CN112700389B - Active sludge microorganism color microscopic image denoising method - Google Patents
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Abstract
The invention relates to the technical field of microimage denoising, in particular to an active sludge microorganism color microimage denoising methodCounting, providing a denoising model, designing a bilateral weighting pseudo-norm denoising algorithm, and setting a weight matrix W 1 And W 2 Finally, optimizing and solving the model; in color image denoising, each channel is independently processed, so that a satisfactory denoising effect cannot be obtained usually, and artifacts are easily generated. Aiming at the multi-channel characteristic of a color image, the text provides a bilateral weighting pseudo-norm denoising method, and two weight matrixes W are introduced 1 And W 2 The method respectively represents the noise in three channels with different colors and different image patches, adaptively processes different noises in RGB channels, balances the multiple channels according to different noise standard deviations, and solves the noise difference among different channels, so that the denoising effect is better.
Description
Technical Field
The invention relates to the technical field of microimage denoising, in particular to a color microimage denoising method for activated sludge microorganisms.
Background
The activated sludge microorganisms have an important indicative function on judging the sewage treatment quality. And the characteristics of color, shape, detail texture and the like in the sludge microorganism microscopic image are important for the automatic detection and identification of the microorganism target. In the process of collecting and imaging sludge microorganism microscopic images, noise of the sludge microorganism microscopic images is mainly additive noise. The purpose of image denoising is to recover a clean image x from a noise observation value y ═ x + n, where n is the image noise.
When the input is a noisy RGB color image, there are generally three main strategies for denoising the color image. The first is to apply a grayscale image denoising algorithm to each channel. However, such a solution does not fully utilize the spectral correlation between RGB channels, and the denoising performance is not satisfactory. The second strategy is to convert the RGB image into a less relevant color space, such as YCbCr, and perform denoising in each channel of the converted space. One representative work in this regard is the CBM3D algorithm. However, color transformation complicates the noise distribution and the correlation between color channels is not fully exploited. The third strategy is to jointly denoise the RGB channels simultaneously to better exploit spectral correlation. For example, image blocks from the three channels RGB are concatenated into one long vector for processing.
The general natural image has the characteristics of sparsity, non-locality, low rank and the like, and the characteristics can be used as a useful basis for designing an image denoising method. Based on image sparsity, a typical denoising method constructs a denoising variational model by using dictionary-based image sparse representation, fuses non-local similar prior and sparse prior into a regular term of the variational model, and then obtains a denoised image by solving the variational model. Based on image nonlocal, the representative denoising method applies unsupervised learning clustering to image denoising, greatly improves the operating efficiency of a nonlocal mean value in image denoising, and effectively improves the denoising effect. Based on low-rank denoising, the algorithm searches similar pixel blocks in a search region for the initially denoised reference pixel block, then the similar blocks at the corresponding positions of the original image form a similarity matrix, and the similarity matrix is subjected to low-rank matrix decomposition, so that noise and signals are effectively separated, and a finally denoised image is obtained.
In addition, a clear natural image and a corresponding data matrix of the image are often low-rank or approximately low-rank, because image information has great correlation, but if noise is introduced into the image, the low-rank of original data is damaged. The low rank matrix recovery is formed by treating the degraded image contaminated by noise as a set of low dimensional data plus noise, so that the data to obtain the pre-degraded image can be approximated by the low rank matrix. However, solving the rank function is an NP hard problem, which is mostly solved by relaxing it to a kernel norm in a practical problem. The Singular Value Threshold (SVT) method makes the standard kernel norm have a closed form solution, but the commonly used soft threshold shrinkage is not an optimal denoising method, and the phenomenon of image over-smoothing is easy to occur. On the basis of the standard nuclear norm, a weighted standard nuclear norm minimum (WNNM) method is proposed, original image information can be well reserved according to the actual meaning of singular values in an image, but the WNNM algorithm needs to set weights manually, and therefore denoising is not ideal. The non-convex norm-based low-dimensional image denoising algorithm replaces a rank function in a model by using a non-convex function on the basis of a traditional low-rank denoising model, so that a better approximate effect of the rank function is obtained, but the algorithm is only effective for gray level images.
Noise in the standard RGB color space can be modeled approximately as additive white gaussian noise, which, due to the optical sensor characteristics and the on-board processing mechanisms in the microscope digital camera pipeline, can produce different noise variances for different color channels. If these three channels are treated equally during the denoising process, false colors and artifacts will appear, which makes the image denoising problem more complicated. How to solve different noise characteristics in color channels and how to effectively utilize channel correlation are the key points for designing a good color image denoising algorithm.
Based on the method, the invention designs the denoising method of the activated sludge microorganism color microscopic image to solve the problems.
Disclosure of Invention
The invention aims to provide a method for denoising an activated sludge microorganism color microscopic image, which aims to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a denoising method of activated sludge microorganism color microscopic images comprises the following steps:
s1: establishing a denoising model: given a color noise image y, assume that N local patches are extracted
And stretching each local patch into a vector
Is shown in which
Is the corresponding patch in channel c, where c e { r, g, b } is the index of the r, g and b channels, for each local image block y i Searching M local image blocks most similar to the local image blocks by Euclidean distance in a local window, superposing each local patch and M similar patches column by column, and then forming N noise patch matrixes
To estimate a clean plaque matrix
Another expression of the noise plaque matrix Y is, wherein Y c Is a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
s2: designing a bilateral weighting pseudo-norm denoising algorithm: (2) w as defined in 1 And W 2 For the weight matrix, two weight matrices W are provided 1 And W 2 Is arranged as a diagonal matrix and is,
the pseudo-norm | | X | | non-conducting phosphor θ Is defined as:
where θ >0, m, n represents the height and width of the matrix X, the pseudo-norm | | X | | purple cells θ Is further shown as
s3: setting a weight matrix W 1 And W 2 : the noise in local patches can be modeled approximately as additive white gaussian noise, W 1 For regularizing the difference of the rows of the residual matrix (Y-X), and W 2 For regularizing the (Y-X) column differences. Noise plaque matrix
Clean noise patch
Determining a weight matrix W using a maximum a posteriori estimate 1 And W 2 ：
Where log-likelihood term lnP (X-Y) has the statistical property of noise, assuming that the noise is independent, identically distributed in each channel and each image block, and each image block is gaussian-distributed:
let P (X) obey the following distribution:
bringing (5) and (6) into (4) yields:
s4: model optimization and solution: the formula (2) is solved by adopting a variable splitting method TSWC, and the formula (2) is converted into a linear equality constraint problem with two variables X and Z by introducing an augmentation variable Z.
Equation (8) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (8) is:
initial variable X 0 ,Z 0 ,Δ 0 Set to 0 matrix, respectively with X k ,Z k ,Δ k Representing the optimization variables and the lagrangian multiplier for the number of iterations k (k ═ 0, 1, 2, …), the variables can be updated alternately by taking the derivative of the lagrangian function L with respect to X and Z and setting the derivative to zero, X being updated by fixing Z and Δ:
its solution satisfies
AX k+1 +X k+1 B k ＝E k ， (11)
Wherein
Equation (11) is a standard Sieve's equation, if and only if
Has a unique solution where σ (F) represents the sequence of the matrix F, i.e. the set of eigenvalues, SE (11) can be rewritten as:
by X k+1 ＝vec -1 (vec(X k+1 ) To obtain a solution X k+1 ，
In the case of the sub-problem of Z,
in machine learning, the theta norm is defined by the definition of equation (3)
This function is known as a concave function with respect to x. The norm can be linearized according to a concave function superstep definition to obtain an explicit solution to the optimization problem using a singular value thresholding method. By definition of the super-gradient of the concave function, let σ i For the ith singular value of the matrix Z, we can obtain:
from equation (15), the solution of equation (14) can be relaxed to obtain the following optimization solution problem:
eliminating the constant term to obtain
Since the non-convex theta norm is a continuous, concave, smooth, and derivable monotonically increasing function at [0, + ∞), the gradient is non-negative and monotonically decreasing, due to the non-increasing nature of singular values, with
Therefore, the problem singular value threshold method solves:
for p k >0, given
And is
Equation (17) has a global optimal solution:
wherein, the first and the second end of the pipe are connected with each other,
is composed of
The explicit solution of equation (15) can be obtained by singular value decomposition of (c). Update Δ by fixing X and Z:
Δ k+1 ＝Δ k +(X k+1 -Z k+1 )， (19)
updating rho: rho k+1 ＝μρ k ,μ≥1。
The above replacement updating steps are repeated until a convergence condition is satisfied or the number of iterations exceeds a preset threshold K1. When satisfying | | X at the same time k -Z k || F ≤Tol，||X k+1 -X k || F Tol and Z are less than or equal to k+1 -Z k || F When the total Tol is less than or equal to, the ADMM algorithm converges, wherein the total>0 is a small tolerance number.
Further, W in the formula (2) 1 Is a block diagonal matrix with three blocks, each block having the same diagonal elements to describe the noise characteristics in the corresponding RGB channel. W is a group of 2 Is used to describe the noise variance, W, in the corresponding image patch matrix 1 And W 2 Are determined by the noise standard deviation in the corresponding channel and image patch matrix, respectively.
Further, in step S1
Is the corresponding patch in channel c, where c ∈ { r, g, b } is the index of the r, g, and b channels.
Further, σ in step S2 r ，σ g ，σ b Respectively representing the noise levels of the three channels of the noise image RGB,
to have a dimension p 2 M is the number of patches in the noise patch matrix.
Further, in the Y expression in step S3
Sub-matrices of similar patches in R, G, B noisy channels, respectively, X in the expression
Are the sub-matrices of similar patches in the R, G, B ideal noise-free channels, respectively.
Further, Δ in equation (9) is an augmented lagrange multiplier, and ρ >0 is a penalty parameter.
Compared with the prior art, the invention has the beneficial effects that:
(1) for a color microorganism microscopic image, the color microorganism microscopic image has the characteristics of low signal-to-noise ratio and low contrast, the noise difference of each channel is obvious, if the three channels are equally processed in the denoising process, a satisfactory denoising effect cannot be obtained generally, and artifacts are easy to generate; in addition, the color microorganism microscopic image has low resolution, more internal details and irregular texture distribution, and the de-noised image is easy to blur. Aiming at the characteristics of a color microorganism microscopic image, the method for denoising the bilateral weighted pseudo-norm is provided, wherein two weight matrixes W1 and W2 are introduced, W1 represents noise in three different color channels, different noises in RGB channels are processed in a self-adaptive mode, the multiple channels are balanced according to different noise standard deviations of the multiple channels, and the noise difference among the different channels is solved; w2 represents noise in different image patches, the algorithm firstly carries out image blocking processing, then extracts N local patches and searches similar patches of the N local patches to form N noise patch matrixes, noise in each patch matrix can be better removed through W2, image blurring is reduced, and the overall denoising effect is better;
(2) conventional low rank denoising generally approximates a rank function by using an L1 norm or a kernel norm, and a pseudo norm is proposed herein to approximate the rank function, and the pseudo norm is a concave function and can be conveniently solved according to the characteristics of a super-gradient. The expression of the pseudo-norm is
The proportion of different singular values in the rank function minimization model can be automatically corrected according to the singular value of the rank function, so that the signal-to-noise ratio of a de-noised image can be effectively improved;
(3) for the color image denoising model, an Alternating Direction Multiplier Method (ADMM) is proposed to solve based on an augmented Lagrangian function, so that each updating step has a closed form solution and convergence can be guaranteed. Compared with other algorithms, the algorithm has better convergence.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is an approximation of the different norms versus rank of the present invention;
FIG. 2 is a table listing algorithm parameters of the present invention;
FIG. 3 is a PSNR value graph of denoising results of different denoising methods of the present invention;
FIG. 4 is a comparison graph of the denoising results of Paramecium when σ is 25 and σ is 50 for each algorithm;
fig. 5 is a comparison graph of denoising results of Coleps when σ is 25 and σ is 50 for each algorithm;
FIG. 6 is a graph of the PSNR variation with respect to the number of iteration steps according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-6, the present invention provides a technical solution: the method for denoising the activated sludge microorganism color microscopic image is characterized by comprising the following steps of:
s1: establishing a denoising model: given a color noise image y, assume that N local patches are extracted
And stretching each local patch into a vector
Is shown in which
Is the corresponding patch in channel c, where c ∈ { r, g, b } is the index of the r, g, and b channels, for each local image block y i Searching M local image blocks most similar to the local image blocks by Euclidean distance in a local window, superposing each local patch and the M similar patches column by column, and forming N noise patch matrixes
To estimate a clean plaque matrix
Another expression of the noise plaque matrix Y is
Wherein Y is c Is a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
the low-rank structure of the matrix is the sparsity defined in its singular values, similar to the minimization of L0, which is a challenging problem, so the rank function is usually bounded by the convex-kernel norm | | X | | * ＝∑ i σ i (X) substitution, whereinσ i (X) singular values representing X, such as the classical method WNNM based on image low rank prior denoising, can be written as follows:
the first term is a fidelity term and is used for restraining noise, and the second term is a regular term, namely a weighted nuclear norm, and is used for describing the low-rank property of the image. On the basis of the existing WNNM method, a kernel norm is replaced by a pseudo norm, and a denoising model is provided:
in this model, two weight matrices W are added 1 And W 2 Noise statistics in each channel and each image block can be represented in a self-adaptive manner, and simultaneously, combined denoising is carried out on RGB channels, so that the noise difference among different channels is solved, spectral correlation can be better utilized, and false colors or artifacts are avoided when the three channels are treated in an equal manner; in addition, the pseudo-norm is used for approximating the rank function, the weight is automatically set according to the singular value, the rank function can be better approximated, and therefore the image can obtain a better denoising effect.
S2: designing a bilateral weighting pseudo-norm denoising algorithm: color images have different noise statistics on the RGB channels, which makes the color image denoising problem more challenging than grayscale image denoising, artifacts may occur if they are extended directly to true color image denoising by connecting image blocks of the RGB channels. The invention utilizes the low rank of the image non-local self-similarity prior image block, introduces two weight matrixes for data items in an RGB channel pseudo-norm minimization model, adaptively processes different noises in the RGB channel, balances multiple channels according to different noise standard deviations, and solves the noise difference between different channels.
W in the formula (3) 1 And W 2 For the weight matrix, two weight matrices are usedW 1 And W 2 Set as a diagonal matrix, W in said formula (3) 1 Is a block diagonal matrix with three blocks, each block having the same diagonal elements to describe the noise characteristics in the corresponding RGB channel. W is a group of 2 Each diagonal element of (a) is used to describe the noise variance in the corresponding image patch matrix,
wherein sigma r ，σ g ，σ b Respectively representing the noise levels of the three channels of the noise image RGB,
to have a dimension p 2 M is the number of patches in the noise patch matrix, W 1 And W 2 Are determined by the noise standard deviation in the corresponding channel and image patch matrix respectively,
the traditional image denoising method uses an L1 norm to replace an L0 norm, because the L0 norm is difficult to be optimally solved, and the L1 norm is a convex approximation of the L0 norm, which is easy to be optimally solved. But since the L1 norm is a loose approximation of the L0 norm, L1 minimises the resulting solution usually sub-optimal. Therefore, the invention provides a pseudo-norm | | | X | | non-conducting phosphor θ Defined as:
where θ >0, m, n represents the height and width of matrix X, and a conventional rank function is generally non-linear using a convex kernel norm | | X | * ＝∑ i σ i (X) indicates that all singular values are treated equally in the conventional rank function minimization model and shrunk by the same threshold. However, this ignores that people are often pragmaticA priori knowledge of the singular values of the data matrix. For natural images, with general a priori knowledge, larger singular values of X are more important than smaller singular values, since they represent the energy of the principal component of X. In denoising applications, singular values are key. An algorithm is adopted to obtain a clean image for the image damaged by the noise, and a larger singular value and a smaller singular value need to be reduced according to different weights. Obviously, the traditional rank function minimization model is not flexible enough to handle these problems.
The invention provides a pseudo norm | | | X | | non-conducting phosphor θ Further expressed as:
S3: setting a weight matrix W 1 And W 2 : the invention relates to W 1 And W 2 Set as a diagonal matrix, W 1 Is a block diagonal matrix composed of three blocks, each having the same diagonal elements to describe the noise characteristics in the corresponding R, G or B channel. The noise in the local patches can be modeled approximately as additive white Gaussian noise, with W 2 Describes the noise variance in the corresponding patch, in general, W 1 For regularizing the difference of the rows of the residual matrix (Y-X), and W 2 For regularizing the (Y-X) column differences.
Noise patch matrix
Therein
Respectively R, G, B containSubmatrix of similar patches in noisy channels, clean noise patches
Therein
Sub-matrixes of similar plaques in R, G and B ideal noise-free channels respectively, and a weight matrix W is determined by adopting maximum posterior estimation 1 And W 2 ：
Where log-likelihood lnP (X-Y) has the statistical property of noise, assuming that the noise is independently and identically distributed in each channel and in each image block, and that each image block is gaussian-distributed:
let P (X) obey the following distribution:
bringing (6) and (7) into (5) yields:
s4: model optimization and solution: the equation (3) is solved by adopting a variable splitting method TSWC, and the equation (3) is converted into a linear equality constraint problem with two variables X and Z by introducing an augmentation variable Z.
Equation (9) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (9) is:
where Δ is the augmented Lagrange multiplier, ρ>0 is a penalty parameter, and the initial variable X 0 ,Z 0 ,Δ 0 Set to 0 matrix, respectively with X k ,Z k ,Δ k Representing the optimization variables and the lagrangian multiplier for the number of iterations k (k ═ 0, 1, 2, …), the variables can be updated alternately by taking the derivative of the lagrangian function L with respect to X and Z and setting the derivative to zero, X being updated by fixing Z and Δ:
its solution satisfies
AX k+1 +X k+1 B k ＝E k (12)
Wherein
Equation (12) is a standard Sieve's equation, if and only if
Has a unique solution where σ (F) represents the sequence of the matrix F, i.e. the set of eigenvalues, SE (12) can be rewritten as:
by X k+1 ＝vec -1 (vec(X k+1 ) To obtain a solution X k+1 ，
In the case of the Z sub-problem,
in machine learning, the theta norm is defined by the definition of equation (4)
This function is known as a concave function with respect to x. The norm can be linearized according to a concave function superstep definition to obtain an explicit solution to the optimization problem using a singular value thresholding method. By definition of the super-gradient of the concave function, let σ i For the ith singular value of matrix Z, we can obtain:
from equation (16), the solution of equation (15) can be relaxed to obtain the following optimization solution problem:
eliminating the constant term to obtain
Since the non-convex theta norm is a continuous, concave, smooth, and derivable monotonically increasing function over [0, + ∞), the gradient is non-negative and monotonically decreasing, due to the non-increasing nature of the singular values, with
Therefore, the problem singular value threshold method solves:
for p k >0, given
And is
Equation (18) has a global optimal solution:
wherein the content of the first and second substances,
is composed of
The explicit solution of equation (15) can be obtained by singular value decomposition of (c). Update Δ by fixing X and Z:
Δ k+1 ＝Δ k +(X k+1 -Z k+1 ) (20)
updating rho: rho k+1 ＝μρ k ,μ≥1。
Repeating the replacing and updating steps until a convergence condition is met or the iteration number exceeds a preset threshold value K 1 . When satisfying | | X at the same time k -Z k || F ≤Tol，||X k+1 -X k || F Tol and Z are less than or equal to k+1 -Z k || F At Tol, the ADMM algorithm converges, wherein Tol>0 is a small tolerance number. Pseudo code of the ADMM algorithm is as follows:
ADMM algorithm:
inputting: y, { sigma., (S) r ,σ g ,σ b }，μ，Tol，K 1 ；
Initialization: x 0 ＝Z 0 ＝Δ 0 ＝0,ρ 0 >0；
For: k is 1: K 1 ；
1. Updating X through (12);
2. updating Z by (19);
3. updating delta through (20);
4. through ρ k+1 ＝μρ k Mu is more than or equal to 1 to update rho;
when the convergence condition is satisfied or K is more than or equal to K 1 Finishing;
and (3) outputting: matrices X and Z.
Given the color noise image y, in view of the low resolution characteristic of the microorganism microscopic image, the image resolution is firstly subjected to linear amplification treatment, and then N local plaques are extracted
And their similar plaques. In view of the characteristic that the internal details of the microbial image are multiple, the window size of the similar image block search is set to be 30 x 30, the calculated amount is increased due to the overlarge window, the algorithm efficiency is reduced, and the algorithm accuracy is reduced due to the overlarge window, so that the denoising effect is influenced. Then N noise patch matrices are formed
To estimate a clean plaque matrix
Will matrix
In the image processing system, patches are gathered to form a denoised image
In order to obtain better denoising effect, the denoising step K is repeatedly executed 2 Next, the process is carried out. The pseudo code of the denoising algorithm of the invention is as follows:
the color microorganism image denoising algorithm based on bilateral weighting and pseudo norm comprises the following steps:
inputting: noisy image y, { sigma } r ,σ g ,σ b }，μ，K 2 ；
Initialization:
y (0) ＝y；
for: k is 1: K 2 ；
1. Make it possible to
2. From y (k) Extracted local patch
For each y j ：
3. Find each y j Non-local similar patch Y j ；
4. For each Y j Using ADMM algorithm to solve to obtain estimated value
End up
5. Handle
Aggregate into images
Ending;
and (3) outputting: de-noised image
And (3) analyzing test results:
the experiment PC is provided with a memory of 4G, a main frequency of 1.7GHz, an operating system of win 1064 bits and a software design platform of MATLAB 2016. Two types of microorganism microscopic images are selected for representation in the experiment, namely Paramecium Paramecium image with the resolution of 185X 172 and Coleps howitches image with the resolution of 223X 226. These two types of images are rich in color and have more internal details. Selecting a representative denoising algorithm: gaussian filtering, non-local mean denoising (NL-means) and WNNM algorithm are compared with the algorithm of the invention, and denoising results are compared from two aspects of objective index and subjective quality respectively.
Objective index:
the classical peak signal-to-noise ratio (PSNR) parameter that measures the denoising effect is defined as follows:
the Structural Similarity (SSIM) parameter is defined as follows:
where M and N are the number of rows and columns of the image, X is the denoised image, Y is the plaque noise matrix, u is the number of rows and columns of the image X ，u Y The average, σ, of the pixels in X and Y, respectively X ，σ Y The variance of the X and Y pixel values, respectively. Sigma XY Is the covariance of X and Y, C 1 ，C 2 Is to adjust the parameter, typically take C 1 ＝(k 1 l) 2 ,C 2 ＝(k 2 l) 2 ,k 1 ＝0.01,k 2 0.03 and 255. SSIM is always less than 1, with 1 indicating complete similarity. For most image denoising algorithms, the standard deviation of noise should be used as a parameter, and the noise standard σ of a color image can be estimated by some noise estimation method.
The noise criteria for the mth patch of Y may be initialized as:
wherein, y m Is the m-th column, x, in the image block matrix Y m Is the m-th image block recovered in the previous iteration. By using modes trained at the same or similar noise levelEach channel is processed to perform denoising of the color image. Parameter definitions and values in the algorithm are shown in fig. 2.
It can be seen from fig. 3 that the method provided by the present invention is superior to other comparison methods in different test images and different noise levels no matter in PSNR indexes or SSIM indexes, and in order to better approximate a rank function, the present invention provides a pseudo-norm to approximate the rank function, and the method can automatically set weights according to the magnitude of singular values, thereby greatly improving the signal-to-noise ratio of the de-noised image.
Subjective quality:
all the denoised images are displayed in an experiment, local details are amplified to observe the removal precision of noise points and the retention degree of image details and edge information, and then qualitative evaluation of the subjective denoising effect is given. Fig. 4 is a comparison graph of the denoising results of Paramecium when σ -25 and σ -50 are provided for each algorithm, and fig. 5 is a comparison graph of the denoising results of Coleps when σ -25 and σ -50 are provided for each algorithm.
Observing the whole images in the figures 4 and 5, the Gaussian filter algorithm is not ideal for removing noise points, the NL-means de-noised images are easy to generate blurs, and the WNNM algorithm and the algorithm of the invention realize better de-noising effect. As can be seen from the detailed enlarged portions of fig. 4 and 5, the internal structure of the microorganism image is better retained in the present invention compared with other methods. The invention provides a bilateral weighting pseudo-norm denoising algorithm, which utilizes the noise characteristics of different channels and local image blocks to denoise. Specifically, two weight matrixes are introduced into a data fidelity term of the weighted pseudo-norm minimization model to adaptively characterize noise statistics in each image block of each channel, so that the algorithm achieves a good denoising effect.
And (3) convergence analysis:
in order to verify the convergence of the algorithm provided by the invention, a PSNR change value curve of the algorithm and the WNNM algorithm when denoising Paramecium and Coleps images is drawn, as shown in FIG. 6. It can be seen from the figure that the algorithm provided by the invention is stable in relative change value in 2 steps or so of iteration, and the WNNM algorithm is stable in relative change value in 5 steps or so of iteration, which shows that the convergence of the algorithm is better than that of the WNNM algorithm from numerical experiments.
The invention provides a bilateral weighting pseudo-norm denoising algorithm for a color microorganism image. The color image has the characteristic of multiple channels, so that the invention introduces two weight matrixes to respectively represent the noise in different color channels and different image patch matrixes, and then uses the pseudo norm to approximate a rank function, thereby greatly improving the signal-to-noise ratio of the de-noised image. Compared with other methods, the algorithm has the best denoising effect, can more completely retain the internal details of the image while denoising, and improves the image quality.
The product model provided by the invention is only used according to the structural characteristics of the product, the product can be adjusted and modified after being purchased so as to be more matched and accord with the technical scheme of the invention, the product model is the best application technical scheme of the technical scheme, the product model can be replaced and modified according to the required technical parameters, and the product model is well known by the technical personnel in the field, so that the technical scheme provided by the invention can clearly obtain the corresponding use effect.
In the description herein, references to the description of "one embodiment," "an example," "a specific example," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise form disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (2)
1. The active sludge microorganism color microscopic image denoising method is characterized by comprising the following steps:
s1: establishing a denoising model: given a color noise image y, assume that N local patches are extracted
And stretching each local patch into a vector
Is shown in which
Is the corresponding patch in channel c, where c e { r, g, b } is the index of the r, g and b channels, for each local image block y i Searching M local image blocks most similar to the local image blocks by Euclidean distance in a local window, superposing each local patch and M similar patches column by column, and then forming N noise patch matrixes
To estimate a clean plaque matrix
Another expression form of the noise plaque matrix Y is
Wherein Y is c Is a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
the low-rank structure of the matrix is the sparsity defined in its singular values, similar to the L0 minimization, with the rank function usually being bounded by the convex-kernel norm | X | | * ＝∑ i σ i (X) in which σ is i The (X) represents the singular value of X, and on the basis of the existing WNNM method, the pseudo norm is used for replacing the nuclear norm, and a denoising model is provided:
s2: designing a bilateral weighting pseudo-norm denoising algorithm: (2) w as defined in 1 And W 2 For the weight matrix, two weight matrices W are provided 1 And W 2 Is arranged as a diagonal matrix and is,
wherein sigma r ，σ g ，σ b Respectively representing the noise levels of the three channels of the noise image RGB,
to have a dimension p 2 M is the number of patches in the noise patch matrix, the pseudo-norm | | X | | survival θ Is defined as follows:
where θ >0, m, n represent a matrix XHeight and width, pseudo-norm | | | X | | non-woven phosphor θ Is further shown as
The weight is
The pseudo-norm can automatically set the weight according to the size of a singular value;
s3: setting a weight matrix W 1 And W 2 : the noise in local patches can be modeled approximately as additive white gaussian noise, W 1 For regularizing the difference of the rows of the residual matrix (Y-X), and W 2 Differences for regularizing (Y-X) columns; noise plaque matrix
Clean noise patch
In the expression Y
Sub-matrices of similar patches in R, G, B noisy channels, respectively, of the X expression
Sub-matrixes of similar patches in R, G and B ideal noise-free channels respectively, and a weight matrix W is determined by adopting maximum posterior estimation 1 And W 2 ：
Where log-likelihood term lnP (X-Y) has the statistical property of noise, assuming that the noise is independent, identically distributed in each channel and each image block, and each image block is gaussian-distributed:
let P (X) obey the following distribution:
bringing (5) and (6) into (4) yields:
s4: model optimization and solution: the formula (2) is solved by adopting a variable splitting method TSWC, the formula (2) is converted into a linear equality constraint problem with two variables X and Z by introducing an augmentation variable Z,
equation (8) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (8) is:
where Δ is the augmented Lagrangian multiplier, ρ>0 is a penalty parameter, and the initial variable X 0 ,Z 0 ,Δ 0 Set to 0 matrix, respectively with X k ,Z k ,Δ k Representing the optimization variable and the lagrangian multiplier for the number of iterations k, the variables can be updated alternately by taking the derivative of the lagrangian function L with respect to X and Z and setting the derivative to zero, X is updated by fixing Z and Δ:
its solution satisfies
AX k+1 +X k+1 B k ＝E k (11)，
Wherein
Equation (11) is a standard Sieve's equation, if and only if
Has a unique solution where σ (F) represents the sequence of the matrix F, i.e. the set of eigenvalues, SE (11) can be rewritten as:
by X k+1 ＝vec -1 (vec(X k+1 ) To obtain a solution X k+1 ，
In the case of the Z sub-problem,
in machine learning, the theta norm is defined by the definition of equation (3)
Knowing that the function is a concave function with respect to x, the norm can be linearized by defining the super-gradient of the concave function, and the maximum is obtained by using a singular value thresholding methodExplicit solutions to the optimization problem, defined by the super-gradient of the concave function, let σ i For the ith singular value of matrix Z, we can obtain:
from equation (15), the solution of equation (14) can be relaxed to obtain the following optimization solution problem:
eliminating the constant term to obtain
Since the non-convex theta norm is a continuous, concave, smooth, and derivable monotonically increasing function over [0, + ∞), the gradient is non-negative and monotonically decreasing, due to the non-increasing nature of the singular values, with
Therefore, the problem singular value threshold method solves for:
for p k >0, given
And is
Equation (17) has a global optimal solution:
wherein the content of the first and second substances,
is composed of
May yield an explicit solution of equation (14);
update Δ by fixing X and Z:
Δ k+1 ＝Δ k +(X k+1 -Z k+1 ) (19)，
updating rho k+1 ＝μρ k ,μ≥1；
And repeating the replacing and updating steps until a convergence condition is met or the iteration number exceeds a preset threshold value K1. When satisfying | | X at the same time k -Z k || F ≤Tol，||X k+1 -X k || F Tol and Z are less than or equal to k+1 -Z k || F At Tol, the ADMM algorithm converges, wherein Tol>0 is a small tolerance number.
2. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: w in the formula (2) 1 Is a block diagonal matrix having three blocks, each block having the same diagonal elements to describe noise characteristics in the corresponding RGB channel; w is a group of 2 Is used to describe the noise variance, W, in the corresponding image patch matrix 1 And W 2 Are determined by the noise standard deviation in the corresponding channel and image patch matrix, respectively.
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