CN101799916A - Biologic chip image wavelet de-noising method based on Bayesian estimation - Google Patents

Abstract

A biologic chip image has a larger noise signal, which is caused by factors, such as manufacture, hybridization and cleaning of a biological chip, pollution of dust in a testing process, interference of a testing sample and an instrument noise, hybridization non-specific reaction and the like. The invention provides a biologic chip image wavelet de-noising method based on the Bayesian estimation, which comprises the following steps of: firstly expanding the biologic chip image containing the noise into a wavelet coefficient through wavelet conversion; determining a Bayesian shrinkage threshold on the basis of estimating signal variance and noise variance; extracting an important wavelet coefficient by using the Bayesian shrinkage threshold to complete threshold processing and de-noising processing of the image; and finally enabling the de-noised wavelet coefficient to subject the wavelet reverse conversion to reconstruct the image and outputting the de-noised image. The invention has the advantages that the method has favorable effect of de-noising the biologic chip image, thereby the background noise is smoothened, and edge details of sample points are reserved so as to lay the foundation on further analyzing the chip data and ensuring the correctness of a detection result.

Description

Biologic chip image wavelet de-noising method based on Bayesian Estimation

Technical field

The invention belongs to the bio signal image processing field, relate to a kind of biochip image denoising method, particularly a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation.

Background technology

Biochip is meant according to the precalculated position and is fixed on the solid phase carrier microarray array that a lot of nucleic acid molecules in the small size is formed very much.Because biochip is integrated thousands of sampling points on small substrate, and each sampling point has all been expressed certain biological information, use the image after chip scanner scanning and acquisition chip are hybridized, by analyzing biochip image, extract the intensity or the ratio of each target area in the array, the chip in the binding data storehouse is described (sequence of each probe and the probe position on chip) and is determined the biochip test result.

Biochip technology not only is confined to the preparation process of chip, the detection of chip information and analysis also are key contents wherein, the squelch of biochip image and filtering are very important steps in the biochip applications process, the result of its analysis will directly have influence on image subsequent treatment (image segmentation, sampling point identification, brightness are extracted) result's precision and accuracy, and then influence the popularization and the use of biochip.

Biochip image is different with normal image, because the influence of factors such as biochip treatment facility, scanning device, light, the biochip image that causes analyzing be on the background of gradual change, irregularly distributing not of uniform size, the depth is different, the position is unclear, the litura that comes in every shape, uses conventional analytical approach to be difficult to the effect that reaches desirable.And because the pollution of dust is arranged in making, hybridization, cleaning and the mensuration process of chip unavoidably, the interference of working sample amplifying nucleic acid, protein, cell and fragment of tissue, and the factors such as nonspecific reaction of the interference of noise of instrument, hybridization, often produce bigger noise signal.

Can denoising be the first step that biochip image is analyzed, disturb by filtering noise under the prerequisite that keeps useful information as far as possible, becomes the key factor that influences the chip analysis result.At present, methods such as widespread use mean filter and medium filtering are carried out the research of biochip scanning image denoising.Though mean filter has advantage simply and intuitively, but because the pollution that biochip causes in experimentation and inhomogeneous, and traditional mean filter all adopts identical filtered amplitude for entire image, so that is to say each pixel value all be in its neighborhood each pixel value and the average image sampling point edge fog that caused, and fuzzy degree is directly proportional with the size of template.Mean filter is to be the filtering that cost realizes to sacrifice important half-tone information, is difficult to guarantee the accuracy of later analysis.Medium filtering is a kind of nonlinear signal processing method, does not have the statistical property of considered pixel point, causes losing of the useful details of chip image part.Simultaneously, repeatedly use medium filtering,, can cause the fuzzy and alligatoring of image border though can eliminate impulsive noise fully substantially.In addition, if the space density of impulsive noise is bigger in the biochip image, the effect of medium filtering will descend greatly.For this reason, the present invention proposes a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation.

Summary of the invention

The present invention aims to provide a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation, and not only level and smooth ground unrest, and kept the edge details of sampling point provides assurance for improving accuracy and the reliability that chip data handles.This method should be carried out modeling to the wavelet coefficient of biochip image subband with generalized Gaussian distribution parameter estimation method, by choosing the soft-threshold function, signal variance and noise variance are estimated, determine Bayes's collapse threshold, image is carried out wavelet threshold denoising, at last image is reconstructed the image after the output denoising.

This method step is:

1, adopts the square method of estimation of generalized Gaussian distribution parameter that the biochip image that contains noise is carried out three yardstick wavelet decomposition, obtain containing the biochip image wavelet coefficient of noise;

2, adopt robustness intermediate value method of estimation that wavelet coefficient is analyzed, obtain containing the noise variance and the signal variance of the biochip image of noise, calculate the optimal threshold of determining the Bayes' risk minimum;

3, utilize the optimal threshold of Bayes' risk minimum to extract threshold process and the denoising that important wavelet coefficient is finished biochip image, obtain the biochip image wavelet coefficient after the denoising;

4, the wavelet coefficient after the denoising is reconstructed the image after the output denoising to image through wavelet inverse transformation.

The wavelet image denoising method is that the data that will have noise earlier are launched into wavelet series by wavelet transformation, and the passing threshold method is extracted important wavelet coefficient then, with the process of the wavelet coefficient after denoising wavelet inverse transformation, approaches the reconstruction unknown signaling again.With the prior model of generalized Gaussian distribution as image wavelet coefficient, employing is based on Bayes's atrophy method (BayesShrink) of Bayes criterion, this method can each subband threshold value of adaptive processing, has better atrophy characteristic than traditional general wavelet threshold.

The present invention adopts generalized Gaussian distribution and parameter estimation thereof that the biochip image wavelet coefficient has been carried out modeling, its wavelet coefficient is obeyed generalized Gaussian distribution, and the typical range of morphological parameters is in [0.5～1], by setting threshold, less biochip image noise figure is removed the purpose that reaches denoising.

The advantage of a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation of the present invention is:

1, adopt the square method of estimation of generalized Gaussian distribution parameter that the biochip image that contains noise is carried out three yardstick wavelet decomposition, obtain containing the biochip image wavelet coefficient of noise and determining its morphological parameters, illustrated that the wavelet coefficient of biochip scanning image subband is obeyed generalized Gaussian distribution.

2, utilization has been carried out denoising based on the wavelet thresholding method of Bayes' risk to the biochip scanning image, has obtained effect preferably, not only level and smooth ground unrest, and kept the edge details of sampling point.

Description of drawings

Fig. 1 is the The general frame of a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation of the present invention

Fig. 2 primeval life chip image

Fig. 3 uses the figure as a result that obtains after mean filter method, Wiener filtering and the inventive method denoising to noisy biochip image

Embodiment

The present invention is described in further detail below in conjunction with accompanying drawing.

The present invention proposes a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation.This method is determined its morphological parameters by the generalized Gaussian distribution method for parameter estimation, has illustrated that the wavelet coefficient of biochip scanning image subband is obeyed generalized Gaussian distribution.By choosing the soft-threshold function, signal variance and noise variance are estimated, determine Bayes's collapse threshold, image is carried out wavelet threshold denoising, at last image is reconstructed the image after the output denoising.This method is not only level and smooth ground unrest, and kept the edge details of sampling point.

Fig. 1 is the The general frame of a kind of biologic chip image wavelet de-noising method based on Bayesian Estimation of the present invention.

At first determine its morphological parameters, illustrated that the wavelet coefficient of biochip image subband is obeyed generalized Gaussian distribution by the generalized Gaussian distribution method for parameter estimation.

Need in the Flame Image Process image is carried out modeling accurately, the statistics prior model of an image even only partly described certain correlativity or rule between inner each pixel of image, also can improve actual image processing effect to a great extent.The present invention adopts the zero-mean generalized Gaussian distribution to describe the statistical distribution of small echo high-frequency sub-band coefficient, and its probability density function is:

$f_{\mathrm{GGD}}\left(x\right)=\frac{\mathrm{\γ}\·\mathrm{\η}\left(\mathrm{\γ}\right)}{2\mathrm{\σ\Γ}(1/\mathrm{\γ})}\exp \{-{\left[\mathrm{\η}\left(\mathrm{\γ}\right)\right|x/\mathrm{\σ}\left|\right]}^{\mathrm{\γ}}\}---\left(1\right)$

Wherein

Γ () is a gamma function, and arithmetic number γ is a form parameter.

Along with reducing of form parameter γ, the shape of generalized Gaussian distribution function is more and more sharp-pointed, and it is more and more longer to trail.Gaussian distribution and laplacian distribution function all are the special cases of generalized Gaussian distribution.γ=1 o'clock, f _GGD(x) deteriorate to laplacian distribution f _L(x); γ=2 o'clock, f _GGD(x) be Gaussian distribution.

Estimate that the generalized Gaussian distribution function parameters is this application of model basis, for sample sequence X=(x ₁, x ₂..., x _n) ^T, establish x _iObey independent identically distributed Generalized Gaussian model, i.e. x _i～f _GGD(x; γ, σ), i=1,2 ..., n, form parameter γ and standard deviation sigma are waited to estimate.

Because generalized Gaussian distribution is to be symmetrically distributed,,, investigate so adopt the single order absolute moment to replace first moment about the origin so its first moment about the origin perseverance is zero

The single order absolute moment: $m_1={\∫}_{-\∞}^{+\∞}\left|x\right|\·f_{\mathrm{GGD}}\left(x\right)\mathrm{dx}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|x_i\right|---\left(2\right)$

Second moment: $m_2={\∫}_{-\∞}^{+\∞}{x}^2\·f_{\mathrm{GGD}}\left(x\right)\mathrm{dx}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i^2---\left(3\right)$

With f _GGD(x) expression formula (1) substitution (2) and (3) obtain

$\left\{\begin{array}{c}{m}_1=\frac{{2\mathrm{k\σ}}^2}{\mathrm{\γ}}\mathrm{\Γ}(2/\mathrm{\γ})\\ m_2=\frac{{2\mathrm{k\σ}}^3}{\mathrm{\γ}}\mathrm{\Γ}(3/\mathrm{\γ})\end{array}\right.---\left(4\right)$

Wherein $k=\frac{n\·\mathrm{\γ}}{2\mathrm{\σ}\·\mathrm{\Γ}(1/\mathrm{\γ})}.$

The square of trying to achieve parameter γ and σ is estimated as

$\left\{\begin{array}{c}\widehat{\mathrm{\γ}}=F^{-1}\left(\frac{m_1^2}{m_2\·n}\right)\\ \widehat{\mathrm{\σ}}=\frac{m_2\·\mathrm{\Γ}(1/\widehat{\mathrm{\γ}})}{n\·\mathrm{\Γ}(3/\widehat{\mathrm{\γ}})}\end{array}\right.---\left(5\right)$

Wherein $F\left(x\right)=\frac{{\mathrm{\Γ}}^2(2/x)}{\mathrm{\Γ}(3/x)\·\mathrm{\Γ}(1/x)}.$

Adopt exponential function match original function F (x), set up the model y=a*e of fitting function ^B/x, adopt least square fitting, must antiderivative approximating function be

$y=0.7987*e^{\frac{0.5058}{x}}---\left(6\right)$

Ask the inverse function of approximating function to be

$F^{-1}\left(x\right)=-\frac{0.5058}{\ln x-\ln 0.7987}---\left(7\right)$

Obtain the variances sigma of residual error ²=4.4298 * 10 ^-4The square of form parameter is estimated to become

$\widehat{\mathrm{\γ}}=-\frac{0.5058}{\ln \frac{m_1^2}{m_2\·n}-\ln 0.7987}---\left(8\right)$

To the statistic histogram of biochip image 9 detail subbands after three yardstick wavelet decomposition as can be seen the biochip image wavelet coefficient meet generalized Gaussian distribution, and the form parameter typical range is in [0.5～1].

Secondly, be determining of small echo noise-removed threshold value function.

Wavelet threshold denoising is a kind of non-linear method, and its theoretical premise is, thinks the bigger wavelet coefficient of absolute amplitude mainly by obtaining after the signal transformation, and the less wavelet coefficient of absolute amplitude is then mainly by obtaining after the noise conversion.So just can pass through setting threshold, less noise figure be removed the purpose that reaches denoising.Choosing of threshold function table is the key of wavelet threshold denoising.

Threshold function table has two kinds of soft-threshold function and hard-threshold functions, and the soft-threshold function is

η(x)＝sgn(x)max(|x|-T，0) (9)

Wherein, x is a wavelet coefficient, and T is a threshold value.The soft-threshold function is to allow wavelet coefficient x and T compare earlier, shrinks to 0 according to result relatively then again.

The hard-threshold function is

$\mathrm{\η}\left(x\right)=\left\{\begin{array}{cc}x,& \left|x\right|>T\\ 0,& \left|x\right|\≤T\end{array}\right.---\left(10\right)$

Wherein, x is a wavelet coefficient, and T is a threshold value.The hard-threshold function is that absolute amplitude is kept greater than the wavelet coefficient of T, and other coefficient then is 0.

Comparatively speaking, more near the ideal value of minimax criteria, and the image after handling with soft-threshold is much level and smooth than hard-threshold in the Besov space for the soft-threshold function, so the present invention selects the soft-threshold function.

Be based on the Bayes Shrink biochip image denoising of Bayes' risk once more.

If g _{I, j}=f _{I, j}+ ε _{I, j}, g wherein _{I, j}Be the signal that observes, f _{I, j}Be actual signal, ε _{I, j}For independent same distribution and satisfy the noise of standardized normal distribution, Y _{I, j}=X _{I, j}+ V _{I, j}Be corresponding wavelet coefficient, for given parameter, purpose is to seek a thresholding to make Bayes risk minimum under Bayesian frame,

$r\left(T\right)=E{(\hat{X}-X)}^2=E_X{E}_{Y|X}{(\hat{X}-X)}^2---\left(11\right)$

Wherein, T is a threshold value, Estimation η for wavelet coefficient _r(Y).

If the optimal threshold of Bayes risk minimum is T in (11) formula ^*:

$T^{*}({\mathrm{\σ}}_X,\mathrm{\γ})=\arg \underset{T}{\min }r\left(T\right)---\left(12\right)$

T ^*Do not have the analytic solution of sealing, must obtain by means of numerical evaluation.The present invention has provided an approximate optimal solution under minimum Bayes risk meaning:

$T_B=\frac{{\widehat{\mathrm{\σ}}}^2}{{\widehat{\mathrm{\σ}}}_X}---\left(13\right)$

Wherein,

Be the estimation of noise variance signal,

Estimation for signal variance.

This threshold value is not considered form parameter because the typical range of image subband form parameter is in [0.5～1], and at this interval optimal threshold to form parameter and insensitive.

Noise variance signal

Estimate by the robustness intermediate value

$\widehat{\mathrm{\σ}}=\frac{\mathrm{Median}\left(\right|Y_{i,j}\left|\right)}{0.6745},Y_{i,j}\∈{\mathrm{HH}}_1---\left(14\right)$

Because X and Y are separate, therefore

${\mathrm{\σ}}_Y^2={\mathrm{\σ}}_X^2+{\mathrm{\σ}}^2---\left(15\right)$

σ wherein _YIt is the variance of Y.Because Y is considered to zero-mean, so σ _Y ²Can be desirable think:

${\widehat{\mathrm{\σ}}}_Y^2=\frac{1}{n^2}\underset{i,j=1}{\overset{n}{\mathrm{\Σ}}}{Y}_{i,j}^2---\left(16\right)$

Signal variance

Estimation

${\widehat{\mathrm{\σ}}}_X=\sqrt{\max ({\widehat{\mathrm{\σ}}}_Y^2-{\widehat{\mathrm{\σ}}}^2,0)}---\left(17\right)$

The wavelet coefficient of biochip image is obeyed generalized Gaussian distribution, and the typical range of form parameter is in [0.5～1], so the foregoing denoising that can be used for the genetic chip image based on the Bayes Shrink method of Bayes' risk.

At last, the present invention adopts square error MSE and two performance index of signal to noise ratio snr to estimate the denoising effect of biochip image.

Square error MSE is an index of weighing error degree between reconstructed image and the original image.Least mean-square error is more little, illustrates that the image of rebuilding is on the whole more near original image.Computing formula is

$\mathrm{MSE}=\frac{1}{n^2}\underset{i,j=1}{\overset{n}{\mathrm{\Σ}}}{({\hat{f}}_{i,j}-f_{i,j})}^2---\left(18\right)$

Wherein,

The gray-scale value that recovers the back image pixel, f are rebuild in expression _{I, j}The gray-scale value of expression original image each point.

Signal to noise ratio snr is an index of weighing noise content in the image, and with decibel (dB) expression, the high more presentation video quality of signal to noise ratio (S/N ratio) is good more, and contained noise is few more.Computing formula is

$\mathrm{SNR}=10\·\lg \left(\frac{{\mathrm{\σ}}_{{\hat{f}}_{i,j}}^2}{\mathrm{MSE}}\right)---\left(19\right)$

Wherein,

The variance of recovering back gradation of image value is rebuild in expression.

Fig. 2 is added Gaussian noise (σ=20) obtain biochip image Fig. 3 (a), the image that adopts the denoising of mean filter method to obtain to Fig. 3 (a) is Fig. 3 (d), the image 3 (b) that denoising obtains to Fig. 3 (a) employing Wiener filtering method, the image that adopts method denoising of the present invention to obtain to Fig. 3 (a) is Fig. 3 (c), and Fig. 3 has provided employing mean filter method, Wiener filtering method and method of the present invention concrete outcome to the biochip image denoising of adding Gaussian noise (σ=20).To adding Gaussian noise (σ=10 in various degree, 20,25,30) noisy biochip image Fig. 3 (a) uses mean filter method, Wiener filtering and the inventive method to carry out denoising, calculate the square error MSE and the signal to noise ratio snr of image after the denoising respectively according to formula (18) and formula (19), table 1 has provided related data.

Table 1 contains the performance after by three kinds of method denoisings of the biochip image of noise (Fig. 2) in various degree relatively

Image after the verification experimental verification denoising is compared square error and signal to noise ratio (S/N ratio) and has been improved much with noisy image, the denoising effect of this method is relatively good, not only level and smooth ground unrest, and kept the edge details of sampling point, handling for follow-up chip data provides reliable assurance.

Claims (4)

1. based on the biologic chip image wavelet de-noising method of Bayesian Estimation, it is characterized in that this method may further comprise the steps:

Step 1: adopt the square method of estimation of generalized Gaussian distribution parameter that the biochip image that contains noise is carried out three yardstick wavelet decomposition, obtain containing the biochip image wavelet coefficient of noise;

Step 2: adopt robustness intermediate value method of estimation that wavelet coefficient is analyzed, obtain containing the noise variance and the signal variance of the biochip image of noise, calculate the optimal threshold of determining the Bayes' risk minimum;

Step 3: utilize the optimal threshold of Bayes' risk minimum to extract threshold process and the denoising that important wavelet coefficient is finished biochip image, obtain the biochip image wavelet coefficient after the denoising;

Step 4: the wavelet coefficient after the denoising is reconstructed the image after the output denoising through wavelet inverse transformation to image.

2. the biologic chip image wavelet de-noising method based on Bayesian Estimation according to claim 1, this method only is applied to have the biochip image noise remove of regular point sample.

3. the biologic chip image wavelet de-noising method based on Bayesian Estimation according to claim 1 is characterized in that: the statistical distribution probability density function of the biochip image small echo high-frequency sub-band coefficient that described step 1 adopts is: Wherein

Г () is a gamma function, and arithmetic number γ is a morphological parameters.

4. the biologic chip image wavelet de-noising method based on Bayesian Estimation according to claim 1 is characterized in that: the optimal threshold computing formula of the Bayes' risk minimum of described step 2 is:

Wherein T is a threshold value,

Estimation η for the biochip image wavelet coefficient _r(Y).

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