CN115564680A - Image denoising method based on two-dimensional multipath matching pursuit algorithm - Google Patents

Image denoising method based on two-dimensional multipath matching pursuit algorithm Download PDF

Info

Publication number
CN115564680A
CN115564680A CN202211269808.0A CN202211269808A CN115564680A CN 115564680 A CN115564680 A CN 115564680A CN 202211269808 A CN202211269808 A CN 202211269808A CN 115564680 A CN115564680 A CN 115564680A
Authority
CN
China
Prior art keywords
dimensional
image
algorithm
path
candidate
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202211269808.0A
Other languages
Chinese (zh)
Other versions
CN115564680B (en
Inventor
范虹
李晨曦
罗弋桐
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shaanxi Normal University
Original Assignee
Shaanxi Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shaanxi Normal University filed Critical Shaanxi Normal University
Priority to CN202211269808.0A priority Critical patent/CN115564680B/en
Publication of CN115564680A publication Critical patent/CN115564680A/en
Application granted granted Critical
Publication of CN115564680B publication Critical patent/CN115564680B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G06T5/70—
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/20—Analysis of motion
    • G06T7/246—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
    • G06V10/74—Image or video pattern matching; Proximity measures in feature spaces
    • G06V10/75—Organisation of the matching processes, e.g. simultaneous or sequential comparisons of image or video features; Coarse-fine approaches, e.g. multi-scale approaches; using context analysis; Selection of dictionaries
    • G06V10/757—Matching configurations of points or features

Abstract

An image denoising method based on a two-dimensional multipath matching pursuit algorithm comprises the following steps: s100: inputting a noisy image, dividing the noisy image into image blocks, and performing dictionary learning on the noisy image to obtain a dictionary matching with effective features of the image; s200: performing sparse representation on each image block by using a learned dictionary by adopting a breadth-first two-dimensional multipath matching tracking algorithm and/or a depth-first two-dimensional multipath matching tracking algorithm so as to remove noise of each image block; s300: and reconstructing the denoised image blocks into a complete denoised image. The method improves the matching precision of the two-dimensional sparse representation algorithm, and shows better denoising effect compared with the denoising results of the one-dimensional multipath matching tracking algorithm and the existing two-dimensional orthogonal matching tracking algorithm.

Description

Image denoising method based on two-dimensional multipath matching pursuit algorithm
Technical Field
The disclosure belongs to the technical field of computer vision and image processing, and particularly relates to an image denoising method based on a two-dimensional multipath matching pursuit algorithm.
Background
In both image processing and computer vision tasks, removing noise from an image is a common and important pre-processing step. Let the picture signal be
Figure BDA0003892303280000011
Noise containing the noise ratio σ of
Figure BDA0003892303280000012
Then the noisy image signal
Figure BDA0003892303280000013
It can be expressed as: y = i + v. The objective of removing noise is to recover i from y and to retain as much detail information as possible in the image signal i while suppressing noise, which is a rather challenging task. At present, many methods are applied to the image denoising process, and sparse representation is a theoretical branch of the image denoising process, which is extremely important.
Sparse representation, the objective of which is to represent the signal with as few atoms as possible in a given overcomplete dictionary, thereby simplifying the representation of the signal, the result of the sparse representation relating to the approximation effect on the signal. Setting noisy signals
Figure BDA0003892303280000014
The overcomplete dictionary is
Figure BDA0003892303280000015
Denoising a signal using a sparse representation can be expressed as the following problem:
Figure BDA0003892303280000016
Figure BDA0003892303280000017
wherein epsilon tableIndicating an allowed error;
Figure BDA0003892303280000018
a coefficient matrix of the signal y under the dictionary D is obtained through a sparse representation algorithm; l |. Electrically ventilated margin 0 Is represented by 0 Norm, representing the number of non-zero elements in a; each column in D is called an atom. The signal can be reconstructed through a sparse coefficient matrix and an over-complete dictionary, and the noise in the signal is often accompanied by random characteristics and is difficult to be represented by an atom with a fixed structure, so that the sparse representation can extract effective information in the noise-containing image signal and can achieve the purpose of removing the noise after reconstruction.
In sparse representation models, the choice of dictionary is also very important, since it is the basis of sparse representation and is related to whether the signal can be perfectly reconstructed. Common dictionaries can be divided into two broad categories: a parsing-based dictionary and a learning-based dictionary. The analysis dictionary is generated through existing functions, such as a wavelet dictionary, an over-complete DCT (Discrete Cosine Transformation) dictionary and the like, and the dictionaries are simple and easy to implement, but have poor adaptability and expression capability to signals; on the contrary, the learning dictionary can be well adapted to different image data by performing feature learning on different images, and has strong signal expression capability. In practical applications, sparse representation algorithms are often used in conjunction with Dictionary Learning (DL).
With the proposal of the two-dimensional sparse coding algorithm, separable dictionary learning suitable for the two-dimensional sparse representation algorithm is researched and developed. Given a two-dimensional training signal
Figure BDA0003892303280000021
Left overcomplete dictionary
Figure BDA0003892303280000022
Right overcomplete dictionary
Figure BDA0003892303280000023
And target sparsity
Figure BDA0003892303280000024
The separable dictionary learning problem applicable to two-dimensional signals can be expressed as:
Figure BDA0003892303280000025
s.t.||X n || 0 ≤K，n＝1：N
||d 1i || 2 ＝1，i＝1：n 1
||d 2j || 2 ＝1，j＝1：n 2
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003892303280000026
is a sparse representation matrix.
An Orthogonal Matching Pursuit (OMP) algorithm is widely used as a classical sparse representation method due to its simplicity. With the research in the sparse representation field, the OMP algorithm also reveals the defect of low matching precision. Around the problem of improving matching accuracy, a series of improved sparse representation algorithms are proposed. Kwon, shim, etc. propose a Multipath Matching Pursuit (MMP) algorithm, which can detect multiple candidate objects in each search process, thereby greatly improving the accuracy of the final result.
And the multi-path matching tracking algorithm selects a corresponding number of candidate atoms according to a given path number for each candidate support set in each searching process, and selects one with the minimum residual error as a final estimation support set when the total sparsity iteration is completed. Under the guarantee of a constrained Isometry Property (RIP), the MMP algorithm has good reconstruction performance under the noisy environment and the noiseless environment. The specific search process of the multipath matching pursuit algorithm can be described as follows:
setting the given path number as L; the sparsity is K; at the k-th th The set formed at the time of the sub-iteration is
Figure BDA0003892303280000027
Is contained in a collection
Figure BDA0003892303280000028
The ith set of candidate supports in
Figure BDA0003892303280000029
Firstly, selecting the L atoms with the highest inner product value with the initial residual error (original signal), and adding the L atoms into the initial candidate set phi to form a first set
Figure BDA00038923032800000210
Including L candidate support sets
Figure BDA00038923032800000211
Then, for each candidate support set
Figure BDA00038923032800000212
The corresponding residual errors continue to select L atoms which are most matched according to the principle of highest inner product value, and the L atoms are respectively added into
Figure BDA00038923032800000213
Forming new L candidate support sets; and finally, selecting a support set with the minimum corresponding residual error from a plurality of candidate support sets obtained by K iterations as a final estimation support set of the algorithm.
In practical applications, many signals are two-dimensional signals, such as images, videos, and the like. However, the above algorithm is still designed for one-dimensional signals, and when two-dimensional signals are processed, it is a common practice to vector the sequence of two-dimensional signal columns into a vector form, and convert the two-dimensional signals into two-dimensional signals again after the processing is completed. The two-dimensional signal serialization operation not only increases the calculated amount in the sparse representation and reconstruction process, but also destroys the structural information in the neighborhood of the two-dimensional signal. In order to overcome the above disadvantages and achieve the goal of directly and conveniently realizing sparse representation of two-dimensional signals without a columnar conversion process, fang Yong et al develops the OMP algorithm and proposes a two-dimensional OMP algorithm (2 d orthogonal matching pursuit,2 d-OMP).
Unlike the one-dimensional sparse representation algorithm, two smaller-scale dictionaries, called separable dictionaries, are required in the two-dimensional sparse representation algorithm. Let the signal be
Figure BDA0003892303280000031
Noise containing the noise ratio σ of
Figure BDA0003892303280000032
Noisy signal
Figure BDA0003892303280000033
It can be expressed as: y = I + V, and the total weight of the alloy is less than or equal to zero,
Figure BDA0003892303280000034
in the form of a left overcomplete dictionary,
Figure BDA0003892303280000035
to the right overcomplete dictionary and target sparsity
Figure BDA0003892303280000036
Then the two-dimensional sparse representation denoising problem can be expressed as:
Figure BDA0003892303280000037
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003892303280000038
is a sparse representation matrix and matrix X has at most K non-zero elements; d 1 And D 2 It is a separable dictionary in a two-dimensional sparse representation algorithm.
Let vecM represent the column-order vectorization of matrix M, then the relationship between the two-dimensional sparse representation of the separable dictionary and the standard one-dimensional sparse representation can be summarized as follows:
Figure BDA0003892303280000039
it can be seen that sparse representation of two-dimensional signals, using separable dictionaries, operates on two smaller dictionary matrices, as compared to dictionaries in one-dimensional sparse representation algorithms
Figure BDA00038923032800000310
Less memory space is required for storage of the dictionary. Through the structure separation, the calculation complexity and the storage space of the algorithm are reduced, more importantly, the structure information of the signal can be captured from different directions, and the reconstruction accuracy of the signal is improved.
However, experiments show that the 2D-OMP algorithm still has the problem of low matching precision.
Disclosure of Invention
In order to solve the technical problem, the present disclosure discloses an image denoising method based on a two-dimensional multipath matching pursuit algorithm, including the following steps:
s100: inputting a noisy image, dividing the noisy image into image blocks, and performing dictionary learning on the noisy image to obtain a dictionary matching with effective features of the image;
s200: performing sparse representation on each image block by using a learned dictionary by adopting a breadth-first two-dimensional multipath matching tracking algorithm and/or a depth-first two-dimensional multipath matching tracking algorithm so as to remove noise of each image block;
s300: and reconstructing the denoised image blocks into a complete denoised image.
Through the technical scheme, the Multipath Matching Pursuit algorithm is expanded two-dimensionally, the traversal thought of the combined tree is combined, the optimal search problem of the candidate support set is converted into the tree-shaped search problem, a two-dimensional Multipath Matching Pursuit algorithm (2D Multipath Matching Pursuit, 2D-MMP) is provided, and the two-dimensional Multipath Matching Pursuit algorithm (2D Breadth-First Multipath Matching Pursuit, 2D-MMP-BF) with the priority of the Breadth and the two-dimensional Multipath Matching Pursuit algorithm (2D Depth-First Multipath Matching Pursuit, 2D-MMP-DF) with the priority of the Depth are specific to different search forms, so that the two-dimensional Multipath Matching Pursuit can be directly subjected to sparse decomposition aiming at the two-dimensional signals, and the aim of improving the Matching precision of the two-dimensional signals is also fulfilled.
The multi-path matching tracking algorithm is expanded into a two-dimensional multi-path matching tracking algorithm, the two-dimensional signals can be directly expressed in a sparse mode, and time and space consumption in the signal conversion process is avoided. Meanwhile, by means of a searching mode of a multipath matching pursuit algorithm in searching a candidate support set, the defect of low matching precision of a two-dimensional orthogonal matching pursuit algorithm is overcome, and the matching precision of a two-dimensional sparse representation algorithm is improved.
Drawings
Fig. 1 is a flowchart of an image denoising method based on a two-dimensional multipath matching pursuit algorithm according to an embodiment of the present disclosure;
FIG. 2 is a diagram of a 2D-MMP-BF algorithmic search process provided in an embodiment of the present disclosure;
FIG. 3 is a diagram of a 2D-MMP-DF algorithm search process provided in an embodiment of the present disclosure;
FIGS. 4 (a) to 4 (D) are graphs showing the relationship between the use of the 2D-OMP, 2D-MMP-BF and 2D-MMP-DF algorithms RMSE and the number of dictionary learning times under the exploration of different dictionary atomic numbers provided in one embodiment of the present disclosure;
FIGS. 5 (a) to 5 (g) are graphs of denoising results of a standard test image provided in an embodiment of the present disclosure;
FIGS. 6 (a) -6 (g) are partial enlarged views of a denoised image provided in one embodiment of the present disclosure;
fig. 7 (a) to 7 (g) are diagrams of MR brain image denoising results with different noise ratios provided in one embodiment of the present disclosure.
Detailed Description
In order to make those skilled in the art understand the technical solutions disclosed in the present disclosure, the technical solutions of various embodiments will be described below with reference to the embodiments and the accompanying fig. 1 to 7 (g), where the described embodiments are some, but not all embodiments of the present disclosure. The terms "first," "second," and the like, as used herein, are used to distinguish one object from another, and are not used to describe a particular order. Furthermore, "include" and "have," as well as any variations thereof, are intended to cover and not to exclude inclusions. For example, a process, method, system, or article of manufacture or a device that comprises a list of steps or elements is not limited to the listed steps or elements, but may alternatively include other steps or elements not expressly listed or inherent to such process, method, system, article of manufacture or device.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. One skilled in the art will appreciate that the embodiments described herein may be combined with other embodiments.
Referring to fig. 1, in one embodiment, the present disclosure discloses an image denoising method based on a two-dimensional multipath matching pursuit algorithm, including the following steps:
s100: inputting a noisy image, dividing the noisy image into image blocks, and performing dictionary learning on the noisy image to obtain a dictionary matching with effective features of the image;
s200: performing sparse representation on each image block by using a learned dictionary by adopting a breadth-first two-dimensional multipath matching tracking algorithm and/or a depth-first two-dimensional multipath matching tracking algorithm so as to remove noise of each image block;
s300: and reconstructing the denoised image blocks into a complete denoised image.
In the embodiment, the method provides the breadth-first two-dimensional multipath matching and tracking algorithm and the depth-first two-dimensional multipath matching and tracking algorithm based on two different search forms by means of the traversal thought of the combined tree search problem. The core idea of the method is that a plurality of best atoms matching image features are selected from an over-complete separable dictionary during each iteration, and a candidate support set with the minimum residual error is selected as a final support set during the iteration, so that the matching precision of the two-dimensional sparse representation algorithm is improved.
The main idea of the two-dimensional multipath matching pursuit algorithm is to represent the two-dimensional signal Y as a weighted sum of two-dimensional atoms selected from two separate overcomplete dictionaries. Here, first, a description is given of dictionary, atom, and projection operations in a separate dictionary form applied to a two-dimensional signal.
Let two-dimensional signal
Figure BDA0003892303280000051
Wherein
Figure BDA0003892303280000052
Is a sparse matrix with the sparsity K,
Figure BDA0003892303280000053
is an overcomplete dictionary on the left,
Figure BDA0003892303280000054
to the right overcomplete dictionary, d 1i Is a left dictionary D 1 I th of (1) th Column, d 2j Is a right dictionary D 2 J (d) of th Column, column d through two dictionaries 1i And d 2j Dictionary atoms for a sparse representation of a two-dimensional signal may be defined:
Figure BDA0003892303280000055
it is generally required that d 1i || 2 ＝||d 2j || 2 =1, therefore
Figure BDA0003892303280000056
Then, the two-dimensional signal Y can be represented as atom A i，j The sum of the weights of (c):
Figure BDA0003892303280000061
two-dimensional signal Y at atom A i，j The projection on can be expressed as:
Figure BDA0003892303280000062
wherein
Figure BDA0003892303280000063
And | | | A i，j || 2 Is A i，j The Frobenius norm of (a):
Figure BDA0003892303280000064
the two-dimensional multi-path matching tracking algorithm still converts the atom Search problem into the combined tree Search problem, and in the combined tree Search problem, there are two common traversal forms, namely, breadth-first Search (break-first Search) and Depth-first Search (Depth-first Search). According to the two different searching forms, a breadth-first two-dimensional multipath matching and tracking algorithm and a depth-first two-dimensional multipath matching and tracking algorithm are respectively provided.
The 2D-MMP-BF and 2D-MMP-DF algorithms are generally applicable to sparse representation of two-dimensional signals, but have advantages and disadvantages. The 2D-MMP-BF algorithm is used for executing parallel search of sparsity iteration, more candidate support sets can be reserved in the process, and the selectivity is stronger; also because of this, the 2D-MMP-BF algorithm suffers from a high computational complexity. While the 2D-MMP-DF algorithm carries out the depth search of sparsity in each iteration, the parameter l can also be used max The calculation complexity of the algorithm is controlled, even in a special case of a given error epsilon, the error condition can be met in the first iteration so as to finish the search, and therefore, the 2D-MMP-BF algorithm may have the precision loss.
Step 1 of dictionary learning in S100 is to initialize a dictionary (which may be randomly generated,DCT dictionaries etc. may be used), but these dictionaries are all common, i.e. for different images, the same type or even the same dictionary (matrix) is used. Then, a problem arises in that the content (or features inside the image) contained in each image is different, and the atoms used in the general dictionary initialized in step 1 may generate large errors in the sparse representation process, which is referred to as unmatched image features, so that the reconstructed image is not ideal. Therefore, step 2 of dictionary learning is to cross the formula in the book
Figure BDA0003892303280000071
As a criterion, the elements in the dictionary (matrix) are continuously updated (so-called dictionary learning), and finally a dictionary with smaller error is obtained (this is understood as a dictionary that excludes the interference of noise and matches the image features "valid" under the noise), which is called a dictionary for obtaining valid features of the matched image.
In another embodiment, the breadth-first two-dimensional multi-path matching pursuit algorithm in step S200 comprises the following steps:
s201: if the initial residual error is less than a given error threshold epsilon, the sparse representation matrix is a zero matrix; otherwise, continuing to execute step S202;
s202: when the iteration number k is less than the target sparsity
Figure BDA0003892303280000073
In the case of (2), S is set for each layer k Selecting L atoms with the largest inner product absolute value according to the inner product value of the residual error and the atoms in each candidate support set, wherein L represents the path number;
s203: circularly traversing each path branch, firstly constructing the path branch into a temporary path in the candidate set, and judging whether the temporary path exists in the candidate set S k If so, traversing the next path branch; otherwise, updating the index of the candidate support set, and storing the temporary path at the position of the indexUpdating the path, and finally merging the temporary path into the candidate set to realize the updating of the candidate set; then, according to a least square method, solving coefficients corresponding to the candidate support sets and solving residual errors corresponding to the candidate support sets, wherein each candidate support set stores the corresponding coefficients and residual errors; at this time, a residual error needs to be judged, and if the residual error corresponding to the candidate support set is smaller than a threshold epsilon, a coefficient corresponding to the candidate support set is assigned to the sparse representation matrix for returning and outputting;
s204: and if the target sparsity is reached and the requirement of the error threshold is still not met, finding the index of the candidate support set corresponding to the minimum residual error, finding the corresponding coefficient according to the index, and assigning the coefficient to the sparse representation matrix for returning and outputting.
With this embodiment, at each iteration, the best matching atom in the dictionary is searched, and then the weight corresponding to that atom is updated by means of the following least squares method. The specific process is shown in algorithm 1.
Figure BDA0003892303280000072
Figure BDA0003892303280000081
Figure BDA0003892303280000091
At get k th th After separating the supporting set of the dictionary, because
Figure BDA0003892303280000092
Where tr (×) is the trace of the matrix, and the weights are updated using least squares, then the objective function can be expressed as:
Figure BDA0003892303280000093
because tr (() T ) = tr (, x), we can get:
Figure BDA0003892303280000101
wherein:
Figure BDA0003892303280000102
Figure BDA0003892303280000103
when tr (RR) is enabled T ) At a minimum, it is necessary to:
Figure BDA0003892303280000104
thus:
Figure BDA0003892303280000105
in another embodiment, the inputs to the breadth first two-dimensional multipath matching pursuit algorithm include: two-dimensional signal
Figure BDA0003892303280000106
Left overcomplete dictionary
Figure BDA0003892303280000107
Right overcomplete dictionary
Figure BDA0003892303280000108
Target sparsity
Figure BDA0003892303280000109
The number of paths L and the error ε, where R is a set of real numbers, N, m, N 1 And n 2 Are all non-negative integer sets.
For this embodiment, relative to the 2D-OMP algorithm, except for the two-dimensional signal
Figure BDA00038923032800001010
Separate dictionary
Figure BDA00038923032800001011
And
Figure BDA00038923032800001012
and target sparsity
Figure BDA00038923032800001013
In addition to the input of (2), an input of the number of paths L needs to be provided. R refers to a real number set, and the element in the Y matrix is designated as a real number; n refers to a non-negative integer set.
In another embodiment, the breadth-first two-dimensional multi-path matching pursuit algorithm requires initialization of the number of iterations, the residuals, and the candidate set.
For this embodiment, the definition is also required
Figure BDA00038923032800001014
To represent the residual after removing the selected atom from Y.
In another embodiment, the breadth-first two-dimensional multi-path matching pursuit algorithm derives L search paths for each candidate support set at the next sparsity iteration, and each candidate support set has a respective corresponding residual.
For this embodiment, in the 2D-MMP-BF algorithm, each leaf node represents an optimal atom, and the paths to the optimal atom represent candidate subsets of the reconstructed signal. Since the algorithm generates multiple candidate support sets after each iteration is completed, the number of candidate support sets increases as the number of iterations increases. However, in the actual solution process, since a plurality of candidate atoms may overlap in the path search process, as shown in fig. 2, the number of candidate support sets is limited as the number of iterations increases. The searching process of the path number L =2 and the sparsity K =3,2D-MMP-BF is shown in FIG. 2, and the searching process of the 2D-OMP is given as a comparison.
As can be seen from fig. 2, the 2D-OMP algorithm only selects one candidate atom in each sparsity iteration, and selecting the atom with the smallest residual error has certain limitations. And for each candidate support set, the 2D-MMP-BF algorithm derives L search paths in the next sparsity iteration, the candidate support sets are maintained all the time, each candidate support set has corresponding residual errors, and more selection spaces are provided.
In another embodiment, the breadth-first two-dimensional multi-path matching pursuit algorithm selects the L best atoms one by one for all nodes of the layer at each sparsity iteration.
For this embodiment, the time complexity of the two-dimensional sparse representation algorithm in terms of projection, selection of best atoms, updating weights and updating residuals is O (mn) 1 n 2 ). In the breadth-first two-dimensional multipath matching pursuit algorithm, it is also necessary to select L optimal atoms one by one for all nodes of the layer during each sparsity iteration. In the worst case (i.e., without considering the case of node duplication and completing all sparsity iterations), the time complexity of the breadth-first two-dimensional multipath matching pursuit algorithm can be expressed as:
Figure BDA0003892303280000111
in the best case (i.e., given an error ε such that only one search can be done to satisfy the condition), the temporal complexity of the breadth-first two-dimensional multipath matching pursuit algorithm can be expressed as: o (mn) 1 n 2 )。
Through analysis of time complexity and the operation process of the time complexity, the two-dimensional multipath matching pursuit algorithm with the breadth first is found to be dominant by hierarchical traversal of a combined tree search problem, and all candidate support sets in the layer (namely sparsity) are used as support sets during each sparsity iteration
Figure BDA0003892303280000112
Multipath searching is carried out, and the requirement of total sparsity can be met only after the algorithm is operated at the end. This certainly greatly increases the amount of calculation of the algorithm if the requirement for error is met as a priority condition.
In another embodiment, the depth-first two-dimensional multipath matching pursuit algorithm in step S200 comprises the following steps:
s211: if the initial residual error is less than a given error threshold epsilon, the sparse representation matrix is a zero matrix; otherwise, the step S212 is continued.
S212: searching the candidate support set number l when the order l of the candidate support set is less than the maximum max Under the condition of (1), firstly, calculating the sequence of searched leaf nodes according to a modulus search strategy; then, using the target sparsity K as a constraint to enable K to start cyclic traversal from 1 to K, selecting L atoms with the largest inner product absolute value according to the inner product values of residual errors and atoms, wherein L represents the number of paths, and selecting atoms in the kth position according with the searched leaf node sequence th Constructing a path by a layer, storing the path as a candidate support set of the layer, and storing a corresponding coefficient and a corresponding residual error in each candidate support set, so that the coefficient is solved and the residual error is updated by a least square method;
s213: and judging the residual error, and if the residual error corresponding to the candidate support set is smaller than a threshold epsilon, assigning the coefficient corresponding to the candidate support set to the sparse representation matrix for returning and outputting.
S214: when a complete sparsity traversal is completed each time, the depth-first two-dimensional multipath tracking algorithm stores the minimum residual value and the corresponding coefficient in the current state; and if the error threshold requirement is not met when the maximum number of the search candidate support sets is reached, selecting the coefficient corresponding to the minimum residual error to assign to the sparse representation matrix for returning and outputting.
For this example, algorithm 2 gives the main steps of a Depth-First two-dimensional Multipath Matching Pursuit (2D Depth-First Multipath Matching Pursuit, 2D-MMP-DF) algorithm. Compared with 2D-MMP-BF parallel search, each iteration of 2D-MMP-DF completes a complete sparsity search, and the operation efficiency is much faster than that of 2D-MMP-BF under the condition that the error is met as a priority condition.
Figure BDA0003892303280000121
Figure BDA0003892303280000131
Figure BDA0003892303280000141
In another embodiment, the inputs to the depth-first two-dimensional multipath matching pursuit algorithm comprise: two-dimensional signal
Figure BDA0003892303280000142
Left overcomplete dictionary
Figure BDA0003892303280000143
Right overcomplete dictionary
Figure BDA0003892303280000144
Target sparsity
Figure BDA0003892303280000145
Number of paths L, error ε, and number of search candidate support sets L of maximum max Where R is a set of real numbers, N, m, N 1 And n 2 Are all non-negative integer sets.
For this embodiment, in order to further reduce the computational complexity of the algorithm, in the input parameters of the 2D-MMP-DF algorithm, the parameter l is additionally added max And flexible control over the maximum search candidate support set is realized. Fig. 3 shows the searching process of the 2D-MMP-DF algorithm on the candidate support set when the sparsity K =3 and the number of paths L = 2. The algorithm firstly determines the search of calculating leaf nodes by using a modulus strategy according to the sequence l of the candidate setSequence c k Then according to c k And selecting the corresponding candidate support set, and completing a complete sparsity search once each time the traversal of the candidate set sequence l is completed. Two special cases can be imagined, when given a candidate support set l of maximum search max When the number of the entries is not less than 1, the 2D-MMP-DF only needs to complete one complete sparsity iteration, and the search process of the 2D-MMP-DF is equivalent to 2D-OMP; in the other case, when the candidate support set l of the maximum search is given max ＝L K The search process is equivalent to 2D-MMP-BF.
2D-MMP-DF Algorithm, using l max The computational complexity of the algorithm is flexibly controlled. In the worst case (i.e.: all l are done) max Iteration), the time complexity of the 2D-MMP-DF algorithm can be expressed as: o (l) max Kmn 1 n 2 ) (ii) a At best, the same algorithm as 2D-MMP-BF, namely: given an error epsilon such that only one search is completed can satisfy the condition, the time complexity is also expressed as: o (mn) 1 n 2 )。
In another embodiment, the depth-first two-dimensional multipath matching pursuit algorithm requires initializing candidate support set order and storing the smallest magnitude residuals.
In another embodiment, the depth-first two-dimensional multipath matching pursuit algorithm uses a modulo search strategy to determine the search order.
With this embodiment, in the 2D-MMP-DF algorithm, since the search operation is performed in a serialized manner, one problem that follows is how to set the candidate search order in order to find the best dictionary atom as early as possible. 2D-MMP-DF algorithm using a modulus search strategy [11] The search order is determined, and the main advantage is that the search priority is given to candidate support set objects with smaller residual errors, and meanwhile, the search path of the top layer is diversified, and the candidate objects are prevented from being locally searched. According to a modulo search strategy, th th Support set
Figure BDA0003892303280000151
And leaf node order c k Can be used forIs defined as:
Figure BDA0003892303280000152
this process results in a candidate set order of l and a leaf node order set of (c) 1 ，…，c K ) And correspond to each other.
In another embodiment, the process of dictionary learning is equivalent to the process of extracting signal features, and the dictionary learning strategy used herein is as follows:
inspired by K-SVD algorithm, hold type
Figure BDA0003892303280000153
In addition to D 1 Middle ith column d 1i Other elements not changed, then pair d 1i The update of (a) may be expressed as:
Figure BDA0003892303280000154
for D, the same principle applies 2 Middle j row d 2j The update of (a) may be expressed as:
Figure BDA0003892303280000155
wherein P means D 2 In with d 1i A set of associated columns; q means D 1 In with d 2j A set of associated columns; r is n Can be expressed as:
Figure BDA0003892303280000156
in particular for d 1i The update of (a) may be expressed as follows:
Figure BDA0003892303280000161
updating x i，P ：
Figure BDA0003892303280000162
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003892303280000163
is Moore-Penrose generalized inverse; for D, the same principle applies 2 Middle j column d 2j The update of (c) can be expressed as:
Figure BDA0003892303280000164
updating x Q，j ：
Figure BDA0003892303280000165
In the course of separable dictionary learning, formula
Figure BDA0003892303280000166
The sparse representation matrix X in (b) can still be obtained by a two-dimensional sparse representation algorithm. The dictionary learning process is only the result of one iteration, and in practical applications, multiple iterations are usually required to obtain a separable dictionary that better matches the image features.
In another embodiment, the two-dimensional image signal contains rich information and has a complex texture structure, and if the whole image is directly sparsely represented, not only an ideal denoising effect cannot be achieved, but also the computational complexity is greatly increased. Therefore, in an experiment for denoising a two-dimensional image by using the sparse representation theory, the image is often divided into overlapped image blocks. Firstly, dictionary learning is carried out on a noise-containing image to obtain a dictionary matching with effective characteristics of the image; secondly, sparse representation is carried out on each image block by using the learned dictionary, noise of each image block is removed, and then the image blocks which are denoised are averaged to be reconstructed into a complete image which is denoised.
Denoising experiments will be performed below for 6 standard test images in the Set12 dataset and images in the MR brain image database of university of Mcgcill, respectively. The experimental platform is Windows10, the hardware is Inter (R) Core (TM) i5-6600M 3.30GHz CPU,8G RAM, and all algorithms are realized in MATLAB R2020b environment. Two important experimental parameters also need to be determined in the experiment.
First, the iteration number of the dictionary learning stage. In an experiment, an image is divided into 8X 8 image blocks according to the step length of 1, N =4000 image blocks are randomly selected from the image blocks as training samples, a separable dictionary updating method is adopted to obtain a learning dictionary, and 2D-OMP, 2D-MMP-BF and 2D-MMP-DF algorithms are respectively adopted when a sparse representation matrix sparse X is obtained. FIGS. 4 (a) through 4 (d) show Root Mean Square Error (RMSE) for different numbers of dictionary atoms, as defined by
Figure BDA0003892303280000171
) And the number of iterations of dictionary learning. FIG. 4 (a) number of dictionary atoms n 1 ＝n 2 Number of dictionary atoms n of =16, fig. 4 (b) 1 ＝n 2 =64 number of dictionary atoms n in fig. 4 (c) 1 ＝n 2 Number of dictionary atoms n =96, fig. 4 (d) 1 ＝n 2 ＝128。
Figure BDA0003892303280000172
Wherein I is an image without noise; p is the divided image block size, and p =8.
As can be seen from fig. 4 (a) to 4 (D), under the condition of different numbers of dictionary atoms, the Root Mean Square Error (RMSE) of the separated dictionary learning performed by using the 2D-MMP-BF and 2D-MMP-DF algorithms is smaller than that of the 2D-OMP, so that the effectiveness of the two-dimensional multipath matching pursuit algorithm in improving the matching precision is verified. Meanwhile, the algorithm can be found to be basically converged when the number of dictionary learning iterations is 100. Therefore, in the subsequent denoising experiments of the standard test image and the MR brain image, the iteration number T is selected to be 100.
And secondly, errors in the two-dimensional sparse representation algorithm in the denoising stage. Error parameters in the sparse representation algorithm in the image block denoising stage need to be determined. Since the error in the experiment, ε, should be related to the image block size and noise ratio, ε was chosen as follows:
ε＝c·pσ 2
where c is a constant, typically c =1.15; p is the image block size, and p =8 is taken as above; σ is the noise ratio.
In order to evaluate the denoising result of the image, the adopted measurement indexes of the experiment are as follows: peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) are expressed as follows:
Figure BDA0003892303280000181
Figure BDA0003892303280000182
wherein I and
Figure BDA0003892303280000183
respectively, an original image and a denoised image. The larger the PSNR value is, the better the image restoration effect is represented; mu.s I Is the average value of the I, and,
Figure BDA0003892303280000184
is that
Figure BDA0003892303280000185
Is determined by the average value of (a) of (b),
Figure BDA0003892303280000186
is the variance of the I, and is,
Figure BDA0003892303280000187
is that
Figure BDA0003892303280000188
The variance of (a) is determined,
Figure BDA0003892303280000189
is I and
Figure BDA00038923032800001810
covariance of (a), theta 1 And theta 2 Is a constant for avoiding system instability caused by denominator of 0. SSIM has a value range of [0,1 ]]Also, the larger the value, the smaller the image distortion.
In another embodiment, in a standard test image denoising experiment, 6 images in the Set12 dataset were selected: lena, man, button, part, house, and camera, all of image sizes are 256 × 256, and gaussian white noise of different noise ratios σ is added, respectively. In this section of experiment, the image containing noise is divided into p =8 image blocks, and then N =4000 image blocks are randomly selected as training samples for dictionary learning. Wherein the separable dictionary atoms of 2D-OMP, 2D-MMP-BF and 2D-MMP-DF are all selected as n 1 ＝n 2 =16, i.e. D 1 And D 2 The size of (a) is 8 x 16,2D-OMP, 2D-MMP-BF, and 2D-MMP-DF using the above separable dictionary learning method; number of paths selected by 2D-MMP-BF and 2D-MMP-DF =2, and the most searched candidate support set in 2D-MMP-DF that can control its computational complexity
Figure BDA00038923032800001811
Dictionaries for 1D-OMP, 1D-MMP-BF and 1D-MMP-DF are all chosen as
Figure BDA00038923032800001812
The size is 64 multiplied by 256, and a dictionary learning uses a K-SVD algorithm; meanwhile, in an experiment, the number of dictionary learning iterations T =100 and the sparsity K =6 are set; FIGS. 5 (a) to 5 (g) show graphs of the denoising results of the noise-containing graph of FIG. 5 (a), the 1D-OMP of FIG. 5 (b), the 2D-OMP of FIG. 5 (c), the 1D-MMP-BF of FIG. 5 (D), the 2D-MMP-BF of FIG. 5 (e), the 1D-MMP-DF of FIG. 5 (f), and the 2D-MMP-DF of FIG. 5 (g) for a standard test image; and standard test image denoising at different noise ratiosThe PSNR and SSIM values corresponding thereto are shown in table 1 of the results.
Figure BDA00038923032800001813
Figure BDA0003892303280000191
TABLE 1
Figure BDA0003892303280000201
TABLE 2
As can be seen from the data in Table 1, under different noise ratios, the 2D-MMP-BF and 2D-MMP-DF algorithms are used for denoising a standard test image containing Gaussian white noise, and both the PSNR and SSIM values of the denoised image are higher than those of the 2D-OMP, the 1D-MMP-DF and the 1D-MMP-BF, wherein the PSNR value is increased by about 0.0016-1.2832dB, and the SSIM value is increased by about 0.004-0.0139. In most cases, the denoising effect using the 2D-MMP-BF algorithm will be better than that of the 2D-MMP-DF algorithm. In combination with the denoising result graphs in fig. 5 (a) to 5 (g), in subjective vision, the algorithm not only achieves a good noise suppression effect, but also retains the detail information of the image as much as possible. FIGS. 6 (a) to 6 (g) show enlarged partial views of the denoised image of FIG. 6 (a), FIG. 6 (b) 1D-OMP, FIG. 6 (c) 2D-OMP, FIG. 6 (D) 1D-MMP-BF, FIG. 6 (e) 2D-MMP-BF, FIG. 6 (f) 1D-MMP-DF and FIG. 6 (g) 2D-MMP-DF algorithms. Fig. 6 (a) to 6 (g) locally enlarge the denoised image, and it can be seen that the structure between adjacent domains of the image block is destroyed by the serialization operation of the one-dimensional sparse algorithm during denoising, so that the denoised image appears rough at the edge; the two-dimensional sparse algorithm overcomes the defect, and the denoised image is smoother at the edge. The left value in table 2 is the average time for one sparse representation denoising; and the right numerical value is the time for completing the sparse representation denoising of all the image blocks. In terms of runtime, it can be seen from the data in Table 2 that the two-dimensional sparse representation algorithm is sparse at one timeThe time for sparse representation denoising or denoising of all image blocks is shorter than that of a one-dimensional sparse representation algorithm, and the two-dimensional sparse representation algorithm is fully verified to reduce the computational complexity of a program. The 2D-MMP-BF and 2D-MMP-DF algorithms search the number of corresponding paths L for each candidate support set at each iteration, so that the running time of the two algorithms is longer than that of the 2D-OMP algorithm. Candidate support set l using maximum search for 2D-MMP-DF algorithm max After the time complexity is controlled, the running time of the sparse representation denoising for one image block and the running time of the sparse representation denoising for all the image blocks are smaller than that of a 2D-MMP-BF algorithm. The experiment verifies the effectiveness of the algorithm in removing the Gaussian white noise.
In another embodiment, in the acquisition imaging process of the MR image, the real part and the imaginary part of the signal generally have gaussian additive noise interference with the same variance and zero mean, and the noises carried by the real part and the imaginary part are independent of each other, and are generally considered to be distributed in a rice (Rician) characteristic. The experiment was validated using images from the MR brain image database of Mcgcill university. The brain MR image is a T1-weighted image, slices 45, 90, and 115 are selected, the noise level is 1%, 5%, and 9%, and the image size is 217 × 181. The experimental protocol is as above. FIGS. 7 (a) to 7 (g) show the noise-containing maps of FIG. 7 (a), 1D-OMP of FIG. 7 (b), 2D-OMP of FIG. 7 (c), 1D-MMP-BF of FIG. 7 (D), 2D-MMP-BF of FIG. 7 (e), 1D-MMP-DF of FIG. 7 (f), and 2D-MMP-DF of FIG. 7 (g) in the graph of the results of denoising MR brain images with different noise ratios, and PSNR and SSIM values corresponding thereto are shown in Table 3 showing the denoising results of MR brain images with different noise ratios.
Figure BDA0003892303280000211
TABLE 3
Figure BDA0003892303280000212
TABLE 4
As can be seen from the data in Table 3, the noise in the case of a signal containing Rice noiseIn the process of denoising the MR brain image, the denoised image obtained by applying the algorithm still has higher PSNR and SSIM values, wherein the PSNR value is improved by about 0.0972-0.6846, and the SSIM value is improved by about 0.0002-0.0086. The denoising effect of the 2D-MMP-BF algorithm is still better than that of the 2D-MMP-DF algorithm in most cases when the method is applied to the MR image, and the correctness of theoretical analysis is verified more. Clinical diagnosis based on MR images and subsequent processing of the images place high demands on the details of the images. As can be seen from the de-noising result images in fig. 7 (a) to 7 (g), the detail characteristics of the image are well preserved while de-noising. The left value in table 4 is the average time for one sparse representation denoising; and the right numerical value is the time for completing the sparse representation denoising of all the image blocks. In terms of runtime, in conjunction with the data in table 4, even if the present algorithm is applied to clinical MR brain images, the two-dimensional sparse representation algorithm takes less time than the one-dimensional sparse representation algorithm. Candidate support set l due to maximum search at the same time max The introduction of the parameter and the time of the 2D-MMP-DF algorithm are also smaller than the 2D-MMP-BF algorithm. Denoising experiments on MR brain images further prove the effectiveness and robustness of the algorithm.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (10)

1. An image denoising method based on a two-dimensional multipath matching pursuit algorithm comprises the following steps:
s100: inputting a noisy image, dividing the noisy image into image blocks, and performing dictionary learning on the noisy image to obtain a dictionary matching with effective features of the image;
s200: performing sparse representation on each image block by using a learned dictionary by adopting a breadth-first two-dimensional multipath matching tracking algorithm and/or a depth-first two-dimensional multipath matching tracking algorithm so as to remove noise of each image block;
s300: and reconstructing the denoised image block into a complete denoised image.
2. The method as claimed in claim 1, wherein the breadth-first two-dimensional multi-path matching pursuit algorithm in step S200 comprises the following steps:
s201: if the initial residual error is smaller than a given error threshold epsilon, the sparse representation matrix is a zero matrix; otherwise, continuing to execute step S202;
s202: when the iteration number k is less than the target sparsity
Figure FDA0003892303270000014
In the case of (2), set S for each layer k Selecting L atoms with the largest inner product absolute value according to the inner product values of the residual errors and the atoms in each candidate support set, wherein L represents the path number;
s203: circularly traversing each path branch, firstly constructing the path branch into a temporary path in the candidate set, and judging whether the temporary path exists in the candidate set S k If so, traversing the next path branch; otherwise, updating the index of the candidate support set, storing the temporary path in the position of the index for path updating, and finally merging the temporary path into the candidate set to realize the updating of the candidate set; then, according to a least square method, solving coefficients corresponding to the candidate support sets and solving residual errors corresponding to the candidate support sets, wherein each candidate support set stores the corresponding coefficients and residual errors; at the moment, a residual error is required to be judged, if the residual error corresponding to the candidate support set is smaller than a threshold epsilon, a coefficient corresponding to the candidate support set is assigned to the sparse representation matrix for returning and outputting;
s204: if the target sparsity is reached and still the requirement of the error threshold is not met, the index of the candidate support set corresponding to the minimum residual error is found, the corresponding coefficient is found according to the index, and the coefficient is still assigned to the sparse representation matrix for returning and outputting.
3. The method of claim 2, the input to the breadth-first two-dimensional multipath matching pursuit algorithm comprising: two-dimensional signal
Figure FDA0003892303270000011
Left overcomplete dictionary
Figure FDA0003892303270000012
Right overcomplete dictionary
Figure FDA0003892303270000013
Target sparsity
Figure FDA0003892303270000016
The number of paths L and an error ε, wherein
Figure FDA0003892303270000015
Is a set of real numbers, N, m, N 1 And n 2 Are all non-negative integer sets.
4. The method of claim 2, the breadth-first two-dimensional multipath matching pursuit algorithm requires initialization of a number of iterations, residuals, and candidate sets.
5. The method as claimed in claim 2, wherein the breadth-first two-dimensional multi-path matching pursuit algorithm derives L search paths for each candidate support set at the next sparsity iteration, each candidate support set having a respective residual error.
6. The method of claim 2, wherein the breadth-first two-dimensional multi-path matching pursuit algorithm selects the L best atoms one by one for all nodes of the layer at each sparsity iteration.
7. The method of claim 1, wherein the depth-first two-dimensional multipath matching pursuit algorithm of step S200 comprises the steps of:
s211: if the initial residual error is less than a given error threshold epsilon, the sparse representation matrix is a zero matrix; otherwise, continue to step S212;
s212: searching candidate support set number l when the order l of the candidate support sets is less than the maximum max Under the condition of (1), firstly, calculating the sequence of searched leaf nodes according to a modulus search strategy; then, the target sparsity K is used as a constraint, so that the K starts to circulate and traverse from 1 to K, L atoms with the largest inner product absolute value are selected according to the inner product values of residual errors and atoms, wherein L represents the path number, and the atom which accords with the searched leaf node sequence is selected at the kth atom th Constructing a path by a layer, storing the path as a candidate support set of the layer, and storing a corresponding coefficient and a residual error in each candidate support set, so that the coefficient is solved and the residual error is updated by a least square method;
s213: judging the residual error, and if the residual error corresponding to the candidate support set is smaller than a threshold epsilon, assigning the coefficient corresponding to the candidate support set to the sparse representation matrix for returning and outputting;
s214: the depth-first two-dimensional multi-path tracking algorithm can save the minimum residual value and the corresponding coefficient in the current state when a complete sparsity traversal is completed each time; and if the error threshold requirement is not met when the maximum number of the search candidate support sets is reached, selecting the coefficient corresponding to the minimum residual error to assign to the sparse representation matrix for returning and outputting.
8. The method of claim 7, the inputs to the depth-first two-dimensional multipath matching pursuit algorithm comprising: two-dimensional signal
Figure FDA0003892303270000021
Left overcomplete dictionary
Figure FDA0003892303270000022
Right overcomplete dictionary
Figure FDA0003892303270000023
Target sparsity
Figure FDA0003892303270000025
Number of paths L, error ε, and number of search candidate support sets L of maximum max In which
Figure FDA0003892303270000024
Is a set of real numbers, N, m, N 1 And n 2 Are all non-negative integer sets.
9. The method of claim 7, wherein the depth-first two-dimensional multi-path matching pursuit algorithm requires initializing candidate support set order and storing a residual with a minimum magnitude.
10. The method of claim 7, wherein the depth-first two-dimensional multi-path matching pursuit algorithm uses a modulo search strategy to determine the search order.
CN202211269808.0A 2022-10-17 2022-10-17 Image denoising method based on two-dimensional multipath matching pursuit algorithm Active CN115564680B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211269808.0A CN115564680B (en) 2022-10-17 2022-10-17 Image denoising method based on two-dimensional multipath matching pursuit algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211269808.0A CN115564680B (en) 2022-10-17 2022-10-17 Image denoising method based on two-dimensional multipath matching pursuit algorithm

Publications (2)

Publication Number Publication Date
CN115564680A true CN115564680A (en) 2023-01-03
CN115564680B CN115564680B (en) 2023-03-28

Family

ID=84746123

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211269808.0A Active CN115564680B (en) 2022-10-17 2022-10-17 Image denoising method based on two-dimensional multipath matching pursuit algorithm

Country Status (1)

Country Link
CN (1) CN115564680B (en)

Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103646380A (en) * 2013-11-25 2014-03-19 大连海洋大学 A method for removing small area noises in a binary image based on a stack theory
WO2014155026A1 (en) * 2013-03-27 2014-10-02 Toshiba Research Europe Limited Signal processing method and apparatus
US20150227819A1 (en) * 2014-02-07 2015-08-13 Canon Kabushiki Kaisha Image processing method and apparatus using trained dictionary
JP2017094097A (en) * 2015-11-27 2017-06-01 株式会社東芝 Medical image processing device, x-ray computer tomographic imaging device, and medical image processing method
CN107644406A (en) * 2017-09-22 2018-01-30 南京理工大学 A kind of image de-noising method based on improved orthogonal matching pursuit
CN108491868A (en) * 2018-03-12 2018-09-04 广东工业大学 A kind of image processing method and device based on k-means cluster and dictionary learning
US20180284747A1 (en) * 2016-05-09 2018-10-04 StrongForce IoT Portfolio 2016, LLC Methods and systems for optimization of data collection and storage using 3rd party data from a data marketplace in an industrial internet of things environment
CN109191399A (en) * 2018-08-29 2019-01-11 陕西师范大学 Magnetic Resonance Image Denoising based on improved multipath matching pursuit algorithm
CN109727219A (en) * 2019-01-25 2019-05-07 江西省高速公路联网管理中心 A kind of image de-noising method and system based on image sparse expression
WO2019130273A1 (en) * 2017-12-29 2019-07-04 Analytics For Life Inc. Method and system to assess disease using phase space tomography and machine learning
US20210027454A1 (en) * 2019-07-24 2021-01-28 Beijing Boe Optoelectronics Technology Co., Ltd. Method for Defect Classification, Method for Training Defect Classifier, and Apparatus Thereof
CN112330705A (en) * 2020-10-14 2021-02-05 南京理工大学 Image binarization method based on deep learning semantic segmentation
CN112712480A (en) * 2020-12-31 2021-04-27 杭州电子科技大学 SAR image speckle reduction method based on anisotropy and dictionary learning

Patent Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014155026A1 (en) * 2013-03-27 2014-10-02 Toshiba Research Europe Limited Signal processing method and apparatus
CN103646380A (en) * 2013-11-25 2014-03-19 大连海洋大学 A method for removing small area noises in a binary image based on a stack theory
US20150227819A1 (en) * 2014-02-07 2015-08-13 Canon Kabushiki Kaisha Image processing method and apparatus using trained dictionary
JP2017094097A (en) * 2015-11-27 2017-06-01 株式会社東芝 Medical image processing device, x-ray computer tomographic imaging device, and medical image processing method
US20180284747A1 (en) * 2016-05-09 2018-10-04 StrongForce IoT Portfolio 2016, LLC Methods and systems for optimization of data collection and storage using 3rd party data from a data marketplace in an industrial internet of things environment
CN107644406A (en) * 2017-09-22 2018-01-30 南京理工大学 A kind of image de-noising method based on improved orthogonal matching pursuit
WO2019130273A1 (en) * 2017-12-29 2019-07-04 Analytics For Life Inc. Method and system to assess disease using phase space tomography and machine learning
CN108491868A (en) * 2018-03-12 2018-09-04 广东工业大学 A kind of image processing method and device based on k-means cluster and dictionary learning
CN109191399A (en) * 2018-08-29 2019-01-11 陕西师范大学 Magnetic Resonance Image Denoising based on improved multipath matching pursuit algorithm
CN109727219A (en) * 2019-01-25 2019-05-07 江西省高速公路联网管理中心 A kind of image de-noising method and system based on image sparse expression
US20210027454A1 (en) * 2019-07-24 2021-01-28 Beijing Boe Optoelectronics Technology Co., Ltd. Method for Defect Classification, Method for Training Defect Classifier, and Apparatus Thereof
CN112330705A (en) * 2020-10-14 2021-02-05 南京理工大学 Image binarization method based on deep learning semantic segmentation
CN112712480A (en) * 2020-12-31 2021-04-27 杭州电子科技大学 SAR image speckle reduction method based on anisotropy and dictionary learning

Also Published As

Publication number Publication date
CN115564680B (en) 2023-03-28

Similar Documents

Publication Publication Date Title
Liu et al. Retrieval compensated group structured sparsity for image super-resolution
US9668699B2 (en) Method and system for anatomical object detection using marginal space deep neural networks
Ojala et al. Texture discrimination with multidimensional distributions of signed gray-level differences
CN110796625B (en) Image compressed sensing reconstruction method based on group sparse representation and weighted total variation
Singh et al. Dual-tree wavelet scattering network with parametric log transformation for object classification
Rubinstein et al. Dictionary learning for analysis-synthesis thresholding
Khmag Additive Gaussian noise removal based on generative adversarial network model and semi-soft thresholding approach
Naderahmadian et al. Correlation based online dictionary learning algorithm
CN110400276B (en) Hyperspectral image denoising method and device
CN102073999A (en) Natural image noise removal method based on dual redundant dictionary learning
CN112767463B (en) Countermeasure registration method, device, computer equipment and storage medium
CN106960420B (en) Image reconstruction method of segmented iterative matching tracking algorithm
Phan et al. Tensor networks for latent variable analysis: Higher order canonical polyadic decomposition
CN112598069B (en) Hyperspectral target tracking method based on feature extraction and weight coefficient parameter updating
Jin et al. Nonhomogeneous noise removal from side-scan sonar images using structural sparsity
Peng Joint and direct optimization for dictionary learning in convolutional sparse representation
CN107301631B (en) SAR image speckle reduction method based on non-convex weighted sparse constraint
CN113204051B (en) Low-rank tensor seismic data denoising method based on variational modal decomposition
Rusu On learning with shift-invariant structures
Lei et al. A sparse representation denoising algorithm for finger-vein image based on dictionary learning
JP2006065863A (en) Adaptive color information for image matching
CN114005046A (en) Remote sensing scene classification method based on Gabor filter and covariance pooling
CN115564680B (en) Image denoising method based on two-dimensional multipath matching pursuit algorithm
Aljadaany et al. Iris super-resolution via nonparametric over-complete dictionary learning
Tu et al. Texture pattern separation for hyperspectral image classification

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant