Digital speckle based multi-source noise filtering method for composite components

Abstract

The application provides a composite component multi-source noise filtering method based on digital speckle, and aims at solving the technical problems of low measurement sensitivity and low precision of collected digital speckle images; the steps are as follows: firstly, digital speckle light paths are used to collect a digital speckle image before and after deformation of an object, phase information of the digital speckle image is extracted by using Fourier transform, and a composite component defect image is obtained; secondly, homomorphic transformation is performed on the composite component defect image, and multiplicative noise is converted into additive noise; then, the additive noise is filtered by using a compression sensing theory, and the multiplicative noise in the composite component defect image is filtered out; finally, a matrix singular value decomposition algorithm is used to filter out the additive noise in the composite component defect image, and a denoised component defect image is obtained; the K-SVD algorithm is used for denoising, details of the original image can be well recovered, Gaussian white noise can be removed, and the PSNR value of the denoised image is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical image processing, in particular to a composite material component multi-source noise filtering method based on digital speckle. BACKGROUND

[0002] With the development of aerospace, various composite materials are widely used. However, the performance of these composite materials is significantly reduced due to defects such as deformation and displacement during processing, manufacturing and service, and the service life is reduced. Therefore, it is necessary to detect and evaluate these composite materials to provide solutions for subsequent repair and ensure the healthy operation of aerospace equipment.

[0003] Research shows that when the surface of an object irradiated by coherent light deforms or displaces, the deformation of the object surface is converted into the phase change of the speckle on the image surface, which is called digital speckle. Digital speckle pattern interferometry (DSPI) is a non-contact full-field measurement technology, which can measure the displacement, deformation, surface defects and other parameters of composite materials. The collected digital speckle pattern (component defect pattern) contains a large amount of multi-source noise, which includes multiplicative noise and additive noise. These multi-source noises result in low measurement sensitivity and seriously affect the measurement accuracy. Therefore, it is necessary to use appropriate methods to process the component defect pattern and filter out the multi-source noise. SUMMARY

[0004] In view of the technical problem that the collected digital speckle pattern contains a large amount of multi-source noise, resulting in low measurement sensitivity and seriously affecting the measurement accuracy, the present application provides a composite material component multi-source noise filtering method based on digital speckle. In view of the multi-source noise interference in the composite material component defect pattern, the multiplicative noise is filtered out by using homomorphic compressive sensing theory, and the additive noise is removed by using singular value decomposition method, so as to realize multi-source noise filtering and obtain the component pattern after noise reduction.

[0005] The technical scheme of the present application is as follows:

[0006] A composite material component multi-source noise filtering method based on digital speckle, the steps are as follows:

[0007] Step 1: Collect a digital speckle pattern before and after deformation of the object by using digital speckle light path, extract the phase information of the digital speckle pattern by using Fourier transform, and obtain the composite material component defect pattern;

[0008] Step 2: Perform homomorphic transformation on the composite material component defect pattern to convert the multiplicative noise into additive noise;

[0009] Step 3: Filter the additive noise by using compressive sensing theory to filter out the multiplicative noise in the composite material component defect pattern.

[0010] Step four: the additive noise in the composite component defect map is filtered out by using a matrix singular value decomposition algorithm to obtain a denoised component defect map.

[0011] The implementation method of step one is: a digital speckle optical path is built, a digital speckle interferogram is collected before and after the object is deformed, a single digital speckle image is subjected to Fourier transform, the high-frequency part after the transform is extracted, the digital speckle wrapped phase image is calculated by using arctangent, and the component defect map is obtained.

[0012] The method for converting the multiplicative noise into additive noise is:

[0013] The expression of the noisy observation signal is:

[0014] y(t)=s(t)·e(t);

[0015] In the formula, y(t) is the noisy observation signal, t represents a time variable, s(t) is a real signal, e(t) is noise, and the noise type obeys a Gaussian distribution of N(1, σ 2 );

[0016] The expression of the noisy observation signal is subjected to a logarithmic homomorphism transformation to obtain:

[0017] G(t)=ln(s)+ln(e);

[0018] Wherein, G(t) represents a reconstructed signal, s represents a real signal, and e represents a noise signal.

[0019] The implementation method of step three is:

[0020] The signal is subjected to sparse representation: the signal x is a one-dimensional finite-length discrete real signal, x is an N×1-dimensional vector, i.e. N x[n]∈R N , n=1, 2, 3, …, N; any signal in the R space quantity can be represented by an N×1-dimensional basis vector, i.e. i Assuming that the basis elements are orthogonal, the vector {Ψ N} is taken as an N×N-dimensional matrix Ψ={Ψ1|Ψ2|Ψ3…|Ψ

[0021]

[0022] Wherein, s i is a weighting coefficient, is a vector composed of N×1, and x is a time domain or space domain, s iIn the transform domain, if the signal x is a linear combination of k basis vectors, then the signal x is k-sparse, that is, the coefficient s in the above formula is i There are k non-zero numbers and (nk) zeros in ;

[0023] The K-SVD algorithm is used to filter out noise and obtain the denoised image: The K-SVD algorithm trains the dictionary D on the noisy image y, and the noisy image is decomposed into The subgraphs are stored in vector y, i ∈R n ; Passing The denoised subgraph can be restored and, after sparse representation, the following formula can be obtained:

[0024]

[0025] in, represents the sparse representation of the decomposed image block x, T is determined by ε and the standard deviation σ of the sub-image, ‖a‖ represents the number of non-zero elements in a, and ‖.‖2 represents the 2-norm;

[0026] Formula (2) can be transformed into an optimized function, namely:

[0027]

[0028] Among them, arg a min{.} represents the set of values ​​of the independent variable a when the objective function reaches its minimum value, and y is the set of k sub-images. It is composed of columns, that is, y={y1,y2,…,y n}, sparse representation a on a given training dictionary D i , that is, a={a1, a2,…a k}; μ represents the penalty factor; ‖a‖0 represents the number of non-zero elements in the statistics a;

[0029] The K-SVD algorithm first trains a dictionary of the noisy sub-image y, and then reconstructs the denoised image x based on the found dictionary:

[0030]

[0031] in, represents the denoised output image, λ is the lagrange multiplication factor; parameter μ p Determines the dilution of subgraph p; R p represents the matrix of the sub-image p; X represents the noisy image, A represents an M×N matrix with rank r;

[0032] In K-SVD algorithm, firstly, initial dictionary needs to be defined, atoms in initial dictionary are discrete cosine transform signals or subgraphs in original image, output image is initialized as X=Y, then iterations in K-SVD algorithm are executed for multiple times: sparse coding and dictionary updating;

[0033] Sparse coding: sparse representation vector a of each subgraph R, X is calculated p Any matching pursuit algorithm can be used to solve:

[0034]

[0035]

[0036] Wherein, c is a gain factor;

[0037] Dictionary updating: the step of updating each column k of dictionary D is:

[0038] S3.1: define a set of samples Wherein Indicates the kth row of matrix A;

[0039] S3.2: calculate all error matrices E k , Wherein, d j Indicates the jth column of dictionary D, Indicates the jth row in matrix A;

[0040] S3.3: select the column corresponding to w k Constrains E k , and

[0041] S3.4: singular value decomposition is applied to make The column of updated dictionary is selected As the first column of U, the updated sparse coefficient vector As the first column of Δ(1,1)v;

[0042] The training dictionary is obtained by K-SVD algorithm, and the sparse representation of each subgraph is solved under the condition that the dictionary D is known, then the image after denoising can be obtained by solving the following formula:

[0043]

[0044] This quadratic term is in the form of:

[0045]

[0046] Wherein, Is the image after denoising, and I is a unit matrix.

[0047] The implementation method of step four is:

[0048] S4.1: Constructing Hankel matrix, when the length N' of the noisy signal is odd, the row number m of H matrix is N'+1; when the length N' of the noisy signal is even, the row number m of H matrix is N' / 2, and the column number n' of H matrix is N'-m+1;

[0049] S4.2: SVD decomposition: SVD decomposing H matrix to obtain two normalized orthogonal matrices U m×n′ and V M×n′ and a diagonal matrix D m×n′ ;

[0050] S4.3: Singular value selection: arranging singular values contained in matrix D m×n′ in descending order, and the singular values are respectively σ1, σ2…σ r ; if r is even, the median is the average of the position r / 2 and the position (r+2) / 2; if r is odd, the median is the number in the position (r+1) / 2;

[0051] The method for singular values is to set each singular value less than the median of singular values to zero, and to retain each singular value greater than the median of singular values, and to obtain the processed diagonal matrix D' according to the processing method; m×n′ ;

[0052] S4.4: Constructing H Δ : constructing H m×n′ by using orthogonal matrices U m×n′ , V m×n′ and the diagonal matrix D' Δ , and the calculation formula is:

[0053] H Δ = UD'V;

[0054] S4.5: Obtaining the denoised signal: selecting all elements in the first row of H Δ and m-1 elements from the n' column to the n' column of the second row to the m row to obtain the denoised signal.

[0055] Compared with the prior art, the present application has the following beneficial effects:

[0056] 1) The multiplicative noise is often caused by an unideal signal transmission and multiplied with the signal, so it is difficult to eliminate, and the present application proposes that the homomorphic compressive sensing theory can convert the multiplicative noise into additive noise and then filter out the additive noise;

[0057] 2) For the selection of the reconstruction algorithm of the compressed sensing theory, the K-SVD algorithm is compared with the traditional wavelet soft threshold denoising method, the K-SVD algorithm denoising can well restore the detail part of the original image, and remove the Gaussian white noise, and improve the PSNR value of the denoising image;

[0058] 3) The matrix singular value decomposition denoising method provided by the present application can solve the problem that most of the matrices in real life are not square matrices, so that the method of using eigenvalue decomposition to extract the eigenvalue of the matrix is no longer applicable. BRIEF DESCRIPTION OF DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0060] Figure 1 The flowchart of the present application.

[0061] Figure 2 The flowchart of the present application for extracting the component defect map. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0063] As shown in the figure, a composite material component multi-source noise filtering method based on digital speckle, the specific steps are as follows: Figure 1

[0064] Step one: use digital speckle optical path to collect a digital speckle map before and after the deformation of an object, use Fourier transform to extract the phase information of the digital speckle map, and obtain the composite material component defect map; as shown in the figure, build a digital speckle optical path, load the composite material component, and collect a digital speckle interference map before and after the deformation of the object; perform Fourier transform on the collected single digital speckle map, extract the high frequency part after the transform, calculate the digital speckle wrapped phase map by using arctangent, and obtain the component defect map. Figure 2 Step two: perform homomorphic transform on the composite material component defect map to convert the multiplicative noise into additive noise;

[0065]

[0066] ​​The noisy observation signal expression is:

[0067] y(t) = s(t) * e(t);

[0068] In the formula, y(t) is a noisy observation signal, t represents a time variable, s(t) is a real signal, e(t) is noise, and the noise type obeys a Gaussian distribution N(1, σ 2 );

[0069] The noisy observation signal expression is subjected to a logarithmic homomorphism transformation to obtain:

[0070] G(t) = ln(s) + ln(e);

[0071] Wherein, G(t) represents a reconstructed signal, s represents a real signal, and e represents a noise signal.

[0072] Step three: filter the additive noise using the compressive sensing theory to filter out the multiplicative noise in the composite material component defect map;

[0073] Sparse representation of the signal: assuming that the signal x is a one-dimensional finite-length discrete real signal, x is an N*1-dimensional vector, that is, x[n] ∈ R N , n = 1, 2, 3,..., N; any signal in R N space can be represented by an N*1-dimensional basis vector, that is, Assuming that the basis elements are orthogonal, the vector {Ψ i} is an N*N-dimensional matrix Ψ = {Ψ1|Ψ2|Ψ3…|Ψ N}, column, then the signal x can be represented as:

[0074]

[0075] Wherein, s i is a weighting coefficient, is a vector composed of N*1, and x is a time domain or spatial domain, s i In the transform domain, if the signal x is a linear combination of k basis vectors, then the signal x is k-sparse, that is, in the above formula, there are k non-zero numbers in the coefficient s i (n-k) zeros.

[0076] Noise is filtered out using the K-SVD algorithm to obtain the image after denoising: the K-SVD algorithm trains the dictionary D on the noisy image y, and the noisy image is decomposed into sub-images of size The sub-images are stored in the vector y, y i ∈ R n ; the denoising sub-image can be recovered by formula , and the denoising sub-image can be obtained by sparse representation as follows:

[0077]

[0078] where, denotes the sparse representation of the image patch x, T is determined by ε and the standard deviation σ of the sub-patch, ‖a‖0denotes the number of non-zero elements in a, and ‖a‖2denotes the 2-norm.

[0079] The equation (2) can be transformed into an optimization function, i.e.:

[0080]

[0081] where, arg a min{.} denotes the set of values of the argument a when the objective function reaches the minimum value, y is the k sub-patch images composed of columns, i.e. y = {y1, y2, …, y n}, the sparse representation a i on the given training dictionary D, i.e. a = {a1, a2, … a k}; μ denotes the penalty factor, when the appropriate μ is selected, the above equations (2) and (3) are equivalent; ‖a‖0denotes the number of non-zero elements in a.

[0082] The K-SVD algorithm first trains the dictionary containing the noisy sub-patch y, and then reconstructs the denoised image x according to the found dictionary:

[0083]

[0084] where, denotes the denoised output image, λ is the Lagrange multiplier, λ adjusts the similarity between the denoised output image x and the noisy image; the parameter μ p determines the dilution of the sub-patch p; R p denotes the matrix of the sub-patch p; X denotes the noisy image, and A denotes the M × N matrix with rank r.

[0085] In the K-SVD algorithm, the initial dictionary needs to be defined first, the atoms in the initial dictionary are discrete cosine transform signals or sub-patches in the original image, and the output image is initialized as X = Y, and then the iterations in the K-SVD algorithm are performed multiple times: sparse coding and dictionary updating;

[0086] Sparse coding: the sparse representation vector a p of each sub-patch R, X is calculated:

[0087]

[0088]

[0089] where c is a gain factor.

[0090] Dictionary update: the step of updating each column k of the dictionary D is:

[0091] S3.1: define a set of samples where denotes the k-th row of the matrix A;

[0092] S3.2: calculate all error matrices E k , where d j denotes the j-th column of the dictionary D, denotes the j-th row in the matrix A;

[0093] S3.3: select the column of D k corresponding to w k , and obtain

[0094] S3.4: apply singular value decomposition to make select the column of the updated dictionary as the first column of U, the updated sparse coefficient vector as the first column of Δ(1,1)v;

[0095] The training dictionary is obtained by the K-SVD algorithm, and the sparse representation of each subgraph is solved in the known dictionary D, and then the denoised image can be obtained by solving the following equation:

[0096]

[0097] The quadratic term is in the form of:

[0098]

[0099] where, is the denoised image, and I is the unit matrix.

[0100] Step four: use the matrix singular value decomposition algorithm to filter out the additive noise in the composite component defect image, and obtain the denoised component defect image.

[0101] S4.1: construct the Hankel matrix, when the length of the noisy signal N' is odd, the number of rows m of the H matrix is N'+1; when the length of the noisy signal N' is even, the number of rows m of the H matrix is N' / 2, and the number of columns n' of the H matrix is N'-m+1;

[0102] S4.2: SVD decomposition: perform SVD decomposition on the H matrix to obtain two normalized orthogonal matrices U m×n′ , V m×n′ and a diagonal matrix D m×n′;

[0103] S4.3: singular value selection: using the singular value median method to process matrix D m×n′ The singular values contained are arranged in descending order, and are respectively σ1, σ2…σ r ; if r is even, the median is the average of the position r / 2 and the position (r+2) / 2; if r is odd, the median is the number in the position (r+1) / 2;

[0104] The method for processing the singular values is to set the singular values smaller than the singular value median to zero, and to retain the singular values larger than the singular value median, and to obtain the processed diagonal matrix D' according to the processing method m×n′ ;

[0105] S4.4: constructing H Δ : using the orthogonal matrix U m×n′ , V m×n′ and the diagonal matrix D' m×n′ to construct H Δ , and the calculation formula is:

[0106] H Δ = UD'V;

[0107] S4.5: obtaining the noise reduction signal: selecting the first row of H Δ All the elements of the first row and the m-1 elements from the n' column of the second row to the n' column of the m row of H

[0108] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for filtering multi-source noise of composite components based on digital speckle, characterized in that: The steps are as follows: Step 1: Use the digital speckle optical path to collect a digital speckle pattern of the object before and after deformation, and use Fourier transform to extract the phase information of the digital speckle pattern to obtain the defect map of the composite material component; Step 2: Perform homomorphic transformation on the defect map of the composite component to convert the multiplicative noise into additive noise; Step 3: Use compressed sensing theory to filter the additive noise and remove the multiplicative noise in the defect map of the composite component; The implementation method of step 3 is: sparsely represent the signal: the signal x is a one-dimensional finite-length discrete real signal, x is an N×1-dimensional vector, that is, x[n]∈R N ,n=1,2,3,…,N;in R N Any signal of a spatial quantity can be represented by an N×1-dimensional basis vector, that is, Assuming that the basis elements are orthogonal, the vector {Ψ i } as an N×N dimensional matrix Ψ={Ψ1|Ψ2|Ψ3…|Ψ N } column, the signal x is expressed as: Among them, s i is the weighting coefficient, is a vector of N×1 dimensions, x is the time domain or space domain, s i In the transform domain, if the signal x is a linear combination of k basis vectors, then the signal x is k-sparse, that is, the coefficient s in the above formula is i There are k non-zero numbers and (nk) zeros in ; The K-SVD algorithm is used to filter out noise and obtain the denoised image: The K-SVD algorithm trains the dictionary D on the noisy image y, and the noisy image is decomposed into The subgraphs are stored in vector y, i ∈R n ; Passing The denoised subgraph can be restored and, after sparse representation, the following formula can be obtained: in, represents the sparse representation of the decomposed image block x, T is determined by ε and the standard deviation σ of the sub-image, ‖a‖ represents the number of non-zero elements in a, and ‖a‖2 represents the 2-norm; Formula (2) can be transformed into an optimized function, namely: Among them, arg a min{.} represents the set of values ​​of the independent variable a when the objective function reaches its minimum value, and y is the set of k sub-images. It is composed of columns, that is, y={y1,y2,…,y n }, sparse representation a on a given training dictionary D i , that is, a={a1, a2,…a k }; μ represents the penalty factor; ‖a‖0 represents the number of non-zero elements in the statistics a; The K-SVD algorithm first trains a dictionary of the noisy sub-image y, and then reconstructs the denoised image x based on the found dictionary: in, represents the denoised output image, λ is the lagrange multiplication factor; parameter μ p Determines the dilution of subgraph p; R p represents the matrix of the sub-image p; X represents the noisy image, A represents an M×N matrix with rank r; In the K-SVD algorithm, you first need to define an initial dictionary. The atoms in the initial dictionary are discrete cosine transform signals or sub-images in the original image. The output image is initialized to X = Y. Then, multiple iterations of the K-SVD algorithm are performed: sparse coding and dictionary update. The training dictionary is obtained by the K-SVD algorithm. When the dictionary D is known, the sparse representation of each sub-image is solved. The denoised image can be obtained by solving the following formula: The solution to this quadratic term is of the form: in, is the image after denoising, I is the unit matrix; Step 4: Use the matrix singular value decomposition algorithm to filter out the additive noise in the composite component defect map to obtain the denoised component defect map.

2. The method for filtering multi-source noise of composite components based on digital speckle according to claim 1, characterized in that: The implementation method of step one is as follows: build a digital speckle optical path, perform thermal loading on the composite material component, and collect a digital speckle interference pattern before and after the object is deformed; perform Fourier transform on the collected single digital speckle pattern, extract the high-frequency part after transformation, and use inverse tangent to calculate the digital speckle parcel phase map to obtain the component defect map.

3. The method for filtering multi-source noise of composite components based on digital speckle according to claim 1, characterized in that: The method for converting multiplicative noise into additive noise is: The expression of the noisy observation signal is: y(t)=s(t)·e(t); Where y(t) is the noisy observation signal, t represents the time variable, s(t) is the real signal, e(t) is the noise, and the noise type obeys N(1, σ 2 )’s Gaussian distribution; The noisy observation signal expression is transformed by logarithmic homomorphism to obtain: G(t)=ln(s)+ln(e); Where G(t) represents the reconstructed signal, s represents the true signal, and e represents the noise signal.

4. The method for filtering multi-source noise of composite components based on digital speckle according to claim 3, characterized in that: Sparse coding: Calculate the sparse representation vector a of each subgraph R, X p It can be solved using any matching pursuit algorithm: Where c is the gain factor; Dictionary update: The steps to update each column k of dictionary D are: S3.1: Define a set of samples in represents the kth row of matrix A; S3.2: Calculate all error matrices E k , Among them, d j represents the j-th column of dictionary D, represents the j-th row in matrix A; S3.3: Selection and w k The corresponding column constraint E k , we can get S3.4: Apply singular value decomposition to Select the columns of the updated dictionary As the first column of U, the updated sparse coefficient vector As the first column of Δ(1,1)v.

5. The method for filtering multi-source noise of composite components based on digital speckle according to claim 4, characterized in that: The implementation method of step four is: S4.1: Construct the Hankel matrix. When the length N′ of the noisy signal is odd, the number of rows m in the H matrix is ​​N′+1. When the length N′ of the noisy signal is even, the number of rows m in the H matrix is ​​N′ / 2, and the number of columns n′ in the H matrix is ​​N′-m+1. S4.2: SVD decomposition: Perform SVD decomposition on the H matrix to obtain two standardized orthogonal matrices U m×n′ 、V m×n′ and the diagonal matrix D m×n′ ; S4.3: Singular value selection: Use the singular value median method to select the matrix D m×n′ The singular values ​​contained are arranged in descending order, namely σ1, σ2…σ r ; If r is an even number, then the median is the average of the sum of the numbers at position r / 2 and position (r+2) / 2; if r is an odd number, then the median is the number at position (r+1) / 2; The method used for singular values ​​is to set each singular value smaller than the median singular value to zero and retain each singular value larger than the median singular value. According to this method, the processed diagonal matrix D' is obtained. m×n′ ; S4.4: Construct H Δ : Using the orthogonal matrix U m×n′ 、V m×n′ and the diagonal matrix D′ m×n′ Structure H Δ , the calculation formula is: H Δ =UD′V; S4.5: Obtain noise-reduced signal: Select H Δ All elements in the first row and m-1 elements from the n′th column of the second row to the n′th column of the mth row are used to obtain the denoised signal.

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