CN104657942A - Medical ultrasound image noise reduction method based on thresholding improved wavelet transform and guide filter - Google Patents

Abstract

The invention relates to a medical ultrasound image noise reduction method based on thresholding improved wavelet transform and guide filter. The medical ultrasound image noise reduction method based on thresholding improved wavelet transform and guide filter comprises the following steps: step one, establishing a medical ultrasound image model; step two, carrying out wavelet decomposition on images after logarithmic transformation obtained in the first step to obtain four frequency domains (LL1, LH1, HL1 and HH1); carrying out wavelet decomposition on the low frequency domain LL1, and then obtaining four frequency domains (LL2, LH2, HL2 and HH2); then repeating the step until the maximum number of layers J is decomposed; step three, carrying out threshold value method shrinkage treatment on wavelet coefficients of high frequency parts (LHj, HLj and HHj, j is equal to 1, 2,..., J) on each layer; step four, carrying out filtering processing on wavelet coefficients of low frequency part (LLJ) on the last layer by utilizing the guide filter; step five, carrying out wavelet inverse transformation to obtain medical ultrasound images after noise reduction.

Description

Based on improving the wavelet transformation of threshold value and guiding the medical ultrasound image denoising method of wave filter

Technical field

The present invention is applied to medical ultrasonic figurepicture denoising field.

Background technology

At medical imaging field, the imaging technique such as ultrasonic imaging, CT, MRI has been applied in medical clinic applications.Because ultrasonic imaging technique has without wound, "dead" infringement, the characteristic such as efficient and convenient, therefore ultrasonic imaging technique has become a kind of widespread use and the high medical diagnostic techniqu of security.Especially, in observation pregnant woman body in the clinical practice such as fetus growth situation and diagnosis of abdominal organ lesion, the use of ultrasonic imaging technique is even more important.

Gave a women the statistics suffered from breast cancer according to American Cancer Society in 2013, in the past year, have in American Women 232340 example new breast cancer case and 39620 people die from breast cancer.The major technique carrying out detecting for the mammary gland of human body and other organs of belly is ultrasonic imaging technique, namely usually said B ultrasonic figurepicture.Therefore medical ultrasonic is improved figurepicture element amount, for doctor provides more clear muting figurepicture has very important significance.

Due to the restriction of ultrasonic imaging mechanism, the existence of speckle noise has a strong impact on ultrasonic figurethe quality of picture, result in ultrasonic figureas second-rate.The generation of speckle noise is the unevenness because the institutional framework of human organ has, and causes ultrasound wave can not differentiate the smaller institutional framework of volume; The wavelength of incident ultrasound wave is all generally fixing simultaneously, scattering phenomenon is there is when the size of human tissue structure is close with it or be less than its wavelength, scatter echo has the therefore easily interference mutually of different phase places, thus creates speckle noise, and it is very little by covering those gray scale difference figurepicture feature.Due to the difference of ultrasonic image-forming system, thus make the scattering situation that occurs in cell resolution when imaging different, therefore the probability distribution situation of final speckle noise is also different, and speckle noise can be considered to Rayleigh distributed, and this is a kind of conventional model.For clinician, the Accurate Diagnosis of speckle noise to them causes very large interference, is not particularly that the impact that very abundant doctor causes is larger for experience.Therefore, from the angle of clinical practice, need research to remove the method for speckle noise, provide technical support for doctor makes diagnosis more accurately, reduce the risk of Artificial Diagnosis.

Due to the limitation of hospital resources, the quantity that particularly doctor carries out Artificial Diagnosis patient every day cannot meet the demand of social whole stratum, is namely faced with the few situation of the many doctors of patient.Therefore, the demand of various automatic diagnosis instrument is increasing, the appearance of automatic diagnosis instrument, can save doctor's resource on the one hand, more patient can be facilitated to diagnose on the other hand.Along with developing by leaps and bounds of society economy, people's own health situation but allows of no optimist, so the demand of people to domestic type medical treatment automatic diagnosis instrument is also very large, and such as domestic ultrasound figurepicture automatic diagnostic instrument etc.But it is ultrasonic figurebe faced with equally as automatic diagnostic instrument figureas problem of low quality, and automatic diagnostic instrument needs ultrasonic figurepicture does the intellectual analysis in later stage, as feature extraction, rim detection and figurepicture Classification and Identification etc.Therefore, from the angle of automated diagnostic technology, need research to remove the method for speckle noise, for figurethe later stage Intelligent treatment of picture provides technical guarantee, promotes the development of automatic diagnostics.

In sum, Research of Medical is ultrasonic figurehave very important significance as denoising method:

(1) medical ultrasonic is improved figurethe quality of picture, improves visual effect;

(2) facilitate doctor to judge for focal area more exactly, reduce the risk of auxiliary diagnosis;

(3) promote ultrasonic figurethe development of picture automated diagnostic technology, has immeasurable value.

In numeral figurepicture process field, filtering is commonly used to amendment or strengthens figurepicture, right figuresome feature of picture, as profile, edge, details and contrast etc. carry out sharpening, improves figurethe visual quality of picture, so that observe better figurepicture or carry out next step analyzing and processing, particularly at medical ultrasonic figurewhat become in the process of picture is particularly important.The ultimate principle of filtering be by figureseveral pixels that each pixel in picture is adjacent make neighborhood operation, are namely weighted average convolution algorithm.Owing to suppressing speckle noise to have very important significance, numerous researcher has dropped into a large amount of energy in this problem.The method of current denoising is mainly divided into filter in spatial domain and the large class of frequency filtering two.In Space domain, directly process figurepicture pixel, carries out operation to pixel value and reaches figurethe object of picture denoising.Common are mean filter and medium filtering etc., but work as figurewhen picture exists obvious marginal information, common neighborhood operation can change figurethe gray-scale value of picture marginal point, thus make figurethe edge of picture thickens.So the two-sided filter of Retain edge information very well everybody accreditation can be obtained, but due to two-sided filter computational complexity higher and there is " gradient reversion " phenomenon, the requirement of real-time of medical ultrasonic imaging system can not be met.So the people such as He proposed the concept guiding wave filter in 2010, greatly improve the performance (according to concept, two-sided filter also belongs to the category guiding wave filter) of denoising.In frequency field method, first will figurepicture is transformed in frequency field, namely right figurepicture carries out Fourier transform, figurethe Fourier transform of picture carries out filtering operation, more right figurepicture carries out inverse Fourier transform, obtains final figurepicture.In frequency field method, the denoising method based on wavelet transformation obtains general application, makes full use of correlativity between yardstick, maintains preferably figurepicture edge.

Summary of the invention

The present invention will overcome prior art can not take into account noise removal capability and maintenance figurethe shortcoming of picture edge details, provides a kind of based on improving the wavelet transformation of threshold value and guiding the medical ultrasonic of wave filter figurepicture denoising method.

The present invention to analyze in ongoing frequency territory and denoising method in spatial domain, and the feature of the model of nexus spot noise and medical ultrasonic figurethe processing demands of picture proposes a kind of new denoising method, by the wavelet filtering improved and the method guiding filtering to combine.Wavelet transformation has the superiority such as time frequency analysis and multiscale analysis, and it exists figurebe widely used as process field.When processing additive noise problem, the denoising effect of small echo is better, can meet common product demand.But, only utilize the denoising method of wavelet transformation to medical ultrasonic figurein picture, the inhibition of speckle noise is bad.For guiding wave filter, it is in process figureduring picture noise, on the one hand there is very strong noise removal capability, can keep on the other hand figurepicture edge details.Therefore, the present invention is by the advantage in conjunction with Wavelet Denoising Method and guiding wave filter.Concrete thought is as follows, on the basis of traditional Wavelet noise-eliminating method, according to ultrasonic in wavelet field figurethe statistical property of picture and speckle noise, improves wavelet threshold function and contraction method, more effectively can remove the speckle noise of HFS.Due to medical ultrasonic figurestill there is speckle noise in the low frequency part of picture in wavelet field, therefore uses denoising effect good and the guiding wave filter that efficiency is high, can retain in lower frequency region in suppression lower frequency region while noise figurepicture marginal information.Of the present invention based on improving the wavelet transformation of threshold value and guiding the medical ultrasonic of wave filter figuretechnical scheme as denoising method is:

Step 1) medical ultrasonic figurethe foundation of picture model

If think that the factor that ultrasonic image-forming system can affect acoustic power to those makes appropriate dynamic compensation, then the envelope signal of ultrasonic image-forming system collection is made up of two parts, and one is the reflected signal of significant in-vivo tissue, and another part is noise signal.Wherein noise signal can be divided into multiplicative noise and additive noise.Multiplicative noise is relevant with the principle of ultrasonic signal imaging, is mainly derived from random scattered signal.Additive noise thinks system noise, as the noise etc. of sensor.The envelope signal that ultrasonic image-forming system tentatively obtains is f ^pre, universal model is as follows

f ^pre＝g ^pren ^pre+w ^pre(1)

Here, subscript ^prethe signal that expression system tentatively obtains.Function g ^prerepresent noise-free signal, n ^preand w ^prerepresent multiplicative noise and additive noise respectively, n in formula ^preit is the principal ingredient of noise.

With multiplicative noise n ^precompare, additive noise w ^preproportion is very little, therefore by w ^premodel after ignoring is

f ^pre＝g ^pren ^pre(2)

In order to adapt to the Dynamic Announce scope of ultrasonic image-forming system display screen, log-compressed process is carried out to the envelope signal that ultrasonic image-forming system collects.Multiplicative noise can be converted into approximate additive white Gaussian noise like this, as follows

log(f ^pre)＝log(g ^pre)+log(n ^pre) (3)

Now, the signal log (f obtained ^pre) be namely the medical ultrasonic usually seen figurepicture.

Step 2) after log-transformation that the first step is obtained figurepicture carries out wavelet decomposition, obtains four frequency domain (LL ¹, LH ¹, HL ¹and HH ¹).Wavelet decomposition is proceeded to lower frequency region LL1, then obtains four frequency domain (LL ², LH ², HL ²and HH ²).Then this step is repeated, until decompose maximum number of plies J.

Because wavelet transformation is linear transformation, therefore formula (3) model obtains lower surface model after two-dimensional discrete wavelet conversion:

$W_{l,k}^j\left(\log \left(f^{\mathrm{pre}}\right)\right)=W_{l,k}^j\left(\log \left(g^{\mathrm{pre}}\right)\right)+W_{l,k}^j\left(\log \left(n^{\mathrm{pre}}\right)\right)---\left(4\right)$

Wherein with represent respectively containing noise figurethe wavelet coefficient of picture, noiseless figurethe wavelet coefficient of picture and the wavelet coefficient of speckle noise.Wherein subscript j is the Decomposition order of wavelet transformation, and subscript (l, k) is the coordinate in wavelet field.Conveniently represent, formula (4) is reduced to

$F_{l,k}^j=G_{l,k}^j+N_{l,k}^j---\left(5\right)$

The wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows

p _G(g)＝C(σ _g,β)exp{-[K(σ _g,β)|g|] ^β},-∞<g<+∞,σ _g>0,β>0 (6)

Wherein

$K({\mathrm{\&sigma;}}_g,\mathrm{\&beta;})={\mathrm{\&sigma;}}_g^{-1}{[\mathrm{\&Gamma;}(3/\mathrm{\&beta;})/\mathrm{\&Gamma;}(1/\mathrm{\&beta;})]}^{1/2}$

C(σ _g,β)＝βK(σ _g,β)/[2Γ(1/β)]

Wherein C (σ _g, β) and be normalized factor, it is gamma function.σ _gbe the standard deviation without noise cancellation signal wavelet coefficient, determine the diffusion of broad sense laplacian distribution probability density function; β is form parameter, controls the rate of decay of broad sense laplacian distribution probability density function.When β=1, formula (6) will become laplacian distribution, be the particular module of broad sense laplacian distribution.

In order to better describe the characteristic of speckle noise in different scattered signal situation, the wavelet coefficient of speckle noise be considered to Rayleigh distributed

$p_N\left(n\right)=\frac{n}{{\mathrm{\&sigma;}}_n^2}\exp (-\frac{n^2}{{2\mathrm{\&sigma;}}_n^2})---\left(7\right)$

σ in formula _nfor the standard deviation of noise in wavelet field.

Step 3) HFS (LH to every one deck ^j, HL ^jand HH ^j, j=1,2 ..., J) wavelet coefficient carry out threshold method shrink process.

In Wavelet noise-eliminating method, the selection of threshold function table can directly have influence on final figurepicture denoising result.When Threshold selection is less, the noise figure that a part is greater than this threshold value can be taken as useful signal and remain, and this just causes after denoising figurestill there is much noise in picture; When Threshold selection is larger, the useful information that a lot of coefficient is very little can be used as noise and zero setting, this will make after denoising figurepicture becomes very level and smooth, loses a lot of detailed information.Therefore select appropriate wavelet threshold function extremely important.

The people such as Donoho propose a kind of typical Research on threshold selection, and demonstrate this threshold value theoretically and be directly proportional to the standard deviation of noise, and change threshold function table and be also called uniform threshold function, its formula is as follows

${T=\mathrm{\&sigma;}}_n\sqrt{2\log M}\left(8\right)$

Wherein, namely M is the overall number of wavelet coefficient in corresponding wavelet field, σ _nit is the standard deviation of noise.In this threshold function table, threshold value T affects comparatively large by the number of wavelet coefficient, and namely when M is excessive, larger threshold value may smooth out the less useful information of those coefficients.

On the basis of formula (8), the present invention proposes one and be more applicable to ultrasonic figurethe threshold function table of picture, its formula is as follows

${T=\mathrm{\&alpha;}}_j{\mathrm{\&sigma;}}_n\sqrt{2\log M}---\left(9\right)$

Wherein, σ _nthe standard deviation of noise, a _jgeneration table jthe auto-adaptive parameter of layer.This is kind of the method that common threshold value is improved, a _jchoose and experimentally determine, if select appropriately will obtain better effect, select in the present invention's test

In Wavelet noise-eliminating method, a first selected given threshold value, then shrinks wavelet coefficient according to certain rule, just completes the denoising to wavelet coefficient.An i.e. given threshold value, the coefficient that all absolute values are less than this threshold value is taken as noise, then does zero setting process to it; Wavelet coefficient absolute value being greater than to threshold value reduces by certain method, then obtains the new value after reducing.

Classical wavelet shrinkage method has Soft thresholding and hard threshold method, but in Soft thresholding, larger wavelet coefficient is always reduced by threshold value, and the mathematical expectation of the signal after therefore shrinking is different from before contraction, so after process figurepicture relative smooth some.The shortcoming of hard threshold method be wavelet coefficient near null value territory by unexpected zero setting, result in the uncontinuity of wavelet data, and this makes the variance of signal larger, these conversion for figuredetails impact in picture is larger.But in actual applications, when particularly noise level is very high, after hard threshold method process figurepicture can produce concussion around point of discontinuity, impact figurethe denoising effect of picture.

Because the threshold value contraction method of classics can not meet medical ultrasonic figurethe requirement of picture denoising, so the present invention improves contraction method.

Without the wavelet coefficient of noise cancellation signal obey broad sense laplacian distribution, the speckle noise part in wavelet field rayleigh distributed.In order to simplify calculating, the present invention selects β=1, then formula (6) becomes laplacian distribution

$p_G\left(g\right)=\frac{1}{\sqrt{2}{\mathrm{\&sigma;}}_g}\exp (-\frac{\sqrt{2}\left|g\right|}{{\mathrm{\&sigma;}}_g})---\left(10\right)$

In order to obtain the Signal estimation value in wavelet field, use the method that Bayesian MAP is estimated.In the computation process of posterior probability, use Bayesian formula as follows

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}{p}_{F|G}\left(f\right|g)\&CenterDot;p_G\left(g\right)=\\ \frac{1}{p_F\left(f\right)}{p}_N(f-g)\&CenterDot;p_G\left(g\right)\end{array}---\left(11\right)$

Bring formula (7), formula (10) into above formula (11), obtain

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}\&CenterDot;\frac{f-g}{\sqrt{2}{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g}\&times;\\ \exp (-\frac{2\sqrt{2}{\mathrm{\&sigma;}}_N^2\left|g\right|+{\mathrm{\&sigma;}}_g{(f-g)}^2}{2{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g})\end{array}---\left(12\right)$

In order to obtain maximum a posteriori probability, by ln (p _g|F(g|f)) g is asked to the equation zero setting of first order derivative, finally obtain

$\hat{g}=\mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+{2\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)---\left(13\right)$

for the estimation of g, and suppose f and without noise cancellation signal g jack per line.So just obtain new contraction method

$\hat{g}=\left\{\begin{array}{cc}0& f\&le;T_j\\ \mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+{2\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)& f>T_j\end{array}\right.---\left(14\right)$

The wavelet shrinkage function that the present invention improves is at curve figurepicture upper tableexisting is more level and smooth, especially when wavelet coefficient is greater than in the interval range of wavelet threshold.

Step 4) utilize guiding wave filter to do filtering process to the wavelet coefficient in the low frequency part (LLJ) of last one deck

Generally based on the denoising method of small echo, the wavelet coefficient namely retaining lower frequency region (LL) is constant, only does threshold process to the wavelet coefficient of high-frequency domain (LH, HL, HH).But the method is applied to medical ultrasonic figureperform poor as during denoising.Through many experiments, find that the wavelet coefficient in lower frequency region still has a lot of speckle noise, in order to the speckle noise in more effectively filtering lower frequency region, the present invention selects to guide wave filter to do filtering process to the wavelet coefficient in lower frequency region.

Guide figuredeveloped by Local Linear Model as filtering, this method ultimate principle is shown below

$q_i=\underset{j}{\mathrm{\&Sigma;}}{W}_{\mathrm{ij}}\left(I\right)p_j---\left(15\right)$

In formula (15), I is for guiding figurepicture, p is input figurepicture, q is for exporting figurepicture, W _ijfor about guiding figurethe function of picture I, i and j is the position of pixel, and I is determined by particular problem, can make I=p.

Suppose at window w _kin, the linear transformation of central point to be rear k, q be I, shown in (16)

$q_i=a_k{I}_i+b_k,\&ForAll;i\&Element;w_k---\left(16\right)$

? figurein picture filtering, it is desirable to minimize input under the prerequisite reaching filter effect figurepicture and output figurethe difference of picture, reduces original figurethe loss of picture details, therefore determine coefficient a by the difference minimizing p and q _kand b _keven if formula (17) is minimum

$E(a_k,b_k)=\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}[{(a_k{I}_i+b_k-p_i)}^2+{\mathrm{\&epsiv;a}}_k^2]---\left(17\right)$

In formula (17), ε is regularization parameter, and object is to prevent a _kexcessive.Solve formula (17),

$a_k=\frac{\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{I}_i{p}_i-{\mathrm{\&mu;}}_k{\stackrel{\&OverBar;}{p}}_k}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}}$

$b_k={\stackrel{\&OverBar;}{p}}_k-a_k{\mathrm{\&mu;}}_k---\left(18\right)$

${\stackrel{\&OverBar;}{p}}_k=\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{p}_i$

In formula, μ _kwith be respectively I at w _kin average and variance.| w| is w _kin number of pixels, it is input figurepicture p is at w _kin average.After obtaining this linear model, bring view picture into figurepicture, because each pixel has multiple window w comprising this pixel _k, so work as at different windows w _kduring calculating, q _ivalue can be different.Therefore need to be averaging processing it

$q_i=\frac{1}{\left|w\right|}\underset{k,i\&Element;w_k}{\mathrm{\&Sigma;}}(a_k{I}_i+b_k)=\stackrel{\&OverBar;}{a_i}{I}_i+\stackrel{\&OverBar;}{b_i}---\left(19\right)$

In formula, $\stackrel{\&OverBar;}{a_i}=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{a}_k,\stackrel{\&OverBar;}{b_i}=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{b}_k.$

In sum, kernel function W _ijcan be defined as follows

$W_{\mathrm{ij}}=\frac{1}{{\left|w\right|}^2}\underset{k,(i,j)\&Element;w_k}{\mathrm{\&Sigma;}}(1+\frac{(I_i-{\mathrm{\&mu;}}_k)(I_j-{\mathrm{\&mu;}}_k)}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}})---\left(20\right)$

From above principle, guide the process of wave filter denoising as follows:

(1) input figurepicture p;

(2) input filter window w _ksize and regularization parameter ε;

(3) average of I, p and I*p is calculated;

(4) covariance of (I, p) is calculated;

(5) calculate the average of (I*I) and calculate the variance of I;

(6) design factor a, b;

(7) average of a and b is calculated respectively;

(8) exported figurepicture q.

Step 5) do wavelet inverse transformation process, obtain the medical ultrasonic after denoising figurepicture.

If obtain the ultrasonic envelope signal after denoising, to the 5th step obtain ultrasonic figureexponential transform done by picture.The signal of the overall step of this method figure is as Fig. 1shown in.

The invention has the advantages that:

The present invention is respectively by noise with without making an uproar figurepicture is designed to Rayleigh distributed and broad sense laplacian distribution, improves the method that threshold value is shunk, has very strong noise removal capability to the tiny noise of high-frequency domain; On the other hand, guide wave filter to carry out filtration treatment to low frequency part because the present invention utilizes, therefore for the speckle noise (being present in low frequency part) that particle is larger, there is very strong rejection ability equally.Simultaneously for medical ultrasonic figurethe feature of picture, the method for this combination well can not only suppress speckle noise, can also retain simultaneously figurein picture, the detail section at focus edge etc., can better help doctor to carry out illness analysis.

Accompanying drawing explanation

fig. 1it is overall flow of the present invention figure

fig. 2emulation of the present invention figurethe denoising effect of picture compares, wherein fig. 2a is noiseless figurepicture, fig. 2b is noise figurepicture, fig. 2c is the effect of wavelet soft thresholding denoising figurepicture, fig. 2d is the effect of the denoising of the inventive method figurepicture

fig. 3it is clinical ultrasound figurethe denoising result of picture compares, fig. 3a is noise figurepicture, fig. 3b is the effect of wavelet soft thresholding denoising figurepicture, fig. 3c is the effect of the denoising of the inventive method figurepicture

Embodiment

For making the object, technical solutions and advantages of the present invention more clear, below in conjunction with accompanying drawingtechnical scheme of the present invention is further described. as Fig. 1shown in, of the present invention based on improving the wavelet transformation of threshold value and guiding the medical ultrasonic of wave filter figurepicture denoising method, comprises the steps:

Step 1) set up medical ultrasonic figurethe model of picture.

If think that the factor that ultrasonic image-forming system can affect acoustic power to those makes appropriate dynamic compensation, then the envelope signal of ultrasonic image-forming system collection is made up of two parts, and one is the reflected signal of significant in-vivo tissue, and another part is noise signal.Wherein noise signal can be divided into multiplicative noise and additive noise.Multiplicative noise is relevant with the principle of ultrasonic signal imaging, is mainly derived from random scattered signal.Additive noise thinks system noise, as the noise etc. of sensor.The envelope signal that ultrasonic image-forming system tentatively obtains is f ^pre, its universal model is as follows

f ^pre＝g ^pren ^pre+w ^pre(1)

Here, subscript ^prethe signal that expression system tentatively obtains.Function g ^prerepresent noise-free signal, n ^preand w ^prerepresent multiplicative noise and additive noise respectively, n in formula ^preit is the principal ingredient of noise.

With multiplicative noise n ^precompare, additive noise w ^preproportion is very little, therefore by w ^premodel after ignoring is

f ^pre＝g ^pren ^pre(2)

In order to adapt to the Dynamic Announce scope of ultrasonic image-forming system display screen, log-compressed process is carried out to the envelope signal that ultrasonic image-forming system collects.Formula (2) model be now multiplied will become the model of addition, as follows

log(f ^pre)＝log(g ^pre)+log(n ^pre) (3)

Now, the signal log (f obtained ^pre) be namely the medical ultrasonic usually seen figurepicture.If the target of process is common medical ultrasonic figurepicture, namely did log-transformation, then omit this step.Speckle noise log (n after log-transformation ^pre) can be similar to be expressed as Gaussian noise.

Step 2) to the medical ultrasonic after log-transformation figurepicture carries out wavelet decomposition.

Because wavelet transformation is linear transformation, therefore formula (3) model obtains lower surface model after two-dimensional discrete wavelet conversion:

$W_{l,k}^j\left(\log \left(f^{\mathrm{pre}}\right)\right)=W_{l,k}^j\left(\log \left(g^{\mathrm{pre}}\right)\right)+W_{l,k}^j\left(\log \left(n^{\mathrm{pre}}\right)\right)---\left(4\right)$

Wherein with represent respectively containing noise figurethe wavelet coefficient of picture, noiseless figurethe wavelet coefficient of picture and the wavelet coefficient of speckle noise.Wherein subscript j is the Decomposition order of wavelet transformation, and subscript (l, k) is the coordinate in wavelet field.Conveniently represent, formula (4) is reduced to

$F_{l,k}^j=G_{l,k}^j+N_{l,k}^j---\left(5\right)$

For discrete two dimension figurepicture f (n, m), to the step that it carries out 2-d wavelet decomposition is: first right figureevery one-row pixels of picture carries out one-dimensional discrete wavelet decomposition, then to again figureeach row of picture carry out one-dimensional discrete wavelet decomposition, so just by a width figurepicture is decomposed into four sub-band signals.

It is considered herein that the wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows

P _g(g)=C (σ _g, β) and exp{-[K (σ _g, β) | g|] ^β,-∞ <g<+ ∞, σ _g>0, β >0 (6) wherein

$K({\mathrm{\&sigma;}}_g,\mathrm{\&beta;})={\mathrm{\&sigma;}}_g^{-1}{[\mathrm{\&Gamma;}(3/\mathrm{\&beta;})/\mathrm{\&Gamma;}(1/\mathrm{\&beta;})]}^{1/2}$

C(σ _g,β)＝βK(σ _g,β)/[2Γ(1/β)]

Wherein C (σ _g, β) and be normalized factor, it is gamma function.σ _gbe the standard deviation without noise cancellation signal wavelet coefficient, determine the diffusion of broad sense laplacian distribution probability density function; β is form parameter, controls the rate of decay of broad sense laplacian distribution probability density function.When β=1, formula (6) will become laplacian distribution, and it is the particular module of broad sense laplacian distribution.

In order to better describe the characteristic of speckle noise in different scattered signal situation, the wavelet coefficient of speckle noise be considered to Rayleigh distributed

$p_N\left(n\right)=\frac{n}{{\mathrm{\&sigma;}}_n^2}\exp (-\frac{n^2}{{2\mathrm{\&sigma;}}_n^2})---\left(7\right)$

σ in formula _nfor the standard deviation of noise in wavelet field.

Step 3) HFS (LH to every one deck ^j, HL ^jand HH ^j, j=1,2 ..., J) wavelet coefficient carry out threshold method shrink process.

In Wavelet noise-eliminating method, the selection of threshold function table can directly have influence on final figurepicture denoising result.When Threshold selection is less, the noise figure that a part is greater than this threshold value can be taken as useful signal and remain, and this just causes after denoising figurestill there is much noise in picture; When Threshold selection is larger, the useful information that a lot of coefficient is very little can be used as noise and zero setting, this will make after denoising figurepicture becomes very level and smooth, loses a lot of detailed information.Therefore select appropriate wavelet threshold function extremely important.

The people such as Donoho propose a kind of typical Research on threshold selection, and demonstrate this threshold value theoretically and be directly proportional to the standard deviation of noise, and change threshold function table and be also called uniform threshold function, its formula is as follows

${T=\mathrm{\&sigma;}}_n\sqrt{2\log M}\left(8\right)$

Wherein, namely M is the overall number of wavelet coefficient in corresponding wavelet field, σ _nit is the standard deviation of noise.In this threshold function table, threshold value T affects comparatively large by the number of wavelet coefficient, and namely when M is excessive, larger threshold value may smooth out the less useful information of those coefficients.

On the basis of formula (8), the present invention proposes one and be more applicable to ultrasonic figurethe threshold function table of picture, its formula is as follows

${T=\mathrm{\&alpha;}}_j{\mathrm{\&sigma;}}_n\sqrt{2\log M}---\left(9\right)$

Wherein, σ _nthe standard deviation of noise, a _jgeneration table jthe auto-adaptive parameter of layer.This is kind of the method that common threshold value is improved, a _jchoose and experimentally determine, if select appropriately will obtain better effect, select in the present invention's test

In Wavelet noise-eliminating method, a first selected given threshold value, then shrinks wavelet coefficient according to certain rule, just completes the denoising to wavelet coefficient.An i.e. given threshold value, the coefficient that all absolute values are less than this threshold value is taken as noise, then does zero setting process to it; Wavelet coefficient absolute value being greater than to threshold value reduces by certain method, then obtains the new value after reducing.

Classical wavelet shrinkage method has Soft thresholding and hard threshold method, but in Soft thresholding, larger wavelet coefficient is always reduced by threshold value, and the mathematical expectation of the signal after therefore shrinking is different from before contraction, so after process figurepicture relative smooth some.The shortcoming of hard threshold method be wavelet coefficient near null value territory by unexpected zero setting, result in the uncontinuity of wavelet data, and this makes the variance of signal larger, these conversion for figuredetails impact in picture is larger.But in actual applications, when particularly noise level is very high, after hard threshold method process figurepicture can produce concussion around point of discontinuity, impact figurethe denoising effect of picture.

Because the threshold value contraction method of classics can not meet medical ultrasonic figurethe requirement of picture denoising, so the present invention improves contraction method.

Without the wavelet coefficient of noise cancellation signal obey broad sense laplacian distribution, the speckle noise part in wavelet field rayleigh distributed.In order to simplify calculating, the present invention selects β=1, then formula (6) becomes laplacian distribution

$p_G\left(g\right)=\frac{1}{\sqrt{2}{\mathrm{\&sigma;}}_g}\exp (-\frac{\sqrt{2}\left|g\right|}{{\mathrm{\&sigma;}}_g})---\left(10\right)$

In order to obtain the Signal estimation value in wavelet field, use the method that Bayesian MAP is estimated.In the computation process of posterior probability, use Bayesian formula as follows

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}{p}_{F|G}\left(f\right|g)\&CenterDot;p_G\left(g\right)=\\ \frac{1}{p_F\left(f\right)}{p}_N(f-g)\&CenterDot;p_G\left(g\right)\end{array}---\left(11\right)$

Bring formula (7), formula (10) into above formula (11), obtain

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}\&CenterDot;\frac{f-g}{\sqrt{2}{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g}\&times;\\ \exp (-\frac{2\sqrt{2}{\mathrm{\&sigma;}}_N^2\left|g\right|+{\mathrm{\&sigma;}}_g{(f-g)}^2}{2{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g})\end{array}---\left(12\right)$

In order to obtain maximum a posteriori probability, by ln (p _g|F(g|f)) g is asked to the equation zero setting of first order derivative, finally obtain

$\hat{g}=\mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+{2\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)---\left(13\right)$

for the estimation of g, and suppose f and without noise cancellation signal g jack per line.So just obtain new contraction method

$\hat{g}=\left\{\begin{array}{cc}0& f\&le;T_j\\ \mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+{2\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)& f>T_j\end{array}\right.---\left(14\right)$

The wavelet shrinkage function that the present invention improves is at curve figurepicture upper tableexisting is more level and smooth, especially when wavelet coefficient is greater than in the interval range of wavelet threshold.

Step 4) utilize guiding wave filter to do filtering process to the wavelet coefficient in the low frequency part (LLJ) of last one deck

Generally based on the denoising method of small echo, the wavelet coefficient namely retaining lower frequency region (LL) is constant, only does threshold process to the wavelet coefficient of high-frequency domain (LH, HL, HH).But the method is applied to medical ultrasonic figureperform poor as during denoising.Through many experiments, find that the wavelet coefficient in lower frequency region still has a lot of speckle noise, in order to the speckle noise in more effectively filtering lower frequency region, the present invention selects to guide wave filter to do filtering process to the wavelet coefficient in lower frequency region.

Guide figuredeveloped by Local Linear Model as filtering, this method ultimate principle is shown below

$q_i=\underset{j}{\mathrm{\&Sigma;}}{W}_{\mathrm{ij}}\left(I\right)p_j---\left(15\right)$

In formula (15), I is for guiding figurepicture, p is input figurepicture, q is for exporting figurepicture, W _ijfor about guiding figurethe function of picture I, i and j is the position of pixel, and I is determined by particular problem, can make I=p.

Suppose at window w _kin, the linear transformation of central point to be rear k, q be I, shown in (16)

$q_i=a_k{I}_i+b_k,\&ForAll;i\&Element;w_k---\left(16\right)$

? figurein picture filtering, it is desirable to minimize input under the prerequisite reaching filter effect figurepicture and output figurethe difference of picture, reduces original figurethe loss of picture details, therefore determine coefficient a by the difference minimizing p and q _kand b _keven if formula (17) is minimum

$E(a_k,b_k)=\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}[{(a_k{I}_i+b_k-p_i)}^2+{\mathrm{\&epsiv;a}}_k^2]---\left(17\right)$

In formula (17), ε is regularization parameter, and object is to prevent a _kexcessive.Solve formula (17),

$a_k=\frac{\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{I}_i{p}_i-{\mathrm{\&mu;}}_k{\stackrel{\&OverBar;}{p}}_k}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}}$

$b_k={\stackrel{\&OverBar;}{p}}_k-a_k{\mathrm{\&mu;}}_k---\left(18\right)$

${\stackrel{\&OverBar;}{p}}_k=\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{p}_i$

In formula, μ _kwith be respectively I at w _kin average and variance.| w| is w _kin number of pixels, it is input figurepicture p is at w _kin average.After obtaining this linear model, bring view picture into figurepicture, because each pixel has multiple window w comprising this pixel _k, so work as at different windows w _kduring calculating, q _ivalue can be different.Therefore need to be averaging processing it

$q_i=\frac{1}{\left|w\right|}\underset{k,i\&Element;w_k}{\mathrm{\&Sigma;}}(a_k{I}_i+b_k)=\stackrel{\&OverBar;}{a_i}{I}_i+\stackrel{\&OverBar;}{b_i}---\left(19\right)$

In formula, $\stackrel{\&OverBar;}{a_i}=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{a}_k,\stackrel{\&OverBar;}{b_i}=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{b}_k.$

In sum, kernel function W _ijcan be defined as follows

$W_{\mathrm{ij}}=\frac{1}{{\left|w\right|}^2}\underset{k,(i,j)\&Element;w_k}{\mathrm{\&Sigma;}}(1+\frac{(I_i-{\mathrm{\&mu;}}_k)(I_j-{\mathrm{\&mu;}}_k)}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}})---\left(20\right)$

From above principle, guide the process of wave filter denoising as follows:

(1) input figurepicture p;

(2) input filter window w _ksize and regularization parameter ε;

(3) average of I, p and I*p is calculated;

(4) covariance of (I, p) is calculated;

(5) calculate the average of (I*I) and calculate the variance of I;

(6) design factor a, b;

(7) average of a and b is calculated respectively;

(8) exported figurepicture q.

Step 5) do wavelet inverse transformation process, obtain the medical ultrasonic after denoising figurepicture.

Through threshold value shrink process with guide filter process just can obtain the wavelet coefficient after denoising, ultrasonic in order to what obtain after denoising figurepicture, needs to carry out wavelet inverse transformation to wavelet coefficient, thus can obtain being beneficial to after the denoising that doctor analyzes figurepicture, also demonstrates the present invention by experiment and really can meet for medical ultrasonic figurethe requirement of picture denoising.

Experimental verification

In order to evaluate the denoising method that the present invention proposes objectively, using Y-PSNR (PSNR), structural similarity (SSIM), FoM (Pratt ' s Figure of Merit) and working time as figurepicture criteria of quality evaluation.The computing formula of Y-PSNR is as follows

$\mathrm{PSNR}(X,\hat{X})=101g\left(\frac{{255}^2}{\mathrm{MSE}}\right)---\left(21\right)$

In formula, for the estimated value of signal X, MSE is obtained by formulae discovery below

$\mathrm{MSE}=\frac{1}{\mathrm{MN}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(X_{i,j}-{\hat{X}}_{i,j})}^2\left(22\right)$

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

Structural similarity can quantize two width figurepicture difference structurally, formula is defined as follows

$\mathrm{SSIM}(X,\hat{X})=\frac{({2\mathrm{\&mu;}}_X{\mathrm{\&mu;}}_{\hat{X}}+c_1)({2\mathrm{\&sigma;}}_{X,\hat{X}}+c_2)}{({\mathrm{\&mu;}}_X^2+{\mathrm{\&mu;}}_{\hat{X}}^2{+c}_1)({\mathrm{\&sigma;}}_X^2+{\mathrm{\&sigma;}}_{\hat{X}}^2+c_2)}---\left(23\right)$

In formula, μ _x, with reference respectively figurepicture and estimation figurethe average of picture and variance. be X and covariance, c ₁and c ₂for constant.Work as c ₁and c ₂when being all chosen as positive number, the span of SSIM is [01], and wherein 1 is best result, represents two width figurestructure identical.

FoM can compare denoising objectively figurethe rim detection quality of picture, formula is defined as follows

$\mathrm{FoM}(X,\hat{X})=\frac{1}{\max (N_X,N_{\hat{X}})}\underset{i=1}{\overset{N_X}{\mathrm{\&Sigma;}}}\frac{1}{1+{\mathrm{\&alpha;d}}_i^2}---\left(24\right)$

In formula, N _xwith represent desirable with the actual edge pixel number detected respectively.α is constant (usually getting α=1/9), d _ibe expressed as the distance of the i-th edge pixel point to nearest ideal edge pixel.The span of FoM is [01], wherein 1 is best result, is expressed as to detect figurepicture edge and desirable figurepicture edge is consistent.Here Canny detection algorithm (standard deviation value σ=3 of Gaussian filter) is used during detection of edge pixels.

Certainly in order to better represent advantage of the present invention, next mainly by contrast experiment, quantize to compare each figuremake objects and advantages of the present invention more clear as evaluation criterion.

In order to the effect of quantitative predication denoising of the present invention, first emulate figurethe experiment of picture.Obtain fig. 2's figurepicture and table 1in data.

table 1the Performance comparision of denoising method

For what emulate figuresimilarly be by making an uproar to nothing figurepicture adds the (medical ultrasonic that Gaussian noise obtains figurethe speckle noise of picture meets Gaussian distribution).The data quantitatively drawn by emulation experiment can be found out, the effect in speckle noise is being suppressed to be not fine iff utilizing the denoising method of wavelet transformation, certain speckle noise is still there is in low frequency part, so need to introduce wave filter to do filtering process to low frequency part, what the present invention introduced is guide wave filter.By relatively finding, experimental result of the present invention also can find out the method being better than wavelet soft-threshold intuitively, and Utilization assessment index also demonstrates the present invention and greatly improves denoising effect.

This method is to clinical ultrasound figurepicture is tested, selection be the ultrasonic of mammary glands in women tissue containing focus figurepicture, as Fig. 3.

Muting ultrasonic owing to not existing in reality figurepicture, therefore, the quality index such as PSNR here cannot use effectively, so just introduce another index, without reference figurepicture element figureofmerit (NIQE).Obtain table 2

table 2the Performance comparision of denoising method

Denoising method	NIQE
		Noise FigurePicture	5.7915
Wavelet soft-threshold	7.3725
		The inventive method	9.0108

By relatively finding that the present invention is being applied to medical ultrasonic figurein picture, denoising effect is significantly improved.Can more retain while removal noise figurepicture marginal information, thus reach medical ultrasonic figurepicture is for the requirement of denoising.

Content described in this instructions embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (1)

1. improve the wavelet transformation of threshold value and guide the medical ultrasound image denoising method of wave filter, comprising:

Step 1) foundation of medical ultrasonic image model

If think that the factor that ultrasonic image-forming system can affect acoustic power to those makes appropriate dynamic compensation, then the envelope signal of ultrasonic image-forming system collection is made up of two parts, and one is the reflected signal of significant in-vivo tissue, and another part is noise signal; Wherein noise signal can be divided into multiplicative noise and additive noise; Multiplicative noise is relevant with the principle of ultrasonic signal imaging, is mainly derived from random scattered signal; Additive noise thinks system noise, as the noise etc. of sensor; The envelope signal that ultrasonic image-forming system tentatively obtains is f ^pre, universal model is as follows

f ^pre＝g ^pren ^pre+w ^pre(1)

Here, subscript ^prethe signal that expression system tentatively obtains; Function g ^prerepresent noise-free signal, n ^preand w ^prerepresent multiplicative noise and additive noise respectively, n in formula ^preit is the principal ingredient of noise;

With multiplicative noise n ^precompare, additive noise w ^preproportion is very little, therefore by w ^premodel after ignoring is

f ^pre＝g ^pren ^pre(2)

In order to adapt to the Dynamic Announce scope of ultrasonic image-forming system display screen, log-compressed process being carried out to the envelope signal that ultrasonic image-forming system collects, multiplicative noise is converted into approximate additive white Gaussian noise, as follows

log(f ^pre)＝log(g ^pre)+log(n ^pre) (3)

Now, the signal log (f obtained ^pre) be namely the medical ultrasonic image usually seen;

Step 2) image after the log-transformation that obtains the first step carries out wavelet decomposition, obtains four frequency domain (LL ¹, LH ¹, HL ¹and HH ¹); To lower frequency region LL ¹proceed wavelet decomposition, then obtain four frequency domain (LL ², LH ², HL ²and HH ²); Then this step is repeated, until decompose maximum number of plies J;

Because wavelet transformation is linear transformation, therefore formula (3) model obtains lower surface model after two-dimensional discrete wavelet conversion:

$W_{l,k}^j\left(\log \left(f^{\mathrm{pre}}\right)\right)=W_{l,k}^j\left(\log \left(g^{\mathrm{pre}}\right)\right)+W_{l,k}^j\left(\log \left(n^{\mathrm{pre}}\right)\right)---\left(4\right)$

Wherein with represent the wavelet coefficient containing the wavelet coefficient of noise image, the wavelet coefficient of noise-free picture and speckle noise respectively; Wherein subscript j is the Decomposition order of wavelet transformation, and subscript (l, k) is the coordinate in wavelet field; Conveniently represent, formula (4) is reduced to

$F_{l,k}^j=G_{l,k}^j+N_{l,k}^j---\left(5\right)$

The wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows

p _G(g)＝C(σ _g,β)exp{-[K(σ _g,β)|g|] ^β},-∞＜g＜+∞,σ _g＞0,β＞0 (6)

Wherein

$K({\mathrm{\&sigma;}}_g,\mathrm{\&beta;})={\mathrm{\&sigma;}}_g^{-1}{[\mathrm{\&Gamma;}(3/\mathrm{\&beta;})/\mathrm{\&Gamma;}(1/\mathrm{\&beta;})]}^{1/2}$

C(σ _g,β)＝βK(σ _g,β)/[2Γ(1/β)]

Wherein C (σ _g, β) and be normalized factor, it is gamma function; σ _gbe the standard deviation without noise cancellation signal wavelet coefficient, determine the diffusion of broad sense laplacian distribution probability density function; β is form parameter, controls the rate of decay of broad sense laplacian distribution probability density function; When β=1, formula (6) will become laplacian distribution, be the particular module of broad sense laplacian distribution;

In order to better describe the characteristic of speckle noise in different scattered signal situation, the wavelet coefficient of speckle noise be considered to Rayleigh distributed

$p_N\left(n\right)=\frac{n}{{\mathrm{\&sigma;}}_n^2}\exp (-\frac{n^2}{2{\mathrm{\&sigma;}}_n^2})---\left(7\right)$

σ in formula _nfor the standard deviation of noise in wavelet field;

Step 3) HFS (LH to every one deck ^j, HL ^jand HH ^j, j=1,2 ..., J) wavelet coefficient carry out threshold method shrink process;

Set a kind of threshold function table of applicable ultrasonoscopy, its formula is as follows

$T={\mathrm{\&alpha;}}_j{\mathrm{\&sigma;}}_n\sqrt{2\log M}---\left(9\right)$

Wherein, namely M is the overall number of wavelet coefficient in corresponding wavelet field, σ _nthe standard deviation of noise, a _jrepresent the auto-adaptive parameter of j layer, select in the present invention's test

Without the wavelet coefficient of noise cancellation signal obey broad sense laplacian distribution, the speckle noise part in wavelet field rayleigh distributed, select β=1, then formula (6) becomes laplacian distribution

$p_G\left(g\right)=\frac{1}{\sqrt{2}{\mathrm{\&sigma;}}_g}\exp (-\frac{\sqrt{2}\left|g\right|}{{\mathrm{\&sigma;}}_g})---\left(10\right)$

In order to obtain the Signal estimation value in wavelet field, use the method that Bayesian MAP is estimated; In the computation process of posterior probability, use Bayesian formula as follows

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}{p}_{F|G}\left(f\right|g)\&CenterDot;p_G\left(g\right)=\\ \frac{1}{p_F\left(f\right)}{p}_N(f-g)\&CenterDot;p_G\left(g\right)\end{array}---\left(11\right)$

Bring formula (7), formula (10) into above formula (11), obtain

$\begin{array}{c}{p}_{G|F}\left(g\right|f)=\frac{1}{p_F\left(f\right)}\&CenterDot;\frac{f-g}{\sqrt{2}{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g}\&times;\\ \exp (-\frac{2\sqrt{2}{\mathrm{\&sigma;}}_N^2\left|g\right|+{\mathrm{\&sigma;}}_g{(f-g)}^2}{2{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g})\end{array}---\left(12\right)$

In order to obtain maximum a posteriori probability, by ln (p _g|F(g|f)) g is asked to the equation zero setting of first order derivative, finally obtain

$\hat{g}=\mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+2{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)---\left(13\right)$

for the estimation of g, and suppose f and without noise cancellation signal g jack per line; So just obtain new contraction method

$\hat{g}=\left\{\begin{array}{cc}0& f\&le;T_j\\ \mathrm{sign}\left(f\right)\&CenterDot;\max \left(\right|f|-\frac{{\mathrm{\&sigma;}}_n^2+\sqrt{{\mathrm{\&sigma;}}_n^4+2{\mathrm{\&sigma;}}_n^2{\mathrm{\&sigma;}}_g^2}}{\sqrt{2}{\mathrm{\&sigma;}}_g},0)& f>T_j\end{array}\right.---\left(14\right)$

Step 4) utilize guiding wave filter to the low frequency part (LL of last one deck ^j) in wavelet coefficient do filtering process

In order to the speckle noise in filtering lower frequency region effectively, select to guide wave filter to do filtering process to the wavelet coefficient in lower frequency region;

The ultimate principle of navigational figure filtering is shown below

$q_i=\underset{j}{\mathrm{\&Sigma;}}{W}_{\mathrm{ij}}\left(I\right)p_j---\left(15\right)$

In formula (15), I is navigational figure, and p is input picture, and q is output image, W _ijfor the function about navigational figure I, i and j is the position of pixel, and I is determined by particular problem, can make I=p;

Suppose at window w _kin, the linear transformation of central point to be rear k, q be I, shown in (16)

$q_i=a_k{I}_i+b_k,\&ForAll;i\&Element;w_k---\left(16\right)$

In image filtering, wish the difference that can minimize input picture and output image under the prerequisite reaching filter effect, reduce the loss of original image details, therefore determine coefficient a by the difference minimizing p and q _kand b _keven if formula (17) is minimum

$E(a_k,b_k)=\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}[{(a_k{I}_i+b_k-p_i)}^2+\mathrm{\&epsiv;}{a}_k^2]---\left(17\right)$

In formula (17), ε is regularization parameter, and object is to prevent a _kexcessive.Solve formula (17),

$a_k=\frac{\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{I}_i{p}_i-{\mathrm{\&mu;}}_k{\stackrel{\&OverBar;}{p}}_k}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}}$

$b_k={\stackrel{\&OverBar;}{p}}_k-a_k{\mathrm{\&mu;}}_k---\left(18\right)$

${\stackrel{\&OverBar;}{p}}_k=\frac{1}{\left|w\right|}\underset{i\&Element;w_k}{\mathrm{\&Sigma;}}{p}_i$

In formula, μ _kwith be respectively I at w _kin average and variance.| w| is w _kin number of pixels, that input picture p is at w _kin average.After obtaining this linear model, bring entire image into, because each pixel has multiple window w comprising this pixel _k, so work as at different windows w _kduring calculating, q _ivalue can be different; Therefore need to be averaging processing it

$q_i=\frac{1}{\left|w\right|}\underset{k,i\&Element;w_k}{\mathrm{\&Sigma;}}(a_k{I}_i+b_k)={\stackrel{\&OverBar;}{a}}_i{I}_i+{\stackrel{\&OverBar;}{b}}_i---\left(19\right)$

In formula, ${\stackrel{\&OverBar;}{a}}_i=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{a}_k,{\stackrel{\&OverBar;}{b}}_i=\frac{1}{\left|w\right|}\mathrm{\&Sigma;}{b}_k;$

In sum, kernel function W _ijcan be defined as follows

$W_{\mathrm{ij}}=\frac{1}{{\left|w\right|}^2}\underset{k,(i,j)\&Element;w_k}{\mathrm{\&Sigma;}}(1+\frac{(I_i-{\mathrm{\&mu;}}_k)(I_j-{\mathrm{\&mu;}}_k)}{{\mathrm{\&sigma;}}_k^2+\mathrm{\&epsiv;}})---\left(20\right)$

From above principle, guide the process of wave filter denoising as follows:

(1) input picture p;

(2) input filter window w _ksize and regularization parameter ε;

(3) average of I, p and I*p is calculated;

(4) covariance of (I, p) is calculated;

(5) calculate the average of (I*I) and calculate the variance of I;

(6) design factor a, b;

(7) average of a and b is calculated respectively;

(8) output image q is obtained;

Step 5) do wavelet inverse transformation process, obtain the medical ultrasonic image after denoising; If obtain the ultrasonic envelope signal after denoising, exponential transform is done to the ultrasonoscopy that the 5th step obtains.