CN110097503B - Super-resolution method based on neighborhood regression - Google Patents
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Abstract
In order to improve the quality of the reconstructed image in the single image super-resolution method, a super-resolution reconstruction method utilizing mutual inconsistency of training dictionaries and local regularization anchoring neighborhood regression is provided. In the training stage, dictionary atoms and mutual consistency among atoms are introduced into the dictionary training process, so that the obtained training atomic dictionaries are independent as far as possible, and the mutual inconsistency in the larger training dictionary is obtained. Then, the local constraint regression method is added to the ridge regression process, and each atom in the dictionary is allocated with degrees of freedom to more flexibly calculate the projection matrix. Experiments show that under the condition of almost the computational complexity, the performance of the method is better than that of the ANR method with the optimal performance at present, and the quality of the reconstructed image can be further improved.
Description
Technical Field
The invention provides a single image-based image super-resolution method in the technical field of digital image processing, by using the method, a high-resolution image can be obtained for an input low-resolution image by means of a dictionary obtained in a training stage. The method can be widely applied to the fields of video monitoring, satellite remote sensing, medical images, biological feature recognition and the like.
Background
Classical image super-resolution methods can be divided into the following categories: 1. interpolation-based methods, 2. Reconstruction-based methods, and 3. Learning-based methods. In the first method, the magnitude of an unknown pixel value is estimated and predicted using known pixel values around the unknown pixel value, which is known as a method of interpolation. In the second method, a large number of training images are utilized, and filtering and downsampling processing are performed on the high-resolution original image in a training stage to obtain a corresponding low-resolution image. Then, the high resolution image and the low resolution image of the training stage are segmented to obtain high resolution image blocks and low resolution image blocks, and each pair of the high resolution image blocks and the low resolution image blocks is stored. For the image block to be super-resolution amplified, firstly, the image block is segmented to obtain a low-resolution image block, and then, several image blocks closest to the low-resolution image block are found in the low-resolution image block obtained in the training process. The weighted average of the high resolution blocks obtained in the training phase and corresponding to these low resolution blocks is then used to obtain the amplified high resolution blocks. After these operations are performed on each low resolution image block on the image to be enlarged, many high resolution image blocks can be obtained. A high resolution image can be obtained using an averaging method on the overlapping areas of these high resolution image blocks. This approach is referred to as a sample-based approach. In a third class of methods, the high resolution image of the training phase is utilized, and the corresponding low resolution image is obtained by filtering and downsampling processes. Then, a sparse dictionary representing the low-resolution image block and a sparse dictionary representing the high-resolution image block are obtained by using a sparse representation method. For the image blocks extracted from the on-line image amplification stage and the low resolution image, the coefficients of the sparse representation of the image blocks are obtained by using a trained low resolution dictionary. Then, according to the assumption that the high resolution image block and the low resolution image block are on the same flow pattern, the high resolution image block is obtained by multiplying the high resolution dictionary by the sparsely represented coefficients. After all the image blocks in the low-resolution image are processed, a high-resolution image can be reconstructed through the obtained high-resolution image blocks. Such methods are known as sparse representation methods. In a fourth class of methods, a convolutional neural network is first trained by training high resolution image blocks and corresponding low resolution image blocks in a set of images. After training the network, high resolution tiles can be obtained with the network for tiles to be enlarged. After this operation is performed on all low resolution image blocks in the low resolution image, all corresponding high resolution image blocks can be obtained. Then, a high resolution image can be obtained by using the method of image block overlap region averaging. Such methods are referred to as deep learning based methods.
Disclosure of Invention
The proposed method differs from the conventional super resolution method in the following two points: 1. the low-resolution dictionary is trained by utilizing mutual inconsistency, local regularization terms are added into an objective function, so that different atoms in the dictionary have degrees of freedom, the correlation among dictionary atoms is smaller, the distribution is wider, and the dictionary is more accurate in representing low-resolution image block vectors. 2. In the process of solving the projection matrix by the method, locality prior information is introduced, so that a more optimized projection matrix can be obtained. The detail part of the obtained high-resolution image block is richer and more accurate.
1. Proposed method for solving low resolution dictionary
In the training stage of the proposed method, a method for solving the following problem is adopted to solve a dictionary with low resolution, so that the representation capability is stronger.
Wherein Y is a matrix of low resolution image feature blocks, each of which constitutes a column of the matrix: y= [ Y ] 1 ，...，y N ]∈R S×N S is the dimension of the low resolution image feature block, N is the number of all low resolution training image blocks, i.e. the number of training samples, A is the matrix formed by the sparse coefficients: a= [ a ] 1 ，...，a N ]∈R M×N ，D l A low resolution dictionary representing training: d (D) l ＝[d 1 ，...，d M ]∈R S×M M represents the number of columns of the low resolution dictionary, I.I F Frobenius norms, d representing a matrix i Representation dictionary D l The atoms of the ith column of the formula (I),the term is the constraint term introduced by the invention to reduce the mutual consistency among dictionary atoms and increase the range of dictionary atom distribution, and lambda is required to be set for better performance of representing image feature blocks of a training dictionary 1 Lambda is lambda 1 Parameters > 0, objective function of previous methodsThe number is not this, s.t. indicates the subject to in mathematics, i.e. indicates the constraint that must be met later, +.>The symbols represent any given meaning in mathematics, i.e. for any m, d m The binary norm of the letter atom is 1, and for any n, the nth column a of matrix A n 0 norm of (2) satisfies less than K 1 Conditions of (a), i.e. a n The number of non-zero elements in the matrix is less than K 1 Condition of (d), parameter K 1 For controlling the degree of sparseness.
To solve the problem (1), a low resolution dictionary D may be fixed l Taking A as a variable, this objective function is minimized. At this time, the liquid crystal display device,and->Fixing, only need to optimize->Due to D l Fixed, this problem translates into solving a sparse coefficient problem, which can be solved using an optimal matching method (optimal matching pursuit, OMP). Then, the sparse coefficient matrix A is fixed to D l To minimize this objective function, a gradient descent method may be used to solve this problem. One variable is then fixed and the other variable is optimized to solve this problem until the solution converges or the solution reaches a predetermined accuracy. At this time, the optimized solved low resolution dictionary D can be output l And a corresponding sparse matrix a.
Training the image training set to obtain a low-resolution dictionary, and then obtaining a high-resolution dictionary by using a pseudo-inversion method, namely
D h ＝Q h A T (AA T ) -1 (2)
Wherein Q is h Representing high resolution imagesThe constructed matrix of feature blocks, i.e. the ith high resolution feature image block, forms the ith column therein.
2. Proposed method for solving projection matrix
In the previous method, atoms of a low-resolution dictionary are taken as anchor points, and nearest neighbors of the anchor points are all obtained in the same way, so that the method is not only inflexible, but also can not obtain a projection matrix according to an input low-resolution image in a self-adaptive manner. Many studies have shown that: locality is a very important feature in exploring nonlinear data structures, locality being more important than sparsity, since locality necessarily leads to sparsity, and vice versa. For this purpose, in the proposed method, local regularization terms are added to the objective function to find the projection matrix. The problem to be solved in the proposed method is
Wherein y is F Representing vectors formed after vectorization by low resolution image feature blocks, lambda 2 Is a parameter that balances the reconstruction error with the local solution of vector a,the local regularization term provided by the invention, G is a matrix for measuring the distance between an anchor point e and dictionary atoms, which provides different degrees of freedom for each atom in the dictionary, and the definition of the diagonal matrix G is as follows:
wherein the element of G is obtained by the following formula (5)
g i ＝(1/|e T ⊙c i |) b ，i＝1，2，...，k (5)
Wherein c i Is the ith atom closest to anchor e in the low resolution dictionary, k is the nearest neighbor number, +.The point multiplication of two vectors, the anchor point takes k nearest atoms in the low resolution dictionary to form the neighborhood matrix N l The parameter b is used to adjust the decay rate. Here, introducing localized prior information may allow for a more accurate representation of the image block. It may obtain relatively optimized reconstruction weights. I.e. large reconstruction weights will be assigned to training image blocks that are similar to the input image block, while small reconstruction weights will be assigned to training image blocks that are slightly less similar to the input image block.
Solving the problem (3) can be achieved:
thus, the projection matrix can be solved offline by the following equation (7):
wherein, the anchor point e takes K atoms nearest to the anchor point e in the low-resolution dictionary, and the position of the anchor point e is l k K is equal to or greater than 1 and K is equal to or greater than 1, and all the atoms are at the corresponding position l of the high-resolution dictionary k The column vectors at which may form a matrix N h 。
Here, the k nearest neighbors thereof are found in the low resolution dictionary according to the correlation between atoms, and the larger the correlation coefficient, the closer the representing distance. After the neighborhoods of all the anchors are obtained, the projection matrix of all the anchors can be calculated offline according to the formula (7). Since it is generally assumed that the high resolution image block and the low resolution image block are on the same manifold, sharing the same sparse coefficient, the high resolution image feature block vector can be solved by the following equation (8).
x＝P G y F (8)
Then, a high-resolution feature block is obtained by the high-resolution feature block vector, a low-resolution image block is subjected to bicubic interpolation to obtain a high-resolution low-frequency block, the high-resolution low-frequency block and the high-resolution feature block are added to obtain a high-resolution image block, and the high-resolution image block is subjected to all high valuesThe resolution image blocks are spliced together according to the position information of the resolution image blocks, and the average value is taken from the overlapping place, so that the output high resolution image X can be obtained 0 。
Finally, for high resolution image X 0 Iterative back projection is continuously modified until a predetermined number of iterations is reached or a satisfactory high resolution image is obtained.
In summary, the invention includes an off-line training stage and an on-line single image magnification stage, innovating in solving the dictionary with low resolution in the training stage and solving the projection matrix in the training and magnification stage, so as to magnify an image with high resolution from a low resolution image to a high resolution image with more abundant detail information.
3. Training phase of the invention
The process of the training phase of the present invention may be described as follows.
Input a: a large number of high resolution images, magnification s of the images f ×s f 。
Output a: transformation matrix T in principal component analysis l Dictionary D of low resolution l Dictionary atom d i For dictionary D l And the dictionary atom d i Corresponding projection matrix P G (d i ) High resolution dictionary D h 。
Step A1) filtering and downsampling all the input high resolution images, the downsampling factor being s f ×s f And obtaining all corresponding low-resolution images. Blocking all low resolution images and corresponding high resolution images to obtain a set { (p) containing low resolution image blocks and high resolution image block pairs l (i)，p h (i) 1.ltoreq.i.ltoreq.N }, where p l (i) For the ith low resolution block, p h (i) For the ith high resolution image block, the total number of blocks is N. The following four templates M are adopted 1 ＝[-1，0，1]，M 2 ＝[-1，0，1] T ，M 3 ＝[1，0，-2，0，1]，M 4 ＝[1，0，-2，0，1] T For all low in turnResolution image block p l (i) Performing convolution operation to obtain a low-resolution image block p l (i) High frequency information of (a) extended image block p l (i) Adding these high frequency information to the picture block p l (i) In the extended rows, an initial low resolution feature block is obtained. Then, the dimension of all the initial low-resolution feature blocks is reduced by a principal component analysis method to obtain a transformation matrix T l And a low resolution image feature block p lf (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite Output transformation matrix T l . For low resolution image block p l (i) And performing bicubic interpolation amplification processing to obtain a low-frequency high-resolution image block. Block p of high resolution pictures h (i) And the high-resolution image block with low frequency is subtracted to obtain a high-resolution image feature block p containing high-frequency feature information lh (i)。
Step A2) solving the problem (1) described above to obtain a low resolution dictionary D l And a corresponding sparse matrix a.
Wherein Y is defined by a low resolution image feature block p lf (i) Matrix of each low resolution image feature block p lf (i) One column constituting the matrix: y= [ Y ] 1 ，...，y N ]∈R S×N Here y i Is composed of p lf (i) The vectors being formed by stacking of rows of (i) in the feature block p lf (i) The element of the mth row and the nth column in the table is a vector y i (m.times.N) l +n) elements, where N l Is a feature block p lf (i) S is the number of elements in each row of the low resolution image feature block p lf (i) N is the number of all low resolution training image blocks, i.e. the number of training samples, a is the matrix of sparse coefficients: a= [ a ] 1 ，...，a N ]∈R M×N ，D l A low resolution dictionary representing training: d (D) l ＝[d 1 ，...，d M ]∈R S×M M represents the number of columns of the low resolution dictionary,||·|| F frobenius norms, d representing a matrix i Representation dictionary D l The atoms of the ith column of the formula (I),the term is the constraint term introduced by the invention to reduce the mutual consistency among dictionary atoms and increase the range of dictionary atom distribution, and lambda is required to be set for better performance of representing image feature blocks of a training dictionary 1 Lambda is lambda 1 The parameter > 0, which was not present in the objective function of the previous method, s.t. represents the mathematical subject to, i.e. the constraint that must be satisfied later, +.>The symbols represent any given meaning in mathematics, i.e. for any m, d m The binary norm of the letter atom is 1, and for any n, the nth column a of matrix A n 0 norm of (2) satisfies less than K 1 Conditions of (a), i.e. a n The number of non-zero elements in the matrix is less than K 1 Condition of (d), parameter K 1 For controlling the degree of sparseness.
To solve the problem (1), an initial D l Consisting of M columns in a randomly selected matrix Y, a low resolution dictionary D is first fixed l Taking A as a variable, this objective function is minimized. At this time, the liquid crystal display device,and->Fixing, only need to optimize->Due to D l Fixed, this problem translates to solving a sparse coefficient problem, which is solved by an optimal matching method (optimal matching pursuit, OMP). Then, the sparse coefficient matrix A is fixed to D l For variables, this objective function is minimized and the gradient descent method is used to solve this problem. Then, continuouslyOne variable is fixed and the other variable is optimized to solve the problem until the solution reaches a predetermined accuracy or number of iterations. At this time, the optimized solved low resolution dictionary D can be output l And a corresponding sparse matrix a.
After obtaining the low resolution dictionary, the high resolution dictionary is obtained by pseudo-inversion method, i.e
D h ＝Q h A T (AA T ) -1 (2)
Wherein Q is h ＝[q 1 ，q 2 ，...，q N ]Representing the image characteristic block p formed by all high resolution images lh (i) Wherein p is vectorized lh (i) As a matrix Q h I.e. in feature block p hf (i) The element of the mth row and the nth column in the table is a vector q i (m.times.N) h + n) elements. Outputting a high resolution dictionary D h 。
Step A3) for the ith column in the low resolution dictionary, i.e., the ith atom d i Solving the following problem (9)
Wherein d i Representing the ith dictionary atom, lambda 2 Is a parameter that balances the reconstruction error with the local solution of vector a,is a local regularization term proposed by the present invention, G is a measure d i And a matrix of distances between dictionary atoms, which gives each atom in the dictionary a different degree of freedom, the definition of the diagonal matrix G is as follows:
wherein element G of G i The following formula (5) is used to obtain
g i ＝(1/|e T ⊙c i |) b ，i＝1，2，...，k (5)
Wherein e=d i ，c i Is the i-th distance d in the low resolution dictionary i The nearest atom, k is nearest neighbor number, "-symbol represents the dot product of two vectors, and k nearest atoms from e are taken in the low resolution dictionary to form its neighborhood matrix N l The parameter b is used to adjust the decay rate. Here, introducing localized prior information may allow for a more accurate representation of the image block. It may obtain relatively optimized reconstruction weights. I.e. large reconstruction weights will be assigned to training image blocks that are similar to the input image block, while small reconstruction weights will be assigned to training image blocks that are slightly less similar to the input image block.
Solving the problem (9) can be achieved:
thus, the projection matrix can be solved offline by the following equation (11):
wherein for d i Taking K nearest atoms in the low resolution dictionary, the position of which is l k K is equal to or greater than 1 and K is equal to or greater than 1, and all the atoms are at the corresponding position l of the high-resolution dictionary k The column vectors at which may form a matrix N h 。
After the projection matrix is obtained in this step for all columns in the low resolution dictionary. These projection matrices are output and the off-line training phase is completed.
4. The online treatment stage of the invention
The process of online image magnification of the present invention can be described as follows.
Input B: a low resolution image L, a transformation matrix T of principal component analysis l Low resolution obtained in training phaseDictionary D of (2) l High resolution dictionary D h And each column d of the low resolution dictionary i Corresponding projection matrix P G (d i )。
Output B: amplified s f ×s f A double high resolution image.
Step B1) the input low-resolution image is segmented to obtain an image block pb l (i) The following four templates M are adopted 1 ＝[-1，0，1]，M 2 ＝[-1，0，1] T ，M 3 ＝[1，0，-2，0，1]，M 4 ＝[1，0，-2，0，1] T Sequentially for all low resolution image blocks pb l (i) Performing convolution operation to obtain a low-resolution image block pb l (i) High frequency information of (b) extended pb l (i) Adding this information to the low resolution image block pb l (i) In the following row, an initial low resolution feature block is obtained. Then, the feature blocks pfb of the low-resolution image are obtained by performing the feature reduction of all the initial low-resolution feature blocks by the same principal component analysis method as in the training phase A1 lf (i) Vectorization pfb lf (i) The low-resolution image characteristic block vector pb can be obtained lf (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite For low resolution image block pb l (i) Performing bicubic interpolation amplification processing to obtain an image block pbf l (i) Vectorized pbf l (i) The low-frequency high-resolution image block vector pblf can be obtained l (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite In the above process of vectorizing a certain block bl to a certain vector bv, the element in the mth row and the nth column in the block bl is the (mxn) th element of the vector bv l +n) elements, N l The number of elements for each row of the block bl.
Step B2) i=1,
step B3) for low resolution image feature block vector pb lf (i) Finding distances pb in all columns in the low resolution dictionary based on vector correlation lf (i) The nearest columnI.e. distance pb lf (i) Nearest dictionary atom->And note the location of the dictionary atom in the low resolution dictionary. Accordingly, find the dictionary atom which has been found offline +.>Projection matrix of->Thereby calculating a high resolution image feature block vector x using the following formula (12) F (i)。
Handle x F (i) And pblf l (i) Adding to obtain a high resolution image block vector BHV (i), i.e
BHV(i)＝x F (i)+pblf l (i) (13)
Obtaining a high resolution image block BH (i) from the high resolution image block vector BHV (i), i.e., the element of the mth row and the nth column in the block BH (i) is the (mxn) th element of the vector BHV (i) h +n) elements, N h The number of elements for each row of block BH (i).
Step B4) let i=i+1, for the next low resolution image feature block vector pb lf (i) The process of step B3 is performed to find its high resolution image block BH (i) until all low resolution feature block vectors extracted from the low resolution image have been subjected to the process of step B3 above.
Step B5) stitching all the high-resolution image blocks according to the position information, and averaging the overlapped areas of the high-resolution image blocks to obtain the values of the high-resolution pixels so as to obtain an initial high-resolution image X 0 。
Step B6) iterative correction of the high resolution image using the following equation (14)
X t+1 ＝X t +((L-DHX t )↑(s f ×s f ))*p (14)
Wherein L represents an input low resolution image, H represents a filtering operation on a high resolution image, D is a downsampling matrix, X t Representing the high resolution image obtained after t iterations, +.f(s) f ×s f ) Representing upsampling of an image s f ×s f The multiple, p, represents the coefficient matrix in the gaussian filter and the symbol "×" represents the convolution operation. In the invention, the result X after I times of iteration is obtained l As a final output high resolution image.
Drawings
1. Fig. 1 is a flow chart of the offline training phase of the proposed method.
2. FIG. 2 is a flow chart of the on-line amplification stage of the proposed method, where N p For the number of all image blocks extracted from an image.
3. Fig. 3 is a graph of the effect of the four methods of Zeyde, ANR, jiang, and proposed by the present invention on super-resolution reconstruction of leave images.
4. Fig. 4 is an effect diagram of four methods of Zeyde, ANR, jiang, and proposed by the present invention on super-resolution reconstruction of a camera image.
5. Fig. 5 is a graph showing the effect of four methods of Zeyde, ANR, jiang, and proposed methods on super-resolution reconstruction of parrots images.
Detailed Description
Specific embodiments of the present invention will be described below with reference to the accompanying drawings. As shown in fig. 1, the offline training phase of the proposed method comprises the following steps.
Input a: a large number of high resolution images, magnification s of the images f ×s f 。
Output a: transformation matrix T of principal component analysis method l Dictionary D of low resolution l Dictionary atom d i For dictionary D l And the dictionary atom d i Corresponding projection momentArray P G (d i ) High resolution dictionary D h 。
Step A1) filtering and downsampling all the input high resolution images, the downsampling factor being s f ×s f And obtaining all corresponding low-resolution images. Blocking all low resolution images and corresponding high resolution images to obtain a set { (p) containing low resolution image blocks and high resolution image block pairs l (i)，p h (i) 1.ltoreq.i.ltoreq.N }, where p l (i) For the ith low resolution block, p h (i) For the ith high resolution image block, the total number of blocks is N. The following four templates M are adopted 1 ＝[-1，0，1]，M 2 ＝[-1，0，1] T ，M 3 ＝[1，0，-2，0，1]，M 4 ＝[1，0，-2，0，1] T For all low resolution image blocks p in sequence l (i) Performing convolution operation to obtain a low-resolution image block p l (i) High frequency information of (a) extended image block p l (i) Adding these high frequency information to the picture block p l (i) In the extended rows, an initial low resolution feature block is obtained. Then, the dimension of all the initial low-resolution feature blocks is reduced by a principal component analysis method to obtain a low-resolution image feature block p lf (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite For low resolution image block p l (i) And performing bicubic interpolation amplification processing to obtain a low-frequency high-resolution image block. Block p of picture h (i) And the high-resolution image block with low frequency is subtracted to obtain a high-resolution image feature block p containing high-frequency feature information lh (i)。
Step A2) solving the following problem (1) to obtain a low-resolution dictionary D l And a corresponding sparse matrix a.
Wherein Y is defined by a low resolution image feature block p lf (i) Matrix of each low resolution image feature block p lf (i) One column constituting the matrix: y= [ Y ] 1 ，...，y N ]∈R S×N Here y i Is composed of p lf (i) The vectors being formed by stacking of rows of (i) in the feature block p lf (i) The element of the mth row and the nth column in the table is a vector y i (m.times.N) l +n) elements, where N l Is a feature block p lf (i) S is the number of elements in each row of the low resolution image feature block p lf (i) N is the number of all low resolution training image blocks, i.e. the number of training samples, a is the matrix of sparse coefficients: a= [ a ] 1 ，...，a N ]∈R M×N ，D l A low resolution dictionary representing training: d (D) l ＝[d 1 ，...，d M ]∈R S×M M represents the number of columns of the low resolution dictionary, I.I F Frobenius norms, d representing a matrix i Representation dictionary D l The atoms of the ith column of the formula (I),the term is the constraint term introduced by the invention to reduce the mutual consistency among dictionary atoms and increase the range of dictionary atom distribution, and lambda is required to be set for better performance of representing image feature blocks of a training dictionary 1 Lambda is lambda 1 The parameter > 0, which was not present in the objective function of the previous method, s.t. represents the mathematical subject to, i.e. the constraint that must be satisfied later, +.>The symbols represent any given meaning in mathematics, i.e. for any m, d m The binary norm of the letter atom is 1, and for any n, the nth column a of matrix A n 0 norm of (2) satisfies less than K 1 Conditions of (a), i.e. a n The number of non-zero elements in the matrix is less than K 1 Condition of (d), parameter K 1 For controlling the degree of sparseness.
Initial D l Consisting of M columns in a randomly selected matrix Y, a low resolution dictionary D is first fixed l Taking A as a variable, this objective function is minimized. At this time, an optimal matching method is adopted(optimal matching pursuit, OMP) to solve for a sparse matrix a. Then, the sparse coefficient matrix A is fixed to D l For variables, this objective function is minimized and the gradient descent method is used to solve this problem. One variable is then fixed and the other variable is optimized to solve the problem until the solution reaches a predetermined number of iterations of 20. At this time, the optimized solved low resolution dictionary D can be output l And a corresponding sparse matrix a.
After obtaining the low resolution dictionary, the high resolution dictionary is obtained by pseudo-inversion method, i.e
D h ＝Q h A T (AA T ) -1 (2)
Wherein Q is h ＝[q 1 ，q 2 ，...，q N ]Representing the image characteristic block p formed by all high resolution images lh (i) Wherein p is vectorized lh (i) As a matrix Q h I.e. in feature block p hf (i) The element of the mth row and the nth column in the table is a vector q i (m.times.N) h + n) elements.
Step A3) for the ith column in the low resolution dictionary, i.e., the ith atom d i Solving the following problem (9)
Wherein d i Representing the ith dictionary atom, lambda 2 Is a parameter that balances the reconstruction error with the local solution of vector a,is a local regularization term proposed by the present invention, G is a measure d i And a matrix of distances between dictionary atoms, which gives each atom in the dictionary a different degree of freedom, the definition of the diagonal matrix G is as follows:
wherein element G of G i The following formula (5) is used to obtain
g i ＝(1/|e T ⊙c i |) b ，i＝1，2，...，k (5)
Wherein e=d i ，c i Is the i-th distance d in the low resolution dictionary i The nearest atom, k is nearest neighbor number, "-symbol represents the dot product of two vectors, and k nearest atoms from e are taken in the low resolution dictionary to form its neighborhood matrix N l The parameter b is used to adjust the decay rate.
The solution of problem (9) is:
thus, the projection matrix can be solved offline by the following equation (11):
wherein for d i Taking K nearest atoms in the low resolution dictionary, the position of which is l k K is equal to or greater than 1 and K is equal to or greater than 1, and all the atoms are at the corresponding position l of the high-resolution dictionary k The column vectors at which may form a matrix N h 。
After the projection matrix is obtained in this step for all columns in the low resolution dictionary. These projection matrices are output and the off-line training phase is completed.
The process of the on-line image magnification of the present invention is shown in fig. 2 and can be described as follows.
Input B: the system comprises a low-resolution image, a low-resolution dictionary obtained in a training stage, a high-resolution dictionary and a projection matrix corresponding to each column of the low-resolution dictionary.
Output B: amplified s f ×s f A double high resolution image.
Step B1) the input low-resolution image is segmented to obtain an image block pb l (i) The following four templates M are adopted 1 ＝[-1，0，1]，M 2 ＝[-1，0，1] T ，M 3 ＝[1，0，-2，0，1]，M 4 ＝[1，0，-2，0，1] T Sequentially for all low resolution image blocks pb l (i) Performing convolution operation to obtain a low-resolution image block pb l (i) High frequency information of (b) extended pb l (i) Adding this information to the low resolution image block pb l (i) In the following row, an initial low resolution feature block is obtained. Then, the feature blocks pfb of the low-resolution image are obtained by performing the feature reduction of all the initial low-resolution feature blocks by the same principal component analysis method as in the training phase A1 lf (i) Vectorization pfb lf (i) The low-resolution image characteristic block vector pb can be obtained lf (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite For low resolution image block pb l (i) Performing bicubic interpolation amplification processing to obtain an image block pbf l (i) Vectorized pbf l (i) The low-frequency high-resolution image block vector pblf can be obtained l (i) A. The invention relates to a method for producing a fibre-reinforced plastic composite In the above process of vectorizing a certain block bl to a certain vector bv, the element in the mth row and the nth column in the block bl is the (mxn) th element of the vector bv l +n) elements, N l The number of elements for each row of the block bl.
Step B2) i=1,
step B3) for low resolution image feature block vector pb lf (i) Finding distances pb in all columns in the low resolution dictionary based on vector correlation lf (i) The nearest columnI.e. distance pb lf (i) Nearest dictionary atom->And note the location of the dictionary atom in the low resolution dictionary. Accordingly, find the dictionary atom which has been found offline +.>Projection matrix of->Thereby calculating a high resolution image feature block vector x using the following formula (12) F (i)。
Handle x F (i) And pblf l (i) Adding to obtain a high resolution image block vector BHV (i), i.e
BHV(i)＝x F (i)+pblf l (i) (13)
Obtaining a high resolution image block BH (i) from the high resolution image block vector BHV (i), i.e., the element of the mth row and the nth column in the block BH (i) is the (mxn) th element of the vector BHV (i) h +n) elements, N h The number of elements for each row of block BH (i).
Step B4) let i=i+1, for the next low resolution image feature block vector pb lf (i) The process of step B3 is performed to find its high resolution image block BH (i) until all low resolution feature block vectors extracted from the low resolution image have been subjected to the process of step B3 above.
Step B5) stitching all the high-resolution image blocks according to the position information, and averaging the overlapped areas of the high-resolution image blocks to obtain the values of the high-resolution pixels so as to obtain an initial high-resolution image X 0 。
Step B6) iterative correction of the high resolution image using the following equation (14)
X t+1 ＝X t +((L-DHX t )↑(s f ×s f ))*p (14)
Wherein L represents an input low resolution image, H represents a filtering operation on a high resolution image, D is a downsampling matrix, X t Representing the high resolution image obtained after t iterations, +.f(s) f ×s f ) Representing upsampling of an image s f ×s f The multiple, p, represents the coefficient matrix in the gaussian filter and the symbol "×" represents the convolution operation. In the invention, the result X after I times of iteration is obtained l As a final output high resolution image.
The procedure of the proposed method is implemented on version 2016b of MATLAB software. In the experiment, 91 color images were used as training set. To verify the effectiveness of the proposed method, 10 images were used for testing and compared to the Zeyde method, ANR method, and Jiang method.
Through a large number of experiments, the parameters in the invention are optimally set, and the setting results are as follows: wherein the number of columns m=1024 of the low resolution and high resolution dictionaries, the size of the image block of the low resolution is set to 5×5, the overlapping area size of the adjacent low resolution image blocks of the same row is 5×3, the dimension of the low resolution feature block in steps A1 and B1 is 25×5, the low resolution image feature block p after the dimension reduction by the principal component analysis method lf (i) Is 3 x 5, sparsity constraint parameter K in problem 1 1 Set to K 1 =m/16, parameter λ in problem (1) 1 Set to lambda 1 =0.1, the number of iterations in solving problem 1 is set to 20, i.e. i=20, solving g i The parameter b in (2) is set to b=11, the parameter λ in (9) 2 Set to lambda 2 ＝1×10 -5 The size of the coefficient matrix p in the gaussian filter in the formula (14) is set to 9×9.
Table 1 results of experiments with 2 x magnification of images
TABLE 2 results of experiments with 3 x magnification of images
TABLE 3 results of experiments with 4-fold image magnification
Tables 1, 2, and 3 are experimental results of peak signal to noise ratio (PSNR) (in dB) at 2, 3, and 4 times image magnification, respectively. The experimental results of table 1 show that: the average PSNR index of the high-resolution image reconstructed by the method is improved by 0.31dB compared with that of the Zeyde method; the average PSNR index was increased by 0.25dB compared to the ANR method and 0.09dB compared to the Jiang method. Table 2 experimental results show that: the average PSNR index of the high-resolution image reconstructed by the method is improved by 0.1dB compared with that of the Zeyde method; the average PSNR index is increased by 0.1dB compared with the ANR method, and the average PSNR index is increased by 0.08dB compared with the Jiang method. The experimental results of table 3 show that: the average PSNR index of the high-resolution image reconstructed by the method is improved by 0.08dB compared with that of the Zeyde method; the average PSNR index was increased by 0.09dB compared to the ANR method and by 0.09dB compared to the Jiang method. This demonstrates that the proposed method reconstruction is superior to the existing effective Zeyde method, ANR method, and Jiang method.
Fig. 3, 4, and 5 show visual effect diagrams of the Zeyde method, ANR method, jiang method, and proposed method of the present invention in tables 1, 2, and 3, respectively. As can be seen from the effect diagrams of fig. 3, fig. 4 and fig. 5, the edge portion of the reconstructed image is blurred by the Zeyde method, the local texture details of the reconstructed image by the ANR method are not clear enough, and compared with the Jiang method, the method provided by the invention can reconstruct richer image details, and the visual effect of the image is better.
Claims (2)
1. The super-resolution image method is characterized by comprising the following training stage and a stage of on-line amplification of a low-resolution image;
the process of the training phase may be described as follows:
input a: a large number of high resolution images, magnification s of the images f ×s f ，
Output a: transformation matrix T in principal component analysis l Dictionary D of low resolution l Dictionary atom d i1 For dictionary D l And the dictionary atom d i1 Corresponding projection matrix P G (d i1 ) High resolution dictionary D h ，
Step A1) filtering and downsampling all the input high resolution images, the downsampling factor being s f ×s f Obtaining all corresponding low resolution images, partitioning all low resolution images and corresponding high resolution images to obtain a set { (p) comprising low resolution image blocks and high resolution image block pairs l (i2),p h (i2) 1.ltoreq.i2.ltoreq.N }, where p l (i2) For the i2 th low resolution block, p h (i2) For the i2 th high-resolution image block, the numbers of the low-resolution image block and the high-resolution image block are respectively N, and the following four templates M are adopted 1 ＝[-1,0,1]，M 2 ＝[-1,0,1] T ，M 3 ＝[1,0,-2,0,1]，M 4 ＝[1,0,-2,0,1] T For all low resolution image blocks p in sequence l (i2) Performing convolution operation to obtain a low-resolution image block p l (i2) High frequency information of (a) extended image block p l (i2) Adding these high frequency information to the picture block p l (i2) In the extended row, an initial low-resolution feature block is obtained, and then the dimension of all the initial low-resolution feature blocks is reduced by a principal component analysis method to obtain a transformation matrix T l And a low resolution image feature block p lf (i2) For low resolution image block p l (i2) Performing bicubic interpolation amplification processing to obtain a low-frequency high-resolution image block, and processing the high-resolution image block p h (i2) And the high-resolution image block with low frequency is subtracted to obtain a high-resolution image feature block p containing high-frequency feature information lh (i2)；
Step A2) solving the following problem (1) to obtain a low resolution dictionary D l And a corresponding sparse matrix a, and,
wherein Y is defined by a low resolution image feature block p lf (i2) Matrix of each low resolution image feature block p lf (i2) One column constituting the matrix: y= [ Y ] 1 ,...,y N ]∈R S×N Here y i2 Is composed of p lf (i2) The vectors being formed by stacking of rows of (i) in the feature block p lf (i2) The element of the mth row and the nth column in the table is a vector y i (m.times.N) l +n) elements, where N l Is a feature block p lf (i2) S is the number of elements in each row of the low resolution image feature block p lf (i2) A is a matrix of sparse coefficients: a= [ a ] 1 ,...,a N ]∈R M×N ，D l A low resolution dictionary representing training: d (D) l ＝[d 1 ,...,d M ]∈R S×M M represents the number of columns of the low resolution dictionary, I.I F Frobenius norms, d representing a matrix j Representation dictionary D l The atoms of the j-th column of the group,the term is introduced constraint term to increase the range of dictionary atom distribution, set lambda 1 Lambda is lambda 1 Parameters > 0, s.t. represent subject to in mathematics, i.e. represent constraint that must be satisfied later,/A>The symbols represent any given meaning in mathematics, where this means that for any given m, d m The binary norm of the dictionary atom is 1, for any n, the nth column a of matrix A n 0 norm of (2) satisfies less than K 1 Conditions of (a), i.e. a n The number of non-zero elements in the matrix is less than K 1 Condition of (d), parameter K 1 Is used for controlling the degree of sparseness,
then, initial D l Is composed of M columns in a matrix Y selected randomly, followed by fixing the dictionary D of low resolution l Taking A as a variable, minimizing an objective function in (1), solving a sparse matrix A by adopting an optimal matching method, and then fixing the sparse coefficient matrix A to D l Minimizing this objective function for variables, solving for updated D using gradient descent l Then, solving the problem (1) by continuously fixing one variable and optimizing the other variable until the solution reaches a predetermined number of iterations I, at which time the optimized solved low resolution dictionary D can be output l And a corresponding sparse matrix a, and,
obtaining a low resolution dictionary D l Then, a pseudo-inversion method is used to obtain a high-resolution dictionary, namely
D h ＝Q h A T (AA T ) -1 (2)
Wherein Q is h ＝[q 1 ,q 2 ,...,q N ]Representing the image characteristic block p formed by all high resolution images lh (i2) Wherein p is vectorized lh (i2) As a matrix Q h Column i2 q i2 I.e. at feature block p hf (i2) The element of the mth row and the nth column in the table is a vector q i2 (m.times.N) h +n) elements, N h Is p lh (i2) The number of elements in each row in the image block;
step A3) for column i2, i.e., atom d of i2, in the low resolution dictionary i2 Solving the following problem (9)
Wherein d i2 Representing the i2 nd dictionary atom, lambda 2 Is a parameter that balances the reconstruction error with the local solution of vector a,is the proposed local regularization term, G is the measure d i2 And a matrix of distances between dictionary atoms, which gives each atom in the dictionary a different degree of freedom, the definition of the diagonal matrix G is as follows:
wherein the element G in the matrix G i3 Obtained by the following method
Wherein e=d i2 ，c i3 The i3 rd atom closest to e in the low-resolution dictionary, the "+" symbol represents the dot product of two vectors, |z| represents the absolute value of z, and K atoms closest to e are taken from the low-resolution dictionary to form the neighborhood matrix N l The parameter b is used to adjust the decay rate,
solving the problem (9) can be achieved:
thus, the projection matrix can be solved offline by the following equation (11):
wherein for d i2 Taking K nearest atoms in the low resolution dictionary, the position of which is l k K is equal to or greater than 1 and K is equal to or greater than 1, and all the atoms are at the corresponding position l of the high-resolution dictionary k The column vectors at which may form a matrix N h ，
After the projection matrix is obtained according to the step for all columns in the low-resolution dictionary, outputting and storing the obtained transformation matrix, projection matrix, low-resolution dictionary and high-resolution dictionary, thereby completing the offline training stage;
the processing procedure of on-line image magnification is as follows:
input B: transformation of a low resolution image L, principal component analysisMatrix T l Low-resolution dictionary D obtained in training phase l High resolution dictionary D h And each column d of the low resolution dictionary i1 Corresponding projection matrix P G (d i1 ) Output B: amplified s f ×s f A multiple of the high resolution image is provided,
step B1) the input low-resolution image is segmented to obtain an image block pb l (i4) The following four templates M are adopted 1 ＝[-1,0,1]，M 2 ＝[-1,0,1] T ，M 3 ＝[1,0,-2,0,1]，M 4 ＝[1,0,-2,0,1] T Sequentially for all low resolution image blocks pb l (i4) Performing convolution operation to obtain a low-resolution image block pb l (i4) High frequency information of (b) extended pb l (i4) Adding this information to the low resolution image block pb l (i4) In the latter row, an initial low-resolution feature block is obtained, and then, all the initial low-resolution feature blocks are subjected to dimension reduction by the same principal component analysis method as in the training stage A1 to obtain a low-resolution image feature block pfb lf (i4) Vectorization pfb lf (i4) The low-resolution image characteristic block vector pb can be obtained lf (i4) For low resolution image block pb l (i4) Performing bicubic interpolation amplification processing to obtain an image block pbf l (i4) Vectorized pbf l (i4) The low-frequency high-resolution image block vector pblf can be obtained l (i4) In the above process of vectorizing a certain block bl into a certain vector bv, the element in the mth row and the nth column in the block bl is the (mxn) th element of the vector bv l +n) elements, N l For the number of elements of each row of the block bl,
step B2) i 4 ＝1，
Step B3) for low resolution image feature block vector pb lf (i4) Finding distances pb in all columns in the low resolution dictionary based on vector correlation lf (i4) The nearest columnI.e. distance pb lf (i4) Nearest dictionaryAtom->And the position of the dictionary atom in the low resolution dictionary is noted, and accordingly, the dictionary atom which has been found off-line is found +.>Projection matrix of->Thereby calculating a high resolution image feature block vector x using the following formula (12) F (i4)，
The pblf is taken l (i4) And x F (i4) Adding to obtain a high resolution image block vector BHV (i 4), i.e
BHV(i4)＝x F (i4)+pblf l (i4) (13)
Obtaining a high resolution image block BH (i 4) from the high resolution image block vector BHV (i 4), i.e., the mth row and nth column elements in the block BH (i 4) are the (mxn) th element of the vector BHV (i 4) h +n) elements, where N h For the number of elements per row of block BH (i 4),
step B4) letting i 4 ＝i 4 +1, for the next low resolution image feature block vector pb lf (i4) The process of step B3 is performed to find its corresponding high resolution image block BH (i 4) until all low resolution feature block vectors extracted from the low resolution image have been processed by the process of step B3 above,
step B5) for all the obtained high resolution image blocks, stitching them together according to the position information, and averaging the overlapping areas of the high resolution blocks to obtain the values of the high resolution pixels, thus obtaining an initial high resolution image X 0 ，
Step B6) iterative correction of the high resolution image using the following equation (14)
X t+1 ＝X t +((L-DHX t )↑(s f ×s f ))*p (14)
Wherein L represents an input low resolution image, H represents a filtering operation on a high resolution image, D is a downsampling matrix, X t Representing the high resolution image obtained after t iterations, +.f(s) f ×s f ) Representing upsampling of an image s f ×s f The multiple, p, represents the coefficient matrix in the Gaussian filter, the sign "/represents the convolution operation, and the result X after I iterations I As a final output high resolution image.
2. A method of image super resolution as claimed in claim 1, wherein: wherein the optimized setting of parameters is performed, wherein the number of columns m=1024 of the low resolution and high resolution dictionary, the size of the low resolution image block is set to 5×5, the overlapping area size of the adjacent low resolution image blocks of the same row is 5×3, the dimension of the low resolution feature blocks in steps A1 and B1 is 25×5, the low resolution image feature block p after the dimension reduction by principal component analysis lf (i) Is 3 x 5, sparsity constraint parameter K in problem (1) 1 Set to K 1 =m/16, parameter λ in problem (1) 1 Set to lambda 1 =0.1, the number of iterations in solving problem (1) is set to 20, i.e. i=20, solving g i The parameter b in (2) is set to b=11, the parameter λ in (9) 2 Set to lambda 2 ＝1×10 -5 The size of the coefficient matrix p in the gaussian filter in the formula (14) is set to 9×9.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103020935A (en) * | 2012-12-10 | 2013-04-03 | 宁波大学 | Self-adaption online dictionary learning super-resolution method |
| CN105023240A (en) * | 2015-07-08 | 2015-11-04 | 北京大学深圳研究生院 | Dictionary-type image super-resolution system and method based on iteration projection reconstruction |
| CN108830791A (en) * | 2018-05-09 | 2018-11-16 | 浙江师范大学 | Image super-resolution method based on itself sample and rarefaction representation |
Family Cites Families (1)
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103020935A (en) * | 2012-12-10 | 2013-04-03 | 宁波大学 | Self-adaption online dictionary learning super-resolution method |
| CN105023240A (en) * | 2015-07-08 | 2015-11-04 | 北京大学深圳研究生院 | Dictionary-type image super-resolution system and method based on iteration projection reconstruction |
| CN108830791A (en) * | 2018-05-09 | 2018-11-16 | 浙江师范大学 | Image super-resolution method based on itself sample and rarefaction representation |
Non-Patent Citations (4)
| Title |
|---|
| Xuesen Shang 等.Adaptive Anchor-Point Selection for Single Image Super-Resolution.IEEE Xplore.2018,全文. * |
| 徐川 等.基于卡通纹理分解和稀疏表示的图像超分辨率重建.软件工程.2016,全文. * |
| 朱华生 ; 徐晨光 ; 廖杉杉 ; .改进型字典学习的图像超分辨率重建.南昌工程学院学报.2015,(01),全文. * |
| 端木春江 ; 左德遥 ; .锚点领域回归与稀疏表示的图像超分辨率方法.计算机工程.2018,(05),全文. * |
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