CN116188333B - Multiplicative additive mixed noise removal method based on structured integral least square - Google Patents

Multiplicative additive mixed noise removal method based on structured integral least square Download PDF

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CN116188333B
CN116188333B CN202310485614.2A CN202310485614A CN116188333B CN 116188333 B CN116188333 B CN 116188333B CN 202310485614 A CN202310485614 A CN 202310485614A CN 116188333 B CN116188333 B CN 116188333B
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noise
multiplicative
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structured
image
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CN116188333A (en
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黄华
宋凌飞
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Beijing Normal University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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Abstract

The invention discloses a multiplicative additive mixed noise removal method based on structured integral least square, and belongs to the field of image processing. The implementation method of the invention comprises the following steps: vectorizing an input image into a column vector in a column-first manner
Figure ZY_1
The column vector
Figure ZY_2
Is of the size of
Figure ZY_3
The method comprises the steps of carrying out a first treatment on the surface of the For multiplicative, additive hybrid noise, the noise is modeled using a structured integral least squares method, by adding, in constructing a structured integral least squares objective equation
Figure ZY_4
Disturbance, modeling and representing multiplicative noise and additive noise by combining 2-norm error terms; and solving a structured integral least square target equation by adopting a numerical method, and removing additive noise and multiplicative noise in the image by optimizing the target equation so as to improve the image quality.

Description

Multiplicative additive mixed noise removal method based on structured integral least square
Technical Field
The invention relates to a multiplicative additive mixed noise removing method based on structured integral least square, and belongs to the field of image processing.
Background
The imaging detector inevitably suffers from various types of noise, limited by the processing technology and detection principles. The most typical ones include two types: one is multiplicative noise due to non-uniformity in the response rate of each pixel on the detector array, and the other is additive noise due to thermal noise, electronic noise, and the like. The presence of both types of noise significantly reduces the quality of the infrared image, affecting visual effects and later higher layer (e.g., detection, identification, tracking, etc.) applications. Therefore, removing multiplicative noise and additive noise in an image has a very important application value.
The existing method is aimed at single additive noise, and there are few methods for simultaneously considering multiplicative noise and additive noise. This is because: 1) In normal visible light imaging, additive noise is a key factor that degrades image quality; 2) Additive noise is mathematically easier to handle, and the resulting optimization equation is typically a convex function. As the level of imaging detector technology increases, so does the demand for image quality. As an inherent factor limiting the image quality, removal of multiplicative noise becomes very necessary. In addition, in the field of non-visible light imaging (such as infrared thermal imaging), multiplicative noise tends to be more pronounced, so to improve image quality, both multiplicative noise and additive noise must be removed.
Disclosure of Invention
In order to solve the technical problems, the main purpose of the invention is to provide a multiplicative additive mixed noise removing method based on structured integral least square, wherein for multiplicative and additive mixed noise, a structured integral least square method is used for modeling multiplicative noise and additive noise; the objective equation based on the structured integral least square is constructed, the objective equation of the structured integral least square is solved by adopting a numerical method, additive noise and multiplicative noise in an image are removed by optimizing the objective equation, and the image quality is improved.
The aim of the invention is achieved by the following technical scheme.
The invention discloses a multiplicative additive mixed noise removal method based on structured integral least square, which comprises the following steps:
step 1: acquiring a noise-contaminated input image including a noise-contaminated image
Figure SMS_1
。
The image described in step 1
Figure SMS_2
Is +.>
Figure SMS_3
Wherein>
Figure SMS_4
Representing the image height +.>
Figure SMS_5
Representing the image width.
Step 2: prioritizing input images by columnVectorization into a column vector
Figure SMS_6
。
The column vectors described in step 2
Figure SMS_7
Is +.>
Figure SMS_8
。
Step 3: solving a target equation based on structured integral least squares to obtain a column vector
Figure SMS_9
。
The target equation in step 3 is
Figure SMS_10
In the middle of
Figure SMS_12
Is the variance of additive noise; />
Figure SMS_17
Is the variance of multiplicative noise; />
Figure SMS_22
The weight coefficient is preset; />
Figure SMS_14
Is that
Figure SMS_16
A unit matrix; />
Figure SMS_20
For structured disturbance, by structured disturbance +.>
Figure SMS_23
Characterizing multiplicative noise, namely, only diagonal elements of the matrix are non-zero, and other position elements are zero; />
Figure SMS_11
Is->
Figure SMS_15
A column vector; />
Figure SMS_19
A differential operator in the row direction; />
Figure SMS_24
A differential operator in the column direction; />
Figure SMS_13
Represents a 2-norm; />
Figure SMS_18
Representing the Frobenius norm. By adding->
Figure SMS_21
Disturbance, combining with a 2-norm error term, effectively modeling multiplicative noise and additive noise, and obtaining a denoised image by optimizing a target equation.
Step 4: column vector obtained in step 3
Figure SMS_25
Rearranged into a +.>
Figure SMS_26
Is a matrix of (a)
Figure SMS_27
Obtaining denoised image +.>
Figure SMS_28
I.e. multiplicative additive hybrid noise removal based on structured integral least squares.
The step 3 further comprises the following steps:
step 31: determining additive noise variance
Figure SMS_29
And multiplicative noise variance->
Figure SMS_30
。
The noise variance is obtained from the detector parameters in step 31 or by means of noise measurements.
Step 32: initialization of
Figure SMS_31
、/>
Figure SMS_32
。
Described in step 32
Figure SMS_33
Initializing to a matrix with all elements zero, < >>
Figure SMS_34
Initialized to->
Figure SMS_35
。
Step 33: fixing
Figure SMS_36
Solving->
Figure SMS_37
。
Step 33 solves the following objective equation
Figure SMS_38
In the middle of
Figure SMS_39
Is a matrix in which all the elements except the diagonal elements are zero.
Step 34: fixing
Figure SMS_40
Solving->
Figure SMS_41
。
Step 34 solves the following objective equation
Figure SMS_42
Step 35: and calculating a target equation value, and judging whether the convergence is achieved. If not, steps 33-34 are repeated.
The target equation in step 35 is
Figure SMS_43
If it is
Figure SMS_44
Judging that the convergence is achieved; otherwise, it does not converge. Wherein->
Figure SMS_45
For preset parameters, ++>
Figure SMS_46
、/>
Figure SMS_47
For the result of the latest iteration, +.>
Figure SMS_48
、/>
Figure SMS_49
The result obtained in the previous iteration is obtained.
Step 36: outputting the column vector obtained by solving
Figure SMS_50
。
Advantageous effects
1. The multiplicative and additive mixed noise removing method based on the structured integral least square disclosed by the invention has the advantages that the multiplicative and additive mixed noise is modeled by adopting the structured integral least square, and the multiplicative noise and the additive noise in an image can be effectively removed by solving a target equation based on the structured integral least square, so that the image quality is obviously improved.
2. The invention discloses a multiplicative additive mixed noise removing method based on structured integral least squares, which is implemented by adding in a target equation for constructing structured integral least squares
Figure SMS_51
Disturbance and 2 norm error items are combined, multiplicative noise and additive noise are effectively modeled, and accuracy and robustness of estimated parameters in the image denoising process can be considered.
Drawings
Fig. 1 and fig. 2 are flowcharts of an infrared image rotation motion blur restoration method based on a thermal diffusion model.
FIG. 3 is a comparison of the recovery effect of the method of the present invention with the prior art method.
Wherein fig. 3 (a) is an image contaminated with noise, and fig. 3 (b) is the effect of the method of the present invention after noise reduction.
Description of the embodiments
The present invention will be described in detail with reference to the accompanying drawings and examples. The technical problems and the beneficial effects solved by the technical proposal of the invention are also described, and the described embodiment is only used for facilitating the understanding of the invention and does not have any limiting effect.
The embodiment discloses a multiplicative additive mixed noise removing method based on structured integral least square, which is applied to the field of infrared image noise reduction. The test hardware conditions are: inter 7 6700,8G RAM,Matlab 2016.
As shown in fig. 1, the method for removing multiplicative additive mixed noise based on structured integral least squares disclosed in this embodiment specifically comprises the following implementation steps:
step 10: acquiring images contaminated with noise
Figure SMS_52
。
In the present embodiment, the image size is
Figure SMS_53
The pixel bit depth is 14 bits.
Step 20: image is formed
Figure SMS_54
Vectorizing into a column vector according to the column priority mode>
Figure SMS_55
。
In the present embodiment, vectors
Figure SMS_56
Is a size +.>
Figure SMS_57
Is a one-dimensional vector of (a).
Step 30: solving a target equation based on structured integral least squares to obtain a column vector
Figure SMS_58
。
In the present embodiment, the objective equation is
Figure SMS_59
In the middle of
Figure SMS_62
Is the variance of additive noise; />
Figure SMS_64
Is the variance of multiplicative noise; />
Figure SMS_68
The weight coefficient is preset; />
Figure SMS_63
Is that
Figure SMS_65
A unit matrix; />
Figure SMS_67
For structural disturbance, namely, the matrix only has diagonal elements which are non-zero, and other position elements are zero; />
Figure SMS_70
Is->
Figure SMS_60
A column vector; />
Figure SMS_66
A differential operator in the row direction; />
Figure SMS_69
A differential operator in the column direction; />
Figure SMS_71
Represents a 2-norm;
Figure SMS_61
representing the Frobenius norm.
Step 31: determining additive noise variance
Figure SMS_72
And multiplicative noise variance->
Figure SMS_73
。
In this embodiment, the additive noise variance is 100 and the multiplicative noise variance is 0.10, which are obtained by measurement.
Step 32: initialization of
Figure SMS_74
、/>
Figure SMS_75
。
In the present embodiment of the present invention, in the present embodiment,
Figure SMS_76
initializing as an elementMatrix of all zeros,>
Figure SMS_77
initialized to->
Figure SMS_78
。
Step 33: fixing
Figure SMS_79
Solving->
Figure SMS_80
。
In the present embodiment, the following objective equation is solved
Figure SMS_81
In the middle of
Figure SMS_82
Is a matrix in which all the elements except the diagonal elements are zero. The solving formula is as follows
Figure SMS_83
In the middle of
Figure SMS_85
Refers to matrix->
Figure SMS_88
Diagonal +.>
Figure SMS_90
Element(s)>
Figure SMS_86
Representative vector->
Figure SMS_89
The%>
Figure SMS_91
Element(s)>
Figure SMS_92
Representative vector->
Figure SMS_84
The%>
Figure SMS_87
The elements.
Step 34: fixing
Figure SMS_93
Solving->
Figure SMS_94
。
In the present embodiment, the following objective equation is solved
Figure SMS_95
The solving formula is as follows
Figure SMS_96
Wherein the method comprises the steps of
Figure SMS_97
Is preset to 0.1.
Step 35: and calculating a target equation value, and judging whether the convergence is achieved. If not, steps 33-34 are repeated.
In the present embodiment, the threshold for judging convergence is set to
Figure SMS_98
。
Step 36: outputting the column vector obtained by solving
Figure SMS_99
。
Step 40: column vector
Figure SMS_100
Rearranged into a +.>
Figure SMS_101
Matrix of->
Figure SMS_102
。
Comparing fig. 3 (a) and fig. 3 (b) show that the present embodiment can remove additive noise and multiplicative noise in an image, and improve image quality.
The foregoing detailed description has set forth the objects, aspects and advantages of the invention in further detail, it should be understood that the foregoing description is only illustrative of the invention and is not intended to limit the scope of the invention, but is to be accorded the full scope of the invention as defined by the appended claims.

Claims (2)

1. The method for removing the multiplicative additive mixed noise based on the structured integral least square is characterized by comprising the following steps of: comprises the following steps of the method,
step 1: acquiring a noise-contaminated input image including a noise-contaminated image
Figure QLYQS_1
；
The image described in step 1
Figure QLYQS_2
Is +.>
Figure QLYQS_3
Wherein>
Figure QLYQS_4
Representing the image height +.>
Figure QLYQS_5
Representing the image width;
step 2: vectorizing an input image into a column vector in a column-first manner
Figure QLYQS_6
；
The column vectors described in step 2
Figure QLYQS_7
Is +.>
Figure QLYQS_8
；
Step 3: solving a target equation based on structured integral least squares to obtain a column vector
Figure QLYQS_9
；
The target equation in step 3 is
Figure QLYQS_10
（1）
In the middle of
Figure QLYQS_14
Is the variance of additive noise; />
Figure QLYQS_18
Is the variance of multiplicative noise; />
Figure QLYQS_21
The weight coefficient is preset; />
Figure QLYQS_13
Is->
Figure QLYQS_15
A unit matrix; />
Figure QLYQS_19
For structured disturbance, by structured disturbance +.>
Figure QLYQS_23
Characterizing multiplicative noise, namely, only diagonal elements of the matrix are non-zero, and other position elements are zero; />
Figure QLYQS_11
Is->
Figure QLYQS_17
A column vector; />
Figure QLYQS_22
A differential operator in the row direction; />
Figure QLYQS_24
A differential operator in the column direction; />
Figure QLYQS_12
Represents a 2-norm; />
Figure QLYQS_16
Representing the Frobenius norm; by adding->
Figure QLYQS_20
The disturbance is structured, 2-norm error items are combined, multiplicative noise and additive noise are represented through modeling, and a denoised image is obtained through optimizing a target equation;
step 4: column vector obtained in step 3
Figure QLYQS_25
Rearranged into a +.>
Figure QLYQS_26
Matrix of->
Figure QLYQS_27
Obtaining denoised image +.>
Figure QLYQS_28
Namely, multiplicative additive mixed noise removal is realized based on structured integral least square;
in said step 3 there is included the step of,
step 31: determining additive noise variance
Figure QLYQS_29
And multiplicative noise variance->
Figure QLYQS_30
；
Step 32: initialization of
Figure QLYQS_31
、/>
Figure QLYQS_32
；
Described in step 32
Figure QLYQS_33
Initializing to a matrix with all elements zero, < >>
Figure QLYQS_34
Initialized to->
Figure QLYQS_35
；
Step 33: fixing
Figure QLYQS_36
Solving->
Figure QLYQS_37
；
Step 33 solves the following objective equation
Figure QLYQS_38
（2）
In-structure scramblingDynamic movement
Figure QLYQS_39
A matrix with all the elements except diagonal elements being zero;
step 34: fixing
Figure QLYQS_40
Solving->
Figure QLYQS_41
；
Step 34 solves the following objective equation
Figure QLYQS_42
（3）
Step 35: calculating a target equation value, and judging whether the target equation value is converged or not; if not, repeating steps 33-34;
the target equation in step 35 is
Figure QLYQS_43
（4）
If it is
Figure QLYQS_44
Judging that the convergence is achieved; otherwise, not converging; wherein->
Figure QLYQS_45
For preset parameters, ++>
Figure QLYQS_46
、/>
Figure QLYQS_47
For the result of the latest iteration, +.>
Figure QLYQS_48
、/>
Figure QLYQS_49
The result obtained in the previous iteration is obtained;
step 36: outputting the column vector obtained by solving
Figure QLYQS_50
。
2. The structured integral least squares based multiplicative additive hybrid noise removal method of claim 1, wherein: the noise variance is obtained from the detector parameters in step 31 or by means of noise measurements.
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Publication number Priority date Publication date Assignee Title
CN103886639A (en) * 2014-03-14 2014-06-25 湖州师范学院 Construction method for mixed pixel decomposition model based on noise immunity
CN107292855A (en) * 2017-08-02 2017-10-24 桂林电子科技大学 A kind of image de-noising method of the non local sample of combining adaptive and low-rank

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US5383457A (en) * 1987-04-20 1995-01-24 National Fertility Institute Method and apparatus for processing images
CN107808170B (en) * 2017-11-20 2019-10-29 中国人民解放军国防科技大学 Hyperspectral remote sensing image additive multiplicative mixed noise parameter estimation method
CN113313179A (en) * 2021-06-04 2021-08-27 西北工业大学 Noise image classification method based on l2p norm robust least square method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103886639A (en) * 2014-03-14 2014-06-25 湖州师范学院 Construction method for mixed pixel decomposition model based on noise immunity
CN107292855A (en) * 2017-08-02 2017-10-24 桂林电子科技大学 A kind of image de-noising method of the non local sample of combining adaptive and low-rank

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