CN101799916A

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

Info

Publication number: CN101799916A
Application number: CN 201010124500
Authority: CN
Inventors: 刘国传; 陆琳
Original assignee: Individual
Current assignee: Individual
Priority date: 2010-03-16
Filing date: 2010-03-16
Publication date: 2010-08-11

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

Biological chip image wavelet denoising method based on Bayesian estimation

Technical Field

The invention belongs to the field of biological signal image processing, relates to a biochip image denoising method, and particularly relates to a biochip image wavelet denoising method based on Bayesian estimation.

Background

The biochip is a microarray array composed of many nucleic acid molecules immobilized in a small area on a solid support at predetermined positions. Because a biochip integrates thousands of spots on a tiny substrate, each spot expressing certain biological information, a chip scanner is used to scan and collect images of the hybridized chip, the intensity or ratio of each target area in the array is extracted by analyzing the biochip image, and the detection result of the biochip is determined by combining chip descriptions (the sequence of each probe and the position of the probe on the chip) in a database.

The biochip technology is not limited to the preparation process of the biochip, the detection and analysis of the information of the biochip are key contents, the noise suppression and filtering of the biochip image are very important steps in the application process of the biochip, and the analysis result directly influences the precision and accuracy of the subsequent processing (image segmentation, sampling point identification and brightness extraction) result of the image, so that the popularization and the use of the biochip are influenced.

Different from the common image, due to the influence of factors such as biochip processing equipment, scanning equipment, light and the like, the analyzed biochip image is randomly distributed with fuzzy points with different sizes, different depths, unclear positions and different forms on a gradually changed background, and the ideal effect is difficult to achieve by using the conventional analysis method. Moreover, the chip is difficult to avoid dust pollution in the processes of manufacturing, hybridizing, cleaning and measuring, the interference of nucleic acid, protein, cells and tissue fragments in a measured sample, the interference of instrument noise, nonspecific reaction of hybridization and other factors are often generated to generate larger noise signals.

Denoising is the first step of biochip image analysis, and can filter noise interference on the premise of retaining useful information as much as possible, and becomes an important factor influencing the analysis result of the biochip. At present, methods such as mean filtering and median filtering are widely applied to the research of denoising of biochip scanning images. Although the average filtering has the advantages of simplicity and intuition, the pollution caused by the biochip in the experimental process is not uniform, and the traditional average filtering adopts the same filtering amplitude for the whole image, namely, each pixel value is the average of the sum of all the pixel values in the neighborhood, so that the edge of the image sampling point is blurred, and the blurring degree is in direct proportion to the size of the template. The average filtering is implemented at the expense of important gray scale information, and the accuracy of the subsequent analysis is difficult to ensure. The median filtering is a nonlinear signal processing method, and does not consider the statistical characteristics of pixel points, so that the loss of useful details of the image part of the chip is caused. Meanwhile, the median filtering is used many times, and although impulse noise can be substantially completely eliminated, blurring and coarsening of image edges are caused. In addition, if the spatial density of the impulse noise in the biochip image is large, the effect of median filtering will be greatly reduced. Therefore, the invention provides a biochip image wavelet denoising method based on Bayesian estimation.

Disclosure of Invention

The invention aims to provide a biological chip image wavelet denoising method based on Bayesian estimation, which not only smoothes background noise, but also retains edge details of sampling points, and provides guarantee for improving accuracy and reliability of chip data processing. The method comprises the steps of modeling wavelet coefficients of a biochip image sub-band by using a generalized Gaussian distribution parameter estimation method, estimating signal variance and noise variance by selecting a soft threshold function, determining a Bayesian shrinkage threshold, denoising an image by using a wavelet threshold, reconstructing the image, and outputting the denoised image.

The method comprises the following steps:

1. performing three-scale wavelet decomposition on the biochip image containing the noise by adopting a moment estimation method of generalized Gaussian distribution parameters to obtain a wavelet coefficient of the biochip image containing the noise;

2. analyzing the wavelet coefficient by adopting a robustness median estimation method to obtain the noise variance and the signal variance of the biochip image containing noise, and calculating and determining the optimal threshold with the minimum Bayesian risk;

3. extracting important wavelet coefficients by using the optimal threshold with the minimum Bayesian risk to complete threshold processing and denoising processing of the biochip image, and obtaining the wavelet coefficients of the denoised biochip image;

4. and reconstructing the image by the denoised wavelet coefficient through wavelet inverse transformation, and outputting the denoised image.

The wavelet transform image denoising method is that the data with noise is first expanded into wavelet series through wavelet transform, then the important wavelet coefficient is extracted through a threshold value method, and then the denoised wavelet coefficient is subjected to wavelet inverse transform to approximate to reconstruct the unknown signal. The generalized Gaussian distribution is used as a prior model of an image wavelet coefficient, a Bayes shrinkage method (Bayes shrnk) based on a Bayes criterion is adopted, and the method can adaptively process the threshold of each sub-band and has more ideal shrinkage characteristics than the traditional general wavelet threshold.

The invention adopts generalized Gaussian distribution and parameter estimation thereof to model the wavelet coefficient of the biochip image, the wavelet coefficient obeys the generalized Gaussian distribution, the typical range of morphological parameters is 0.5-1, and the smaller noise coefficient of the biochip image is eliminated by setting a threshold value to achieve the purpose of denoising.

The invention discloses a biochip image wavelet denoising method based on Bayesian estimation, which has the advantages that:

1. the method adopts a moment estimation method of generalized Gaussian distribution parameters to carry out three-scale wavelet decomposition on a biochip image containing noise to obtain a biochip image wavelet coefficient containing noise and determine morphological parameters of the biochip image wavelet coefficient, which shows that the wavelet coefficient of a biochip scanning image sub-band obeys generalized Gaussian distribution.

2. The wavelet threshold method based on Bayesian risk is used for denoising the biochip scanning image, so that a good effect is obtained, background noise is smoothed, and edge details of sampling points are retained.

Drawings

FIG. 1 is a general block diagram of a biochip image wavelet denoising method based on Bayesian estimation

FIG. 2 original biochip image

FIG. 3 is a graph of the results of denoising noisy biochip images using mean filtering, wiener filtering and the method of the invention

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

The invention provides a biological chip image wavelet denoising method based on Bayesian estimation. The method determines the morphological parameters of the biological chip scanning image by a generalized Gaussian distribution parameter estimation method, and shows that the wavelet coefficients of the biological chip scanning image sub-band obey the generalized Gaussian distribution. Estimating the signal variance and the noise variance by selecting a soft threshold function, determining a Bayesian shrinkage threshold, denoising the image by using a wavelet threshold, reconstructing the image, and outputting the denoised image. The method not only smoothes background noise, but also retains edge details of the sampling points.

FIG. 1 is a general block diagram of a biochip image wavelet denoising method based on Bayesian estimation.

Firstly, morphological parameters of the biological chip image are determined by a generalized Gaussian distribution parameter estimation method, which shows that wavelet coefficients of a biological chip image sub-band obey generalized Gaussian distribution.

In the image processing, accurate modeling needs to be carried out on an image, and even if a statistical prior model of the image only partially describes certain correlation or law among pixel points in the image, the actual image processing effect can be improved to a great extent. The invention adopts zero mean generalized Gaussian distribution to describe the statistical distribution of wavelet high-frequency sub-band coefficients, and the probability density function is as follows:

wherein

Γ (·) is a gamma function, and a positive real γ is a shape parameter.

With the reduction of the shape parameter gamma, the shape of the generalized Gaussian distribution function is more and more sharp, and the tail is longer and longer. GaussBoth the distribution and the laplacian distribution function are special cases of the generalized gaussian distribution. When gamma is 1, f_GGD(x) Degenerated to Laplace distribution f_L(x) (ii) a When gamma is 2, f_GGD(x) Is a gaussian distribution.

Estimating the parameters of the generalized Gaussian distribution function is the application basis of the model, and for a sampling sequence, X is (X)₁，x₂，…，x_n)^TLet x_iGeneralized Gaussian model obeying independent homodistributions, i.e. x_i～f_GGD(x; γ, σ), i ═ 1, 2, …, n, and the shape parameter γ is to be estimated from the standard deviation σ.

The generalized Gaussian distribution is symmetrical distribution, so that the first-order origin moment is constantly zero, and the first-order absolute moment is adopted to replace the first-order origin moment to investigate

First order absolute moment:

<math><mrow><msub><mi>m</mi><mn>1</mn></msub><mo>=</mo><msubsup><mo>&Integral;</mo><mrow><mo>-</mo><mo>∞</mo></mrow><mrow><mo>+</mo><mo>∞</mo></mrow></msubsup><mo>|</mo><mi>x</mi><mo>|</mo><mo>·</mo><msub><mi>f</mi><mi>GGD</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>dx</mi><mo>=</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>|</mo><msub><mi>x</mi><mi>i</mi></msub><mo>|</mo><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math>

second moment:

<math><mrow><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><msubsup><mo>&Integral;</mo><mrow><mo>-</mo><mo>∞</mo></mrow><mrow><mo>+</mo><mo>∞</mo></mrow></msubsup><msup><mi>x</mi><mn>2</mn></msup><mo>·</mo><msub><mi>f</mi><mi>GGD</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>dx</mi><mo>=</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math>

will f is_GGD(x) Substituting the expression (1) into the expressions (2) and (3) to obtain

Wherein

Obtaining an estimate of the moments of the parameters gamma and sigma

Wherein

Fitting the original function F (x) by using an exponential function, and establishing a model y ═ a × e of the fitting function^b/xFitting by least square method to obtain approximation function of primitive function as

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

Solving the inverse of the approximation function to

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

The variance sigma of the residual error is obtained²＝4.4298×10^-4. The moment estimate of the shape parameter becomes

The statistical histogram of 9 detail sub-bands after the three-scale wavelet decomposition of the biochip image shows that the wavelet coefficient of the biochip image conforms to the generalized Gaussian distribution, and the typical range of the shape parameter is 0.5-1.

Secondly, determining a wavelet denoising threshold function.

The wavelet threshold denoising is a nonlinear method, and the theoretical premise is that a wavelet coefficient with a larger absolute amplitude is mainly obtained after signal transformation, and a wavelet coefficient with a smaller absolute amplitude is mainly obtained after noise transformation. Therefore, the purpose of denoising can be achieved by setting a threshold value and eliminating a smaller noise coefficient. The selection of the threshold function is the key of wavelet threshold denoising.

The threshold function includes soft threshold function and hard threshold function, the soft threshold function is

η(x)＝sgn(x)max(|x|-T，0) (9)

Where x is the wavelet coefficient and T is the threshold. The soft threshold function is to compare the wavelet coefficients x and T and then shrink to 0 based on the comparison.

Hard threshold function of

Where x is the wavelet coefficient and T is the threshold. The hard threshold function is such that wavelet coefficients with absolute magnitude greater than T are retained, while the other coefficients are 0.

Relatively speaking, the soft threshold function is closer to the ideal value of the minimum maximum criterion in the Besov space, and the image processed by the soft threshold is much smoother than the hard threshold, so the soft threshold function is selected by the invention.

And de-noising the Bayes Shrink biochip image based on the Bayesian risk.

Let g_i，j＝f_i，j+ε_i，jWherein g is_i，jFor observed signals, f_i，jIs a true signal,. epsilon_i，jNoise, Y, independently identically distributed and satisfying a standard normal distribution_i，j＝X_i，j+V_i，jFor the corresponding wavelet coefficients, for a given parameter, the goal is to find a threshold value that minimizes the Bayes risk under the bayesian framework,

r (T) = E {(\hat{X} - X)}^{2} = E_{X} E_{Y | X} {(\hat{X} - X)}^{2} - - - (11)

wherein, T is a threshold value,for estimation of wavelet coefficients eta_r(Y)。

Setting the optimal threshold value T that minimizes the Bayes risk in equation (11)^*：

T^*There is no closed analytical solution, which must be obtained by means of numerical calculations. The invention provides an approximately optimal solution in the sense of minimum Bayes risk:

wherein,

is an estimate of the variance of the noise signal,

is an estimate of the signal variance.

The threshold does not take into account the shape parameter, since the typical range of image subband shape parameters is 0.5-1, while the optimal threshold in this interval is not sensitive to the shape parameter.

Variance of noise signal

By robust median estimation

<math><mrow><mover><mi>σ</mi><mo>^</mo></mover><mo>=</mo><mfrac><mrow><mi>Median</mi><mrow><mo>(</mo><mo>|</mo><msub><mi>Y</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>|</mo><mo>)</mo></mrow></mrow><mn>0.6745</mn></mfrac><mo>,</mo><msub><mi>Y</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>&Element;</mo><msub><mi>HH</mi><mn>1</mn></msub><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>14</mn><mo>)</mo></mrow></mrow></math>

Since X and Y are independent of each other, therefore

Wherein sigma_YIs the variance of Y. Because Y is considered to be zero-mean, σ_Y ²It can be ideally considered that:

variance of signal

Is estimated by

The wavelet coefficient of the biochip image obeys generalized Gaussian distribution, and the typical range of the shape parameter is [ 0.5-1 ], so the Bayes spring method based on the Bayes risk can be used for denoising the gene chip image.

Finally, the invention adopts two performance indexes of mean square error MSE and signal-to-noise ratio SNR to evaluate the denoising effect of the biochip image.

The mean square error MSE is an index for measuring the degree of error between the reconstructed image and the original image. The smaller the minimum mean square error, the closer the reconstructed image is to the original image as a whole. Is calculated by the formula

Wherein,

representing the gray value of the image pixel after reconstruction recovery, f_i，jRepresenting the gray value of each point of the original image.

The SNR is an index for measuring the noise content in an image, and is expressed in decibels (dB), wherein a higher SNR indicates better image quality and less noise. Is calculated by the formula

Wherein,

representing the variance of the gray value of the image after reconstruction recovery.

Fig. 3(a) is a biochip image obtained by adding gaussian noise (σ ═ 20) to fig. 2, fig. 3(d) is an image obtained by denoising with a mean value filtering method to fig. 3(a), fig. 3(b) is an image obtained by denoising with a wiener filtering method to fig. 3(a), fig. 3(c) is an image obtained by denoising with the method of the present invention to fig. 3(a), and fig. 3 shows specific results of denoising a biochip image added with gaussian noise (σ ═ 20) with the mean value filtering method, the wiener filtering method and the method of the present invention. Denoising a noisy biochip image map 3(a) added with Gaussian noises (sigma is 10, 20, 25 and 30) of different degrees by using a mean value filtering method, a wiener filtering method and the method of the invention, respectively calculating the mean square error MSE and the signal-to-noise ratio SNR of the denoised image according to a formula (18) and a formula (19), and giving relevant data in Table 1.

TABLE 1 comparison of the performance of biochip images (FIG. 2) containing different degrees of noise after denoising by three methods

The mean square error and the signal-to-noise ratio of the denoised image are greatly improved compared with the noisy image through test verification, the denoising effect of the method is good, the background noise is smoothed, the edge details of the sampling points are reserved, and reliable guarantee is provided for subsequent chip data processing.

Claims

1. The biochip image wavelet denoising method based on Bayesian estimation is characterized by comprising the following steps:

the method comprises the following steps: performing three-scale wavelet decomposition on the biochip image containing the noise by adopting a moment estimation method of generalized Gaussian distribution parameters to obtain a wavelet coefficient of the biochip image containing the noise;

step two: analyzing the wavelet coefficient by adopting a robustness median estimation method to obtain the noise variance and the signal variance of the biochip image containing noise, and calculating and determining the optimal threshold with the minimum Bayesian risk;

step three: extracting important wavelet coefficients by using the optimal threshold with the minimum Bayesian risk to complete threshold processing and denoising processing of the biochip image, and obtaining the wavelet coefficients of the denoised biochip image;

step four: and reconstructing the image by the denoised wavelet coefficient through wavelet inverse transformation, and outputting the denoised image.

2. The wavelet denoising method for biochip image based on Bayesian estimation according to claim 1, which is applied only to biochip image noise removal with regular spotting.

3. The biochip image wavelet denoising method based on Bayesian estimation as recited in claim 1, wherein: the statistical distribution probability density function of the wavelet high-frequency sub-band coefficient of the biochip image adopted in the first step is as follows:wherein

R (·) is a gamma function, and positive real numbers γ are morphological parameters.

4. The biochip image wavelet denoising method based on Bayesian estimation as recited in claim 1, wherein: the optimal threshold calculation formula with the minimum Bayesian risk in the second step is as follows:

wherein T is a threshold value, and T is a threshold value,

estimation of wavelet coefficients for biochip images_r(Y)。