KR101740647B1 - Apparatus for Processing High Dynamic Range Imaging - Google Patents

Abstract

The HDR image processing apparatus provides the HDR image synthesis technique using the truncated Nuclear Norm minimization method of the low rank matrix and expresses the background and the moving object as the low rank matrix and the sparse matrix on the assumption that the background is static, It is expressed as the completion problem of the low rank matrix. By using the Augmented Lagrange Multiplier (ALM) method, the optimal solution is obtained efficiently, and the resultant image has a remarkably low computational complexity and a higher quality.

Description

[0001] The present invention relates to an HDR image processing apparatus,

The present invention relates to an HDR (High Dynamic Range) image processing apparatus, and more particularly, to an HDR image synthesis method using a truncated nuclear norm minimization method of a low rank matrix, Rank matrices and sparse matrices, the background estimation is expressed as a problem of the completion of the low rank matrix, and the optimal solution is obtained efficiently using the Augmented Lagrange Multiplier (ALM) method, And an HDR image processing apparatus for providing a resultant image.

With the recent development of digital image technology, it is possible to acquire high resolution image by using various devices including smart phone.

On the other hand, a typical digital camera can acquire only an image having a dynamic range much lower than that of a real scene. Therefore, there is a limitation that the acquired image can not include all the information of the scene due to the limited dynamic range. Many studies have been conducted to overcome these drawbacks and obtain information of all dynamic regions of the scene.

An image having such a high dynamic range is called an HDR (High Dynamic Range) image. The most basic method to acquire HDR images is to synthesize LDR (Low Dynamic Range) images photographed at different exposure times.

However, Ghosting Artifact occurs when HDR images are synthesized with this simple method because there is generally motion of object or camera during shooting. Therefore, the technique of obtaining high quality HDR image without Ghosting artifact is a very important research topic.

A method of acquiring high quality HDR image in a moving scene can synthesize an HDR image using the resultant image after matching the input LDR image. However, this technique has a disadvantage of high computational complexity.

Recently, the technique of acquiring the HDR image proposed the HDR synthesis technique applying the low rank matrix completion problem on the assumption that the background part is static and the moving object is rare in the input image.

However, this technique has a disadvantage in that it can not approximate the rank of a matrix accurately.

In order to solve this problem, the present invention provides an HDR image synthesis method using a truncated nuclear norm minimization method of a low rank matrix, and provides a low-rank matrix and a sparse matrix as background and moving objects, respectively, , HDR (Higher Order Reasoning), which provides a higher quality result image with remarkably lower computational complexity by efficiently obtaining the optimal solution using the Augmented Lagrange Multiplier (ALM) method, expresses the background estimation as a completion problem of the low rank matrix, And an object thereof is to provide an image processing apparatus.

According to an aspect of the present invention, there is provided an apparatus for processing an HDR image,

An object image matrix generation unit that receives a target image to be separated from a background and an object and generates a target image matrix that is a matrix according to image signal values of pixels of the target image; And

The target image matrix is set as a sum of a low rank matrix having a rank value smaller than a certain standard and a sparse matrix being a remaining element excluding the low rank matrix element in the target image matrix A weighted sum obtained by applying a factor adjusting the relative importance between the low rank matrix and the sparse matrix to a Truncated Nuclear Norm calculation value for the low rank matrix and an L 1 norm calculation value for the sparse matrix, And an image separation unit for calculating the low rank matrix and the sparse matrix using the cost function.

According to an aspect of the present invention,

An object image matrix generation unit that receives a target image to be separated from a background and an object and generates a target image matrix that is a matrix according to image signal values of pixels of the target image; And

Sets a low rank matrix having a rank value smaller than a certain reference as the target image matrix and sets a constraint condition as a sum of the low rank matrix and a slack variable matrix, A constant first cost function can be minimized or a constant range can be minimized by using an augmented Lagrange Multiplier (ALM) method for obtaining a solution of a first cost function using a low rank matrix and a Lagrangian cost function applied with a Lagrangian multiplier for the extra variable matrix And an optimization algorithm unit for generating a TNNM (Augmented Lagrange Multiplier) algorithm to calculate the low rank matrix and the allowable variable matrix.

According to the above-described configuration, when HDR images are synthesized using a TNMM (Augmented Lagrange Multiplier) algorithm, the computational complexity is remarkably lower than that of conventional methods, It is possible to acquire a high-quality HDR image even in an apparatus equipped with the above-described apparatus.

1 is a block diagram briefly showing a configuration of an image processing apparatus according to an embodiment of the present invention.
FIG. 2 is a diagram illustrating a series of procedures for generating a TNNM-ALM algorithm according to an embodiment of the present invention. Referring to FIG.
3 is a diagram illustrating a method of synthesizing an HDR image using a TNNM-ALM algorithm according to an embodiment of the present invention.

Throughout the specification, when an element is referred to as "comprising ", it means that it can include other elements as well, without excluding other elements unless specifically stated otherwise.

FIG. 1 is a block diagram briefly showing a configuration of an image processing apparatus according to an embodiment of the present invention. FIG. 2 is a diagram illustrating a series of procedures for generating a TNNM-ALM algorithm according to an embodiment of the present invention. Is a diagram illustrating a method of synthesizing an HDR image using a TNNM-ALM algorithm according to an embodiment of the present invention.

The image processing apparatus 100 according to the embodiment of the present invention includes an optimization algorithm unit 102, a target image matrix generation unit 110, an image separation unit 120, and an image synthesis unit 130.

The optimization algorithm unit 102 formulates the problem so that a more accurate matrix rank can be approximated by using the truncated nucleus norm minimization of the matrix, and then, by using the Augmented Lagrange Multiplier (ALM) technique, We propose a technique to obtain

는 행렬 X의 nuclear norm이고,

은 행렬 X의 k번째 특이값(singular value)이며,

는 행렬 X를

에서 샘플링하는 연산자이다.here,

Is the nuclear norm of matrix X,

Is the kth singular value of the matrix X,

Lt; RTI ID = 0.0 >

. ≪ / RTI >

In order to efficiently solve the matrix completion problem for the matrix X, since the rank (X) is nonconvex and separated, it is solved after approximation as in the above-mentioned Equation (1).

However, Equation (1) has a disadvantage in that the nuclear norm can not approximate the rank of the matrix precisely, and is converted into minimization of the truncated nuclear norm as shown in Equation (2) below.

는 행렬 X의 truncated nuclear norm을 나타낸다.here,

Represents the truncated nuclear norm of the matrix X.

The above-described expression (2) has an advantage of exactly approximating the rank of the matrix but it is not efficient because it is solved using iteration.

The optimization algorithm unit 102 initializes the matrix X and the matrix S (S100).

In order to solve the problem of minimizing the truncated nuclear norm of the matrix X, the optimization algorithm unit 102 adds a matrix S, which is a slack variable, to the above-described equation (2) (3). &Quot; (3) "

로 표현된다.Equation (3) takes into account the noise generated in the data acquisition process. That is, the data acquisition process using the noise matrix N

Lt; / RTI >

는 행렬의 프로베니어스 놈(Frobenius norm)이고, δ는 데이터 취득 과정에서 발생하는 잡음의 세기이며, 행렬 X는 구하고자 하는 저 랭크 행렬을 나타낸 것이다. 프로베니어스 놈은 모든 행렬 원소의 절대값의 제곱의 합을 구하는 연산이다.here,

Is the Frobenius norm of the matrix, [delta] is the intensity of the noise occurring in the data acquisition process, and matrix X is the low rank matrix to be sought. The Probenisch norm is an operation that calculates the sum of squares of the absolute values of all matrix elements.

Since it is necessary to apply the sampling operator to the matrix X in Equation (2), it is very difficult to solve the problem directly. Therefore, if the extra variable matrix S is added to easily solve the problem, Equation 3 can be obtained.

=0), 새로운 미지수 행렬 S를 추가하는 대신에 기존 미지수 X에 적용하는 샘플링 연산자를 제거하는 효과가 있다.In Equation (3), there is a term that considers the noise generated in the data acquisition process. If noise is ignored (i.e.,

= 0), there is an effect of removing the sampling operator which applies to the unknown unknown X instead of adding the new unknown matrix S.

In other words, equations (2) and (3) are the same problem, but the problem is easily solved by adding an extra variable matrix.

를 분리하여 각 행렬 변수 X 및 S에 대한 closed form solution을 구할 수 있다.[Mathematical Expression 3] is a problem in which the problem with the existing matrix X is transformed into a problem with the matrix X and the matrix S. We add a new variable, matrix S, and use the projection operator in matrix X,

To obtain a closed form solution for each matrix variable X and S.

The optimization algorithm unit 102 is defined as an Augmented Lagrangian Function for the above-described Equation (3) and expressed as Equation (4) below.

Here, μ is a disadvantage variable (Penalty Parameter) and, Λ is a Lagrangian multiplier matrix, <A, B> = tr (AB T) is the inner product calculation of the two matrices (matrix inner product), X is a low-rank matrix (Low Rank Matrix), and S is a slack variable matrix.

The allowance variable is a variable used to convert to a floating type in the grouping solution in the linear programming, and functions to solve the problem of matrix complementation with sparse errors.

The allowance variable makes it possible to increase the number of optimization variables and obtain the closed form solution of matrix X at each iteration during optimization.

The Lagrangian multiplier matrix is a variable used for constraints to be included in the cost function, that is, the objective function, and serves to determine the weight of the constraint in the overall cost function.

The optimization algorithm unit 102 predicts the Lagrangian multiplier matrix L and the disadvantage variable 占 of Equation 4 and calculates a solution by minimizing the cost function of Equation 4 with respect to the predicted Λ (ALM) algorithm to calculate a matrix X and a matrix S (S102, S104).

The optimization algorithm unit 102 repeatedly predicts the optimized solution and Lagrangian multiplier matrix until it converges to the ALM method.

In the k-th iteration, the optimization problem of the following equation (5) is solved to obtain the matrix X and the matrix S described above.

Here, k represents an Index corresponding to a repetition number of times.

[Mathematical Expression 5] can not solve the problem simultaneously for the matrix X and the matrix S. Therefore, the matrix X and the matrix S are sequentially updated as shown in Equation 6 and Equation 9 below.

Since the above equations (6) and (9) are efficiently calculated by the closed form solution, the computational complexity can be reduced as compared to Equation (5).

In the above-mentioned equation (5), when the matrix X is optimized and rewritten, it is represented as the following equation (6).

Here, S _k and Λ _k represent given estimates, and the closed form solution of Equation (6) can be obtained by the following Equation (8) by the PSVT (Partial Singular Value Thresholding) operator.

The PSVT operator is defined as: &quot; (7) &quot;

는 원소별 소프트 임계치 연산자(soft thresholding operator)인

를 의미한다.Here, T is an operator for calculating the transpose matrix,

Is an elementary soft thresholding operator

.

The PSVT operator has a special case for solving the objective function expressed by the weighted nuclear norm and is used to solve the subproblem used in the optimization problem of the general weighted nuclear norm.

는 [수학식 7]의 PSVT 연산자를 나타낸다.here,

Represents the PSVT operator of Equation (7).

If the matrix S is rewritten as an optimization problem in the above-mentioned equation (5), it can be expressed as the following equation (9), and the matrix S can be estimated by solving equation (9).

는 표기를 단순히 하기 위한 것이며, [수학식 8]에 의해 X_k+1가 주어진다.here,

_{Xk + 1 &quot;} is given by &quot; (8) &quot;

From the above-mentioned equation (9), the closed form solution in the sub-problem can be obtained as the following equation (10).

Equations (8) and (10) are more efficient than the conventional method because X _{k + 1} and S _{k + 1} are calculated using a closed form solution.

The Lagrangian multiplier matrix Λ is updated using the calculated X _{k + 1} and S _{k + 1} and the ALM algorithm (Equation 11, S106).

The matrix X, the matrix S, and the Lagrangian multiplier matrix A are updated with variables optimized by the closed form solution in Equations (8), (10) and (11).

The disadvantageous variable [mu] is updated as in the following Equation (12) using an adaptive update strategy (S108).

는 불이익변수 μ의 최대값이고, ρ>1와 k>0는 미리 정해진 상수이다.here,

Is the maximum value of the disadvantageous variable μ, and ρ> 1 and k> 0 are predetermined constants.

The matrix X, the matrix S, the Lagrangian multiplier matrix LAMBDA, and the disadvantageous variable mu are updated by Equations (8), (10), (11), and (12).

은 다음의 [수학식 13]과 같이 정의되며,

< 10^-4 될 때까지 반복을 계속한다(S110).The optimized variables (X, S, L, μ) continue to be updated repeatedly until convergence. The convergence rate in the kth iteration

Is defined as < EMI ID = 13.0 &gt;

Repeating is continued until <10 ^-4 (S110).

The optimization algorithm unit 102 obtains a closed form solution for the matrix X, the matrix S, and the Lagrangian multiplier matrix Λ by the above-described Equations (8), (10) and (11) Truncated Nuclear Norm Minimization) -ALM (Augmented Lagrange Multiplier) algorithm.

In order to solve the problem expressed by the above-described expression (3), the optimization algorithm unit 102 calculates a matrix X, a matrix S, a Lagrangian multiplier A closed form solution for the matrix Λ is defined as a TNNM (Augmented Lagrange Multiplier) algorithm.

The TNNM-ALM algorithm is summarized as follows.

In the present invention, it is essential to approximate the rank function of a matrix to a Truncated Nuclear Norm and solve the matrix completion problem efficiently.

This is because the Truncated Nuclear Norm property approximates the rank of the matrix more accurately but is nonconvex, making it difficult to solve the problem.

The present invention solves the Maxtrix Completion problem.

Is applied to the image separating unit 120 and the image synthesizing unit 130 of the High Dynamic Range using the TNNM-ALM algorithm generated by the optimization algorithm unit 102.

The image synthesizer 130 synthesizes a plurality of images having motion captured under different exposures to synthesize an HDR image without a ghosting artifact.

The target image matrix generator 110 receives the target image to be separated from the background and the object, and generates a target image matrix, which is a matrix according to the image signal values of the pixels of the target image (S200).

The target image matrix generator 110 forms a matrix having image signal values of pixels in pixels of a target image as elements, with respect to a target image to be separated from a background image. here. The target image matrix represents a matrix constructed for the target image.

Each element value of the target image matrix may be a video signal value of a target image and an image signal value may be signal values acquired using various kinds of color spaces.

이다.The image input to the target image matrix generation unit 110 is a matrix of images captured using different exposure times

to be.

Here, vec (Ii) is the input brightness vector obtained using the camera response function.

The image separator 120 initializes a matrix X, a matrix E, a matrix S and a Lagrangian multiplier (S202).

The image separator 120 may represent the brightness D of the scene as a sum of the background matrix X and the foreground matrix E. [ Since the background is static, matrix X is a Low Rank and E is a sparse matrix.

The sparse matrix is only needed when applying TNNM-ALM to HDR image acquisition. Using a fixed camera, take multiple pictures under different exposure conditions. If there is no moving water in the scene at this time, if the photographed photographs are represented by a matrix, the matrix will simply be a background, and the rank of the matrix will be small.

However, if there are moving objects in the scene (such as a person walking) while you are taking a picture, the rank of the matrix will be large. Since the background is the same, this matrix can be represented by the sum of two matrices (X + E). In this case, the matrix X is a low-rank matrix since it represents the background, and the matrix E is a matrix representing a moving object. Assuming that the size of the moving object is small relative to the size of the image, the matrix E becomes a sparse matrix. Therefore, the matrix E corresponds to a moving object having a small size.

The image separating unit 120 converts the Rank minimization problem into the following Equation (14) for HDR image acquisition.

는 측정 영역

에서의 샘플링 연산자를 나타내며, λ는 X의 랭크와 E의 희소성 사이의 상대적 중요성을 조절한다.here,

Lt; / RTI &

Represents the sampling operator at, and lambda modulates the relative importance between the rank of X and the scarcity of E.

Equation (14) indicates that a measurement matrix D composed of a plurality of input images can be represented by a low rank matrix X representing a background and a rare matrix E representing a moving object. From the measurement matrix D, a low rank matrix X Expresses the optimization problem of estimating the sparse matrix E.

Since the optimization problem of Equation (14) described above is difficult to solve directly, various approximate techniques are used. The image separator 120 approximates the scarcity as a truncated nuclear norm to approximate the Rank function with L1 norm.

를 truncated nuclear norm

및

으로 근사화하여 다시 작성하면 다음의 [수학식 15]와 같이 표현된다.That is, the rank function and scarcity

Truncated nuclear norm

And

, The following equation (15) is obtained.

는 상기 희소 행렬의 L1 norm을 나타낸다.Where l is a factor controlling the relative importance between the rank of X and the scarcity of E, the background is static, the target rank r is set to 1,

Represents the L1 norm of the sparse matrix.

The optimization problem is solved by applying the TNNM-ALM algorithm described above to (15).

The image separating unit 120 rewrites the Slack Variables matrix S into Equation (15) as shown in Equation (3), and expresses it as Equation (16).

The image separating unit 120 defines an augmented Lagrangian function for [Expression 16] and is expressed as [Expression 17].

In other words, the image separating unit 120 separates the target image matrix into a low rank matrix having a rank value lower than a certain standard and a low-rank matrix having a rank matrix excluding the low rank matrix elements Sparse Matrix) E, a weighted sum obtained by applying a truncated Nuclear Norm operation value for the low rank matrix and an adjustment factor (?) To the L1 Norm operation value for the sparse matrix is set as a Lagrangian cost function, and a Lagrangian cost Function, a low-rank matrix, a sparse matrix, and an extra variable matrix are calculated (S204, S206, S208).

The low rank matrix is a matrix corresponding to a principal component composed of eigen vectors having a small number of eigenvalues in principal component analysis of a target image matrix.

Here, a low rank matrix having a rank value smaller than the rank value of the target image matrix can be obtained as a sum of the eigenvectors by selecting a predetermined number of eigenvectors in order of increasing eigenvalues and applying the eigenvalues.

The low rank matrix is a matrix including information on a principal component of a target image, and is a matrix showing a background occupying more area in the target image.

Therefore, a matrix representing an object that includes a sparse matrix obtained by subtracting a low rank matrix from a target image matrix and occupies only a partial area on the background is obtained.

The image separator 120 may use the Lagrangian cost function as shown in Equation (17) to optimally separate the low rank matrix, the sparse matrix, and the extra variable matrix.

[Equation 17] is divided into sub-problems and expressed as an optimization problem, it is expressed as the following Equation (18).

The image separating unit 120 separates the low cost function into a low cost function for minimizing the cost function or converging the cost function within a predetermined range by using an Augmented Lagrange Multiplier (ALM) method, which is a method of finding a solution of a cost function using a Lagrangian cost function using a Lagrangian multiplier. Matrix, a spare variable matrix, and a sparse matrix are calculated (S204, S206, S208).

An optimal solution calculation method can be used to calculate X, E, and S minimizing the Lagrangian cost function.

Here, the calculation of the optimal solution minimizing the Lagrangian cost function means not only a solution that minimizes the cost function but also a solution when the cost function becomes smaller within a certain standard or when the cost function converges It includes meaning.

The Lagrangian multiplier matrix Λ is updated using the calculated X _{k + 1,} S _{k + 1} , and E _{k + 1} (Equation 19, S210).

As shown in Equations (6), (7) and (8) above, the closed form solution of the lower problem of Equation (18) can be obtained by the following Equation (20) by the PSVT operator.

는 단순한 표기로 나타낼 수 있으며, 수학식 18, 19 ,20에 의해 X_k+1, S_k, Λ_k가 주어진다.here,

Can be represented by a simple notation, and X _{k + 1} , S _k , and Λ _k are given by Equations (18), (19) and (20).

The disadvantaged variable updating step (S212) and the convergence determination step (S214) are the same as those of S108 and S110 described above, so that they are omitted.

The above equations (4) and (17) differ in that there is an updated matrix E _{k + 1} . Equation 18 and 19, given a 20 by X _{k + 1,} S _k, Λ _k, it is possible to enjoy the optimized matrix E _{k + 1} as follows: [Equation 21].

-norm 항 및 프로베니어스 놈 항으로 이루어져 있으므로 원소별 소프트 임계치 연산자(soft thresholding operator)

에 의해 효율적으로 최소화한다.The objective function in equation (21)

-norm term and the Probenisch term, the soft thresholding operator for each element,

Thereby effectively minimizing it.

The closed form solution in the above-mentioned expression (21) can be obtained by the following expression (22).

The optimization variables X, E, S and L are updated by equations (19), (20), (21) and (22), respectively.

The image synthesizer 130 obtains the final HDR image by taking an average of the background brightness map of the background matrix X using the following equation (23) (S216).

Where n is the number of input images, Ri is the estimated brightness value at i pixel position, and a constant value varying from j = 1 to integer n.

The present invention provides an HDR image synthesis technique using a truncated nuclear norm minimization method of a low rank matrix, and expresses a background and a moving object as a low rank matrix and a sparse matrix on the assumption that the background is static, Matrices are expressed as the problem of completion, and the optimum solution is efficiently obtained by using the ALM method.

The image processing apparatus 100 of the present invention provides a result image of higher quality with significantly less computation complexity than the conventional technique.

The embodiments of the present invention described above are not implemented only by the apparatus and / or method, but may be implemented through a program for realizing functions corresponding to the configuration of the embodiment of the present invention, a recording medium on which the program is recorded And such an embodiment can be easily implemented by those skilled in the art from the description of the embodiments described above.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, It belongs to the scope of right.

100: image processing device
102: Optimization Algorithm
110: target image matrix generation unit
120:
130:

Claims (11)

An object image matrix generation unit that receives a target image to be separated from a background and an object and generates a target image matrix that is a matrix according to image signal values of pixels of the target image; And
The target image matrix is set as a sum of a low rank matrix having a rank value smaller than a certain standard and a sparse matrix being a remaining element excluding the low rank matrix element in the target image matrix A weighted sum obtained by applying a factor adjusting the relative importance between the low rank matrix and the sparse matrix to a Truncated Nuclear Norm calculation value for the low rank matrix and an L 1 norm calculation value for the sparse matrix, And an image separation unit for calculating the low rank matrix and the sparse matrix using the cost function. The method according to claim 1,
Further comprising an image synthesis unit for obtaining an image of a final HDR (High Dynamic Range) by taking an average of a background brightness map of the low rank matrix, which is a background image, using Equation (1) below.
[Equation 1]

Here, n is the number of input images, Ri is the estimated brightness value at the i pixel position, and a constant value varying from j = 1 to integer n. The method according to claim 1,
Wherein the image separator divides the rank function of the low rank matrix and the sparse matrix into a truncated nuclear norm

And

And the remainder variable matrix S is rewritten by applying Equation (2) to Equation (3), the low rank matrix, the rare matrix, the allowance And the variable matrix is optimized and separated.
&Quot; (2) &quot;

here,

Lambda is a factor controlling the relative importance between the Rank of the low rank matrix X and the scarcity of the sparse matrix E and the target rank r is 1 Setting,

Lt; / RTI &

The sampling operator at,

Represents the L1 norm of the sparse matrix.
&Quot; (3) &quot;

Where S is the allowance variable matrix,

Is the Frobenius norm of the matrix, and [delta] is the intensity of the noise occurring during the data acquisition. The method of claim 3,
The image separator may be expressed as Equation (4), and may be used to optimally separate the low rank matrix, the sparse matrix, and the allowable variable matrix, expressed as Equation (4) below, defined as augmented Lagrangian function of Equation The image processing apparatus characterized in.
&Quot; (4) &quot;

Where A is a Lagrangian multiplier matrix, μ is a disadvantage variable, and A, B> = tr (AB ^T ) represent matrix inner products of two matrices. 5. The method of claim 4,
The image separation unit may sequentially update the low rank matrix, the sparse matrix and the redundant variable matrix, and the Lagrangian multiplier of Equation (4) sequentially through optimization and rewrite them as shown in Equations (5) and Rank matrix that minimizes the cost function or converges within a certain range by using an Augmented Lagrange Multiplier (ALM) method, which is a method of finding a solution of a cost function using a Lagrangian cost function to which Lagrangian multiplier is applied, And calculates the sparse matrix and the extra variable matrix.
&Quot; (5) &quot;

Here, k represents an index corresponding to a repetition number of times.
&Quot; (6) &quot;

An object image matrix generation unit that receives a target image to be separated from a background and an object and generates a target image matrix that is a matrix according to image signal values of pixels of the target image; And
Sets a low rank matrix having a rank value smaller than a certain reference as the target image matrix and sets a constraint condition as a sum of the low rank matrix and a slack variable matrix, A constant first cost function can be minimized or a constant range can be minimized by using an augmented Lagrange Multiplier (ALM) method for obtaining a solution of a first cost function using a low rank matrix and a Lagrangian cost function applied with a Lagrangian multiplier for the extra variable matrix And an optimization algorithm unit for generating a TNMM (Augmented Lagrange Multiplier) algorithm for calculating the low rank matrix and the allowable variable matrix by causing the low rank matrix to converge within a predetermined range. The method according to claim 6,
The remaining TNMM-ALM algorithm is used to set the remainder excluding the low rank matrix component in the target image matrix to a sparse matrix, and a truncated Nuclear Norm computed value for the low rank matrix and a Rank matrix and the sparse matrix is applied to an Ll norm calculation value for the low-rank matrix and a low-rank matrix using the second cost function, And an image separator for calculating the sparse matrix and the freeness matrix. The method according to claim 6,
Wherein the optimization algorithm unit divides the low rank matrix and the extra variable matrix into a truncated nuclear norm

And the rank function is approximated and rewritten by the following equation (1): &quot; (1) &quot;
[Equation 1]

here,

Represents the truncated nuclear norm of the matrix X,

Lt; / RTI &

S is a sampling operator at the above-mentioned spare variable matrix,

Is the Frobenius norm of the matrix, and [delta] is the intensity of the noise occurring during the data acquisition. 9. The method of claim 8,
The optimization algorithm unit may be expressed as Equation (2), and may be used to optimally separate the low rank matrix and the redundant variable matrix, if Equation (1) is defined as a Augmented Lagrangian Function. Device.
&Quot; (2) &quot;

Where A is a Lagrangian multiplier matrix, μ is a disadvantage variable, and A, B> = tr (AB ^T ) represent matrix inner products of two matrices. 10. The method of claim 9,
The optimization algorithm unit predicts the Lagrangian multiplier matrix A by applying an Augmented Lagrange Multiplier (ALM) algorithm until convergence in Equation (2), minimizes the cost function for the predicted Λ, 3 and Equation (4), and calculates the low rank matrix and the extra variable matrix to minimize the cost function or to converge the cost function within a predetermined range.
&Quot; (3) &quot;

&Quot; (4) &quot;

8. The method of claim 7,
Wherein the image separator divides the rank function of the low rank matrix and the sparse matrix into a truncated nuclear norm

And

And the remainder variable matrix S is rewritten by applying Equation (5) to Equation (6), the low rank matrix and the rare matrix, the allowance And the variable matrix is optimized and separated.
&Quot; (5) &quot;

here,

Lambda is a factor controlling the relative importance between the Rank of the low rank matrix X and the scarcity of the sparse matrix E and the target rank r is 1 Setting,

Lt; / RTI &

The sampling operator at,

Represents the L1 norm of the sparse matrix.
&Quot; (6) &quot;

Where S is the allowance variable matrix,

Is the Frobenius norm of the matrix, and [delta] is the intensity of the noise occurring during the data acquisition.

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