CN112700389A - Active sludge microorganism color microscopic image denoising method - Google Patents

Active sludge microorganism color microscopic image denoising method Download PDF

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CN112700389A
CN112700389A CN202110043199.6A CN202110043199A CN112700389A CN 112700389 A CN112700389 A CN 112700389A CN 202110043199 A CN202110043199 A CN 202110043199A CN 112700389 A CN112700389 A CN 112700389A
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周芳
孙照旋
朱志峰
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Anhui University of Technology AHUT
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Abstract

The invention relates to the technical field of microimage denoising, in particular to an activated sludge microorganism color microimage denoising method1And W2Finally, optimizing and solving the model; in color image denoising, each channel is independently processed, so that a satisfactory denoising effect cannot be generally achieved, 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 introduced1And W2The 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

Active sludge microorganism color microscopic image denoising method
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 sludge microorganism microscopic image, the noise is mainly additive noise in the process of collection and imaging. The purpose of image denoising is to recover a clean image x from the noise observation 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 color images. 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 non-local, the representative denoising method applies unsupervised learning clustering to image denoising, greatly improves the operation efficiency of non-local mean values 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 often solved by relaxing it to a nuclear norm in an actual problem. The Singular Value Threshold (SVT) method makes the standard nuclear 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 better kept according to the actual significance of singular values in an image, but a WNNM algorithm needs to set weights manually, so that 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 for 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
Figure BDA0002896680150000031
And stretching each local patch into a vector
Figure BDA0002896680150000032
Figure BDA0002896680150000033
Is shown in which
Figure BDA0002896680150000034
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 yiSearching 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
Figure BDA0002896680150000035
To estimate a clean plaque matrix
Figure BDA0002896680150000036
Another expression of the noise plaque matrix Y is, wherein YcIs a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
Figure BDA0002896680150000037
the low-rank structure of the matrix is the sparsity defined in its singular values, similar to the L0 minimization, the rank function is usually bounded by the convex kernel norm | | X | |*＝∑iσi(X) instead of the above-mentioned (A),where ρ isi(X) represents a singular value of X, and on the basis of the existing WNNM method, a pseudo norm is used for replacing a nuclear norm to provide a denoising model:
Figure BDA0002896680150000038
s2: designing a bilateral weighting pseudo-norm denoising algorithm: (2) w as defined in1And W2For the weight matrix, two weight matrices W are provided1And W2Is set as a diagonal matrix and is,
Figure BDA0002896680150000039
Figure BDA00028966801500000310
the pseudo-norm | | X | | non-conducting phosphorθIs defined as:
Figure BDA00028966801500000311
where θ > 0, m, n represents the height and width of the matrix X, the pseudo-norm | | X | | purple cellsθIs further shown as
Figure BDA00028966801500000312
The weight is
Figure BDA0002896680150000041
The pseudo norm can automatically set weight according to the size of a singular value;
s3: setting a weight matrix W1And W2: the noise in local patches can be modeled approximately as additive white gaussian noise, W1For regularizing the difference of the rows of the residual matrix (Y-X), and W2For regularizing the (Y-X) column differences. Noise plaque matrix
Figure BDA0002896680150000042
Clean noise patch
Figure BDA0002896680150000043
Determining a weight matrix W using a maximum a posteriori estimation1And W2：
Figure BDA0002896680150000044
Where log-likelihood term lnP (X | Y) has the statistical property of noise, assuming that the noise is an independent, identical distribution at each channel and each image block, and each image block is gaussian-distributed:
Figure BDA0002896680150000045
let P (X) obey the following distribution:
Figure BDA0002896680150000046
bringing (5) and (6) into (4) yields:
Figure BDA0002896680150000047
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.
Figure BDA0002896680150000048
Equation (8) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (8) is:
Figure BDA0002896680150000049
initial variable X0，Z0，Δ0Set to 0 matrix, respectively with Xk，Zk，ΔkRepresenting 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:
Figure BDA0002896680150000051
its solution satisfies
AXk+1+Xk+1Bk＝Ek， (11)
Wherein
Figure BDA0002896680150000052
Figure BDA0002896680150000053
Equation (11) is a standard Sieve's equation, if and only if
Figure BDA0002896680150000054
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:
Figure BDA0002896680150000055
by Xk+1＝vec-1(vec(Xk+1) To obtain a solution Xk+1，
In the case of the Z sub-problem,
Figure BDA0002896680150000056
in machine learning, the theta norm is defined by the definition of equation (3)
Figure BDA0002896680150000057
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 concave superstep, let σiFor the ith singular value of matrix Z, we can obtain:
Figure BDA0002896680150000058
from equation (15), the solution of equation (14) can be relaxed to obtain the following optimization solution problem:
Figure BDA0002896680150000059
by approximating the constant term, a
Figure BDA00028966801500000510
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
Figure BDA00028966801500000511
Therefore, the problem singular value threshold method solves:
for pk> 0, given
Figure BDA0002896680150000061
And is
Figure BDA0002896680150000062
Equation (17) has a global optimumSolution:
Figure BDA0002896680150000063
wherein,
Figure BDA0002896680150000064
Figure BDA0002896680150000065
is composed of
Figure BDA0002896680150000066
The explicit solution of equation (15) can be obtained by singular value decomposition of (a). Update Δ by fixing X and Z:
Δk+1＝Δk+(Xk+1-Zk+1)， (19)
updating rho: rhok+1＝μρk，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 timek-Zk||F≤Tol，||Xk+1-Xk||FTol and Z are less than or equal tok+1-Zk||FAt Tol, the ADMM algorithm converges, wherein Tol>0 is a small tolerance number.
Further, W in the formula (2)1Is a block diagonal matrix with three blocks, each block having the same diagonal elements to describe the noise characteristics in the corresponding RGB channel. W2Is used to describe the noise variance, W, in the corresponding image patch matrix1And W2Are determined by the noise standard deviation in the corresponding channel and image patch matrix, respectively.
Further, in step S1
Figure BDA0002896680150000067
Is the corresponding patch in channel c, where c ∈ { r, g, b } is the index of the r, g, and b channels.
Go toStep of, σ in step S2r，σg，σbRespectively representing the noise levels of the three channels of the noise image RGB,
Figure BDA0002896680150000068
to have a dimension p2M is the number of patches in the noise patch matrix.
Further, in the expression of Y in step S3
Figure BDA0002896680150000069
Sub-matrices of similar patches in R, G, B noisy channels, respectively, of the X expression
Figure BDA00028966801500000610
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 Lagrangian 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 generally obtained, and artifacts are easily generated; 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
Figure BDA0002896680150000071
Figure BDA0002896680150000072
The proportion of different singular values in the rank function minimization model can be automatically corrected according to the size of the singular value of the rank function, so that the signal-to-noise ratio of the de-noised image can be effectively improved;
(3) for the color image denoising model, an Alternating Direction Multiplier Method (ADMM) is proposed based on an augmented Lagrange function to solve, so that each updating step has a closed form solution and convergence can be ensured. 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 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 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
Figure BDA0002896680150000081
And stretching each local patch into a vector
Figure BDA0002896680150000082
Figure BDA0002896680150000083
Is shown in which
Figure BDA0002896680150000084
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 yiSearching 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
Figure BDA0002896680150000085
To estimate a clean plaque matrix
Figure BDA0002896680150000086
Another expression of the noise plaque matrix Y is
Figure BDA0002896680150000087
Wherein Y iscIs a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
Figure BDA0002896680150000088
the low-rank structure of the matrix is sparsity defined in its singular values, similar to L0 minimization, which is a challenging problem, so the rank function is usually bounded by a convex kernel norm | | X | |*＝∑iσi(X) in which σ isi(X) singular values representing X, such as the classical method WNNM based on image low rank prior denoising, can be written as follows:
Figure BDA0002896680150000091
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 pseudo norm is used for replacing a nuclear norm, and a denoising model is provided:
Figure BDA0002896680150000092
in this model, two weight matrices W are added1And W2Noise 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 three channels are equally processed; 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 be better denoised.
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)1And W2For the weight matrix, two weight matrices W are provided1And W2Set as a diagonal matrix, W in said formula (3)1Is a block diagonal matrix with three blocks, each block having the same diagonal elements to describe the noise characteristics in the corresponding RGB channel. W2Each diagonal element of (a) is used to describe the noise variance in the corresponding image patch matrix,
Figure BDA0002896680150000093
Figure BDA0002896680150000094
wherein sigmar，σg，σbRespectively representing the noise levels of the three channels of the noise image RGB,
Figure BDA0002896680150000095
to have a dimension p2M is the number of patches in the noise patch matrix, W1And W2Are 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 is extremely smallThe solution obtained by the optimization is usually sub-optimal. Therefore, the invention provides a pseudo-norm | | | X | | non-conducting phosphorθDefined as:
Figure BDA0002896680150000101
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 |*＝∑iσi(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 one's often a priori knowledge of the singular values of the actual data matrix. For natural images, with general a priori knowledge, the larger singular values of X are more important than the smaller singular values because 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 phosphorθFurther expressed as:
Figure BDA0002896680150000102
the weight is
Figure BDA0002896680150000103
The pseudo norm can automatically set weight according to the size of a singular value; as can be seen from fig. 1, the pseudo-norm has a better approximation effect on the rank function than the conventional norm. Thus, the present invention utilizes this norm to characterize the low rank nature, σ, of a noiseless imageiIs the i-th singular value of the matrix X
S3: setting a weight matrix W1And W2: the invention relates to W1And W2Set as a diagonal matrix, W1Is 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 channelAnd (4) sex. The noise in the local patches can be modeled approximately as additive white Gaussian noise, with W2Describes the noise variance in the corresponding patch, in general, W1For regularizing the difference of the rows of the residual matrix (Y-X), and W2For regularizing the (Y-X) column differences.
Noise plaque matrix
Figure BDA0002896680150000104
Therein
Figure BDA0002896680150000105
Sub-matrices of similar patches in R, G, B noisy channels, clean noise patches, respectively
Figure BDA0002896680150000111
Therein
Figure BDA0002896680150000112
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 estimation1And W2：
Figure BDA0002896680150000113
Where log-likelihood term lnP (X | Y) has the statistical property of noise, assuming that the noise is an independent, identical distribution at each channel and each image block, and each image block is gaussian-distributed:
Figure BDA0002896680150000114
let P (X) obey the following distribution:
Figure BDA0002896680150000115
bringing (6) and (7) into (5) yields:
Figure BDA0002896680150000116
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.
Figure BDA0002896680150000117
Equation (9) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (9) is:
Figure BDA0002896680150000118
where Δ is the augmented Lagrange multiplier and ρ > 0 is a penalty parameter, the initial variable X is set to be0，Z0，Δ0Set to 0 matrix, respectively with Xk，Zk，ΔkRepresenting 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:
Figure BDA0002896680150000121
its solution satisfies
AXk+1+Xk+1Bk＝Ek (12)
Wherein
Figure BDA0002896680150000122
Figure BDA0002896680150000123
Equation (12) is a standard Sieve's equation, if and only if
Figure BDA0002896680150000124
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:
Figure BDA0002896680150000125
by Xk+1＝vec-1(vec(Xk+1) To obtain a solution Xk+1，
In the case of the Z sub-problem,
Figure BDA0002896680150000126
in machine learning, the θ norm is defined by the definition of equation (4)
Figure BDA0002896680150000127
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 concave superstep, let σiFor the ith singular value of matrix Z, we can obtain:
Figure BDA0002896680150000128
from equation (16), the solution of equation (15) can be relaxed to obtain the following optimization solution problem:
Figure BDA0002896680150000129
by approximating the constant term, a
Figure BDA00028966801500001210
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
Figure BDA00028966801500001211
Therefore, the problem singular value threshold method solves:
for pk> 0, given
Figure BDA00028966801500001212
And is
Figure BDA00028966801500001213
Equation (18) has a global optimal solution:
Figure BDA00028966801500001214
wherein,
Figure BDA0002896680150000131
Figure BDA0002896680150000132
is composed of
Figure BDA0002896680150000133
The explicit solution of equation (15) can be obtained by singular value decomposition of (a). Update Δ by fixing X and Z:
Δk+1＝Δk+(Xk+1-Zk+1) (20)
updating rho: rhok+1＝μρk，μ≥1。
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 timek-Zk||F≤Tol，||Xk+1-Xk||FTol and Z are less than or equal tok+1-Zk||FAt 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，σg，σb}，μ，Tol，K1；
Initialization: x0＝Z0＝Δ0＝0，ρ0＞0；
For: k is 1: K1；
1. Updating X through (12);
2. updating Z by (19);
3. updating Δ by (20);
4. through rhok+1＝μρkMu is more than or equal to 1 to update rho;
when the convergence condition is satisfied or K is more than or equal to K1Finishing;
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 amplified linearly, and then N local plaques are extracted
Figure BDA0002896680150000134
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
Figure BDA0002896680150000135
To estimate a clean plaque matrix
Figure BDA0002896680150000136
Will matrix
Figure BDA0002896680150000137
In the image processing system, patches are gathered to form a denoised image
Figure BDA0002896680150000138
Repeatedly executing the denoising step K to obtain better denoising effect2Next, 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，σg，σb}，μ，K2；
Initialization:
Figure BDA0002896680150000139
y(0)＝y；
for: k is 1: K2；
1. Make it
Figure BDA0002896680150000141
2. From y(k)Extracted local patch
Figure BDA0002896680150000142
For each yj：
3. Find each yjNon-local similar patch Yj；
4. For each YjUsing ADMM algorithm to solve to obtain estimated value
Figure BDA0002896680150000143
End up
5. Handle
Figure BDA0002896680150000144
Aggregate into images
Figure BDA0002896680150000145
Finishing;
and (3) outputting: de-noised image
Figure BDA0002896680150000146
And (3) analyzing test results:
the configuration memory of the experimental PC is 4G, the main frequency is 1.7GHz, the operating system is win1064 bits, and the software design platform is MATLAB 2016. Two types of microorganism microscopic image representatives are selected in the experiment, namely a Paramecium Paramecium image with the resolution of 185 x 172 and a Coleps grenade image with the resolution of 223 x 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:
Figure BDA0002896680150000147
the Structural Similarity (SSIM) parameter is defined as follows:
Figure BDA0002896680150000148
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, uX，uYThe average values, σ, of the pixels in X and Y, respectivelyX，σYThe variance of the X and Y pixel values, respectively. SigmaXYIs the covariance of X and Y, C1，C2Is to adjust the parameter, typically take C1＝(k1l)2，C2＝(k2l)2，k1＝0.01，k20.03 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.
Figure BDA0002896680150000151
The noise criteria for the mth patch of Y may be initialized as:
Figure BDA0002896680150000152
wherein, ymIs the m-th column, x, in the image block matrix YmIs the m-th image block recovered in the previous iteration. Denoising of color images is performed by processing each channel using a model trained at the same or similar noise level. 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 under different test images and different noise levels no matter on PSNR indexes or SSIM indexes, in order to better approximate the rank function, the present invention provides a pseudo-norm to approximate the rank function, the method can automatically set the weight according to the singular value, and the signal-to-noise ratio of the de-noised image is greatly improved.
Subjective quality:
and displaying all the denoised images in an experiment, amplifying local details to observe the removal precision of noise points and the retention degree of image details and edge information, and then giving qualitative evaluation of the subjective denoising effect. Fig. 4 is a comparison graph of the denoising results of paramecimum when σ is 25 and σ is 50 for each algorithm, and fig. 5 is a comparison graph of the denoising results of Coleps when σ is 25 and σ is 50 for each algorithm.
Observing the whole images in the figures 4 and 5, the Gaussian filtering algorithm is not ideal for removing noise points, the NL-means denoised image is easy to generate blur, and the WNNM algorithm and the algorithm of the invention realize better denoising 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 (Peak signal to noise ratio) change value curve of the algorithm and a 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" or the like are intended to 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 forms 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 (6)

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
Figure FDA0002896680140000011
And stretching each local patch into a vector
Figure FDA0002896680140000012
Figure FDA0002896680140000013
Is shown in which
Figure FDA0002896680140000014
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 yiSearching 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
Figure FDA0002896680140000015
To estimate a clean plaque matrix
Figure FDA0002896680140000016
Another expression of the noise plaque matrix Y is
Figure FDA0002896680140000017
Wherein Y iscIs a sub-matrix of channel c, and image low-rank denoising can be written as the following model:
Figure FDA0002896680140000018
the low-rank structure of the matrix is the sparsity defined in its singular values, similar to the L0 minimization, the rank function is usually bounded by the convex kernel norm | | X | |*＝∑iσi(X) in which σ isi(X) represents a singular value of X, and on the basis of the existing WNNM method, a pseudo norm is used for replacing a nuclear norm to provide a denoising model:
Figure FDA0002896680140000019
s2: designing a bilateral weighting pseudo-norm denoising algorithm: (2) w as defined in1And W2For the weight matrix, two weight matrices W are provided1And W2Is set as a diagonal matrix and is,
Figure FDA00028966801400000110
Figure FDA00028966801400000111
the pseudo-norm | | X | | non-conducting phosphorθIs defined as:
Figure FDA00028966801400000112
where θ > 0, m, n represents the height and width of the matrix X, the pseudo-norm | | X | | purple cellsθIs further shown as
Figure FDA00028966801400000113
The weight is
Figure FDA00028966801400000114
The pseudo norm can automatically set weight according to the size of a singular value;
s3: setting a weight matrix W1And W2: the noise in local patches can be modeled approximately as additive white gaussian noise, W1For regularizing the difference of the rows of the residual matrix (Y-X), and W2For regularizing the (Y-X) column differences. Noise plaque matrix
Figure FDA0002896680140000021
Clean noise patch
Figure FDA0002896680140000022
Determining a weight matrix W using a maximum a posteriori estimation1And W2：
Figure FDA0002896680140000023
Where log-likelihood term lnP (X | Y) has the statistical property of noise, assuming that the noise is an independent, identical distribution at each channel and each image block, and each image block is gaussian-distributed:
Figure FDA0002896680140000024
let P (X) obey the following distribution:
Figure FDA0002896680140000025
bringing (5) and (6) into (4) yields:
Figure FDA0002896680140000026
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.
Figure FDA0002896680140000027
Equation (8) can be solved under the framework of the Alternative Direction Multiplier Method (ADMM), and the augmented lagrange function of (8) is:
Figure FDA0002896680140000028
initial variable X0，Z0，Δ0Set to 0 matrix, respectively with Xk，Zk，ΔkRepresenting 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:
Figure FDA0002896680140000031
its solution satisfies
AXk+1+Xk+1Bk＝Ek (11)，
Wherein
Figure FDA0002896680140000032
Figure FDA0002896680140000033
Equation (11) is a standard Sieve's equation, if and only if
Figure FDA0002896680140000034
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:
Figure FDA0002896680140000035
by Xk+1＝vec-1(vec(Xk+1) To obtain a solution Xk+1，
In the case of the Z sub-problem,
Figure FDA0002896680140000036
in machine learning, the theta norm is defined by the definition of equation (3)
Figure FDA0002896680140000037
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 concave superstep, let σiFor the ith singular value of matrix Z, we can obtain:
Figure FDA0002896680140000038
from equation (15), the solution of equation (14) can be relaxed to obtain the following optimization solution problem:
Figure FDA0002896680140000039
by approximating the constant term, a
Figure FDA00028966801400000310
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
Figure FDA00028966801400000311
Therefore, the problem singular value threshold method solves:
for pk> 0, given
Figure FDA00028966801400000312
And is
Figure FDA00028966801400000313
Equation (17) has a global optimal solution:
Figure FDA0002896680140000041
wherein,
Figure FDA0002896680140000042
Figure FDA0002896680140000043
is composed of
Figure FDA0002896680140000044
The explicit solution of equation (14) can be obtained by singular value decomposition of (a). Update Δ by fixing X and Z:
Δk+1＝Δk+(Xk+1-Zk+1) (19)，
updating rho: rhok+1＝μρk，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 timek-Zk||F≤Tol，||Xk+1-Xk||FTol and Z are less than or equal tok+1-Zk||FBelow Tol, the ADMM algorithm converges, where Tol > 0 is a small number of tolerances.
2. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: w in the formula (2)1Is a block diagonal matrix with three blocks, each block having the same diagonal elements to describe the noise characteristics in the corresponding RGB channel. W2Is used to describe the noise variance, W, in the corresponding image patch matrix1And W2Are determined by the noise standard deviation in the corresponding channel and image patch matrix, respectively.
3. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: in step S1
Figure FDA0002896680140000045
Is the corresponding patch in channel c, where c ∈ { r, g, b } is the index of the r, g, and b channels.
4. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: σ in step S2r，σg，σbRespectively representing the noise levels of the three channels of the noise image RGB,
Figure FDA0002896680140000046
to have a dimension p2M is the number of patches in the noise patch matrix.
5. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: in Y expression in step S3
Figure FDA0002896680140000047
Sub-matrices of similar patches in R, G, B noisy channels, respectively, of the X expression
Figure FDA0002896680140000048
Are the sub-matrices of similar patches in the R, G, B ideal noise-free channels, respectively.
6. The activated sludge microorganism color microscopic image denoising method of claim 1, characterized in that: Δ in equation (9) is the augmented Lagrangian multiplier, and ρ > 0 is a penalty parameter.
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