula, N_XWithRepresent the preferable and actually detected edge pixel number arrived respectively.α be constant (generally take α= 1/9), d_iIt is expressed as the i-th edge pixel point distance to nearest ideal edge pixel.The span of FoM is [0 1], its In 1 be best result, the image border being expressed as detecting is consistent with preferable image border.Here make during detection of edge pixels Be Canny detection algorithm (standard deviation value σ=3 of Gaussian filter).

In the present embodiment, in order to make the present invention more convincing and more preferably represent its advantage, not only experiment is divided into two Individual part, one is speckle noise emulation experiment, and another is real clinical medicine ultrasonoscopy (liver image)；But also do With the contrast experiment of other 5 kinds of classical ways, and combine above-mentioned four kinds of quantizating index and clearly evaluate the excellent of the present invention Gesture, experiment schematic diagram is as shown in Figure 2；

In order to enable to verify more quantitatively and intuitively the superiority of the present embodiment, first by analogous diagram (such as Fig. 3 for emulation without making an uproar figure Picture, size 400 × 400；Fig. 4 is simulator and noise image, speckle noise variances sigma²Shown in=0.1) experiment, to classic algorithm pair Ratio, respectively ridgelet (ridgelet transform), curvelet (warp wavelet), contourlet (profile wave convert), small echo become Change and convert with the most bilateral with bilateral, shearlet conversion, shearlet.Experimental result is shown in as shown in Figure 5-10, six big algorithms Denoising performance compare, i.e. contrast index value see as shown in table 1.As can be seen from Table 1, the present invention is at FOM, PSNR, SSIM The data that middle acquisition is optimal, go up to be improved at runtime.

Recycling clinical ultrasound image carries out verification experimental verification, and selection is the liver clinical ultrasound image such as Figure 11.Experiment Result is as shown in Figure 12-17.

Can intuitively be found out by above quantitative data, the inventive method is being applied to process and the knot of medical ultrasonic image Fruit is exactly the same with during emulating image with application, and not only denoising effect is significantly improved, and preferably retains image limit Edge information, thus reach the medical ultrasonic image requirement for denoising.

Table 1

Claims (6)

1. a shearlet conversion and quick two-sided filter image de-noising method, it is characterised in that comprise the following steps:

1) utilize the envelope signal of noise imaging system acquisition noise image, by logarithmic transformation, set up medical ultrasonic image mould Type；Two-dimensional discrete shearlet coefficient is obtained, described two-dimensional discrete shearlet system after two-dimensional discrete shearlet converts Number includes noise-free picture two-dimensional discrete shearlet coefficient and speckle noise two-dimensional image discrete shearlet coefficient；

2) to described step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes pyramid filter group to carry out Multiple dimensioned multi-direction decomposition, obtains k+1 and the equal-sized sub-band images of medical ultrasonic image model, described sub-band images Including a low frequency part and K HFS, utilizing step 1) the two-dimensional discrete shearlet coefficient that obtains releases radio-frequency head The two-dimensional discrete shearlet conversion coefficient divided；

3) to described step 2) the two-dimensional discrete shearlet conversion coefficient of each sub-band images medium-high frequency part that obtains Carry out threshold method shrink process；

4) quick two-sided filter is utilized to step 2) the shearlet coefficient of medium and low frequency part does Filtering Processing；

5) to through step 3) and step 4) process after all coefficients make shearlet inversion process, obtain the medical science after denoising and surpass Acoustic image.

2. a kind of shearlet conversion as claimed in claim 1 and quick two-sided filter image de-noising method, its feature exists In, described step 1) particularly as follows: the factor that first described ultrasonic image-forming system can affect acoustic power to those is made Appropriate dynamic compensation, the envelope signal of wherein said ultrasonic image-forming system collection includes the reflection of significant in-vivo tissue Signal and noise signal；Wherein said noise signal is divided into multiplicative noise and additive noise, described envelope signal general Model defines as shown in formula (1):

S (x, y)=r (x, y) n (x, y) (1)

It is wherein said that (x, y) the transverse and longitudinal coordinate of representative image respectively, (x, y) represents noise-free signal to r, and (x y) represents and is multiplied n Noise；

Then the envelope signal collected described ultrasonic image-forming system carries out logarithmic compression process, to adapt to ultra sonic imaging system The Dynamic Announce scope of system display screen, i.e. by described formula (1) being become the model being added, as shown in formula (2):

Log (s (x, y))=log (r (x, y))+log (n (x, y)) (2)

Now, (s (x, y)) is medical ultrasonic image model to the signal log obtained；

Again formula (2) model is obtained shown in model such as formula (3) after two-dimensional discrete shearlet converts:

$\begin{array}{ccc}{S}_{l,k}^j=R_{l,k}^j+N_{l,k}^j& j=1,2,...,J.& (l,k)\∈Z^2\end{array}---\left(3\right)$

WhereinWithRepresent respectively containing the shearlet coefficient of noise image, the shearlet of noise-free picture The shearlet coefficient of coefficient and speckle noise；Wherein subscript j is the Decomposition order of shearlet conversion, and (l, k) for becoming for subscript Change the coordinate in territory.

3. a kind of shearlet conversion as claimed in claim 1 and quick two-sided filter image de-noising method, its feature exists In, described step 2) particularly as follows: first to step 1) medical ultrasonic image model after the logarithmic transformation that obtains utilizes gold word Tower bank of filters carries out multiple dimensioned two-dimensional discrete shearlet and decomposes, and image, through k level sampling pyramid, obtains k+1 and doctor Learning the equal-sized sub-band images of ultrasonoscopy model, described sub-band images includes a low frequency part and K HFS； Shearing and filtering device group travel direction is used to decompose each scale subbands image obtained；After two-dimensional discrete shearlet decomposes The conversion coefficient without noise cancellation signalMeet normal state against Gauss model (NIG), mainly had by a dead wind area and one The Gauss distribution of different averages, shown in its probability distribution such as formula (4):

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}}{\mathrm{\π}q\left(r\right)}\exp \left(f\right(r\left)\right)\·K_1\left(\mathrm{\α}q\right(r\left)\right)---\left(4\right)$

In formula,K₁() be index be 1 Equations of The Second Kind The Bessel function revised；Parameter r, α, β, μ, δ be respectively noise-free picture two-dimensional discrete shearlet conversion coefficient, feature because of Son, the deflection factor, shift factor and scale factor, when the deflection factor is zero, be distributed as symmetrical；For scheming after decomposing As coefficient is the most symmetrical, it is assumed that parameter beta in NIG, μ is zero, then the probability density function for NIG is reduced to such as formula (5) shown in:

$p_r\left(r\right)=\frac{\mathrm{\α}\mathrm{\δ}\exp \left(\mathrm{\α}\mathrm{\δ}\right)}{\mathrm{\π}}\frac{K_1\left(\mathrm{\α}\sqrt{r^2+{\mathrm{\δ}}^2}\right)}{\sqrt{r^2+{\mathrm{\δ}}^2}}---\left(5\right)$

The shearlet coefficient of the speckle noise described in Tong ShiObedience zero-mean gaussian is distributed, as shown in formula (6):

$P_n\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{2{\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula_nFor the standard deviation of noise in transform domain, parameter n is speckle noise image.

4. a kind of shearlet conversion as claimed in claim 1 and quick two-sided filter image de-noising method, its feature exists In, described step 3) particularly as follows: the threshold function table of described applicable ultrasonoscopy, shown in formula such as formula (8):

$T_j=t_j{\mathrm{\σ}}_n\sqrt{2\log M}---\left(8\right)$

Wherein, M is i.e. the overall number of correspondent transform territory internal conversion coefficient, σ_nIt is the standard deviation of noise, σ_nIt it is the standard of noise Difference, t_jRepresent the auto-adaptive parameter of j layer；t_jSelect selection based on j layer；In shearlet conversion denoising method, first select A fixed given threshold value, then according to shearlet coefficient is shunk by certain rule, just completes shearlet system The denoising of number.

5. a kind of shearlet conversion as claimed in claim 1 and quick two-sided filter image de-noising method, its feature exists In, described step 4) particularly as follows: utilize quick two-sided filter that the shearlet coefficient in low frequency part is done Filtering Processing； I.e. utilize fast Fourier transform to calculate and replace traditional node-by-node algorithm, thus improve the speed of computing；AssumeThe three-dimensional image matrix that representing input images I obtains after increasing dimension,Represent three-dimensional weight matrix, then the structure of quick two-sided filter is as shown in Equation 9:

$BI\left(x,y\right)=\frac{IY\left(x,y\right)}{EY\left(x,y\right)}=\frac{\mathrm{int}erp\left(G\⊗IX,\frac{x}{s_s},\frac{y}{s_s},\frac{I\left(x,y\right)}{s_r}\right)}{\mathrm{int}erp\left(G\⊗EX,\frac{x}{s_s},\frac{y}{s_s},\frac{I\left(x,y\right)}{s_r}\right)}---\left(9\right)$

In formula, (x, y) is the coordinate of input image pixels point,Representing the linear convolution of matrix, interp is interpolating function, main It is right for wanting functionWithInterpolation arithmetic is carried out to obtain in coordinate three dimensionsOn Value, then result is assigned to IY (x, y) and EY (x, y)；G is spatial neighbor degree factor G after linearisation_sWith gray scale similarity because of Sub-G_rProduct, i.e. gaussian kernel function；Amount of calculation can be accordingly increased after increasing dimension, use down-sampling in this way Mode improves computational efficiency, wherein s_sRepresent spatial domain sample rate, s_rRepresenting pixel codomain sample rate, this is just three-dimensional matrice Being divided into several space sizes is its s_s×s_s×s_rLittle three dimensions.

6. a kind of shearlet conversion as claimed in claim 1 and quick two-sided filter image de-noising method, its feature exists In, described step 5) particularly as follows: after threshold value shrink process and trilateral filter process can be obtained by denoising Shearlet coefficient, in order to obtain the ultrasonoscopy after denoising, needs shearlet coefficient is carried out shearlet inverse transformation, from And the image after the denoising that beneficially doctor analyzes can be obtained.