CN111640059A - Multi-dictionary image super-resolution method based on Gaussian mixture model - Google Patents
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Abstract
The invention discloses a multi-dictionary image super-resolution method based on a Gaussian mixture model. Firstly, extracting the characteristics of a low-resolution image by using stationary wavelet transform, extracting the residual error characteristics of the high-resolution image, and obtaining a training sample pair by overlapping and sampling corresponding regions; classifying the training sample pairs by using a Gaussian mixture model, and then learning corresponding dictionary pairs for each class; in the reconstruction stage, a plurality of dictionaries are used for carrying out super-resolution reconstruction on the image at the same time, and an improved global optimization method is used for further improving the reconstruction quality. The invention can train better dictionaries with generalization, simultaneously avoid the problem that a single global dictionary cannot well reconstruct image blocks with different structures, and can better perform super-resolution reconstruction on low-resolution images.
Description
Technical Field
The invention belongs to the technical field of image super-resolution reconstruction, and particularly relates to a multi-dictionary image super-resolution method based on a Gaussian mixture model.
Background
The image is used as a visual signal carrier reflecting an objective scene, contains abundant edge structure and texture detail information, and the quality of the image not only influences the visual sense quality of human eyes, but also determines the analysis and judgment results of an image processing system. The image quality of the image is improved by a hardware mode, which is often limited by the imaging equipment and the imaging environment, and the direct imaging quality cannot be easily improved. Image super-resolution reconstruction refers to a process of reconstructing a high-resolution image by using one or more observed low-resolution images, and the resolution of the image can be improved from the aspect of software. Because the advantages of low cost, high reliability and the like are more and more favored by people, the product market demand of the image super-resolution reconstruction technology is increasingly expanded and the application is also increasingly wide.
The image super-resolution reconstruction method mainly comprises an image super-resolution reconstruction algorithm based on interpolation and an image super-resolution reconstruction algorithm based on learning. The image super-resolution reconstruction method based on interpolation is based on the assumption that a natural image is smooth in space, and an interpolation kernel is used for restoring a high-resolution image on the basis. The method has simple calculation, low complexity and short running time, but the interpolation kernel can not adapt with different images, so that the reconstructed image is too smooth and the detail edge is fuzzy, such as a common bicubic interpolation algorithm (1.Hou H, Andrews H. client profiles for imaging and digital filtering [ J ]. IEEE Transactions on optics, speed, and signal processing,1978,26(6):508 and 517.). The super-resolution image reconstruction method based on learning is to adaptively learn the mapping relation between high-resolution image blocks and low-resolution image blocks in a training sample, and then to recover the detail information lost in the low-resolution image through the learned mapping relation. yang et al propose a sparse representation-based image super-resolution reconstruction algorithm, which utilizes the same sparse representation coefficients of high-resolution and low-resolution image blocks under a specific sparse basis as constraint conditions, performs joint training on a high-resolution and low-resolution image sample library to obtain redundant dictionary pairs corresponding to high-resolution and low-resolution images, then solves the sparse coefficients of the low-resolution blocks to be reconstructed under a low-resolution dictionary, and then utilizes a high-resolution dictionary to construct, thereby finally obtaining the high-resolution image blocks. (2.Yang J, Wright J, Huang T S, et al. image super-resolution video presentation [ J ]. IEEE transactions on image processing,2010,19(11): 2861-2873.). Zeyde et al improves the Yang's method, utilizes PCA to carry out the dimensionality reduction to the characteristic of training sample, and the study residual replaces the high-resolution image block of direct study, has improved the efficiency of dictionary training. (3.Zeyde R, Elad M, Protter M. on single image scale-up using space-representation [ C ]. International conference on curves and surfaces. Springer, Berlin, Heidelberg,2010: 711-. (4.Timofte R, DeSmet V, Van Gool L. adsorbed neighbor induced regression for fast example-based decoder-resolution [ C ]. Proceedings of the IEEE international conference on computer vision.2013:1920 1927.)
Compared with the image super-resolution reconstruction algorithm based on interpolation, the image super-resolution reconstruction algorithm based on sparse representation can obtain a reconstruction result with clearer edges by using the prior information learned from the sample to constrain the image super-resolution reconstruction. However, due to the fact that the training sample features extracted by the gradient operators are used, the extracted edges are not fine enough, and the performance and generalization capability of the trained dictionary are poor.
Disclosure of Invention
The invention aims to provide a method for extracting image features by utilizing stationary wavelet transform, clustering training samples by using a Gaussian mixture model, and training a corresponding dictionary for each class so as to better perform image super-resolution reconstruction.
The technical solution for realizing the purpose of the invention is as follows: a multi-dictionary image super-resolution reconstruction method based on a Gaussian mixture model comprises the following steps:
firstly, extracting image characteristics, namely performing primary wavelet transformation on a low-resolution image to obtain high-frequency sub-bands in horizontal, vertical and diagonal directions as the characteristics of the low-resolution image, and using a residual error between the high-resolution image and the low-resolution image as the characteristics of the high-resolution image for the high-resolution image;
secondly, acquiring training samples, performing overlapped sampling on the extracted low-resolution training sample characteristic diagram according to corresponding positions, vectorizing the sampled training sample blocks, and performing dimensionality reduction on the low-resolution characteristic vector by using a principal component analysis method;
thirdly, clustering training samples, clustering training sample vectors by using a Gaussian mixture model, and keeping parameters of each type;
fourthly, dictionary learning is carried out, and a dictionary is trained by utilizing a K-SVD algorithm on the training samples of multiple categories obtained in the third step, so that each group of training samples can obtain a group of high-resolution and low-resolution dictionary pairs;
fifthly, performing super-resolution reconstruction, namely performing image feature extraction and blocking on the input low-resolution picture to be subjected to super-resolution reconstruction, and reconstructing a high-resolution image by utilizing a plurality of dictionaries learned in the previous step;
and sixthly, global optimization, namely further optimizing the image reconstructed in the fifth step by using an improved iterative back projection algorithm.
Compared with the prior art, the invention has the following remarkable advantages: (1) the features extracted by the wavelet transform can effectively extract details, increase the features in the diagonal direction, and adopt the residual error features for the high-resolution features, so that the training sample has better anti-noise and generalization capabilities. (2) The used Gaussian mixture model clusters the training samples, and corresponding dictionary pairs are trained for each type of training data after clustering, so that image blocks with different structures can be well represented by corresponding dictionaries. (3) In the super-resolution reconstruction stage, a plurality of dictionaries are used for carrying out super-resolution reconstruction on the image to be reconstructed together, so that image blocks with different forms can be well represented, and the problem that a single global dictionary cannot well represent image blocks with different structures is solved. (4) An improved global optimization process is provided, global optimization is carried out by combining bilateral filtering and an iterative back projection algorithm, block effect influence brought by a dictionary-based super-resolution reconstruction method is well eliminated, and meanwhile the performance of super-resolution reconstruction of an image is further improved.
Drawings
FIG. 1 is a process diagram of the multi-dictionary image super-resolution reconstruction method based on wavelet transformation and Gaussian mixture model.
Fig. 2 is a schematic diagram of a one-level haar stationary wavelet transform performed on a low resolution image.
Fig. 3 is a schematic diagram of residual feature extraction for a high-resolution image.
FIG. 4 is a flow chart diagram of a global optimization method.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
With reference to fig. 1, the multi-dictionary image super-resolution reconstruction method based on wavelet transform and gaussian mixture model of the present invention comprises the following steps:
firstly, image feature extraction: performing first-level haar stationary wavelet transform on the low-resolution image, as shown in fig. 2, acquiring high-frequency sub-bands in horizontal, vertical and diagonal directions as the features of the low-resolution image; for the high resolution image, as shown in fig. 3, a residual between the high resolution image and the low resolution image is used as a feature of the high resolution image.
Step two, obtaining a training sample: selecting image blocks with the size of 6x6 as training sample pairs at corresponding positions on the low-resolution image features and the high-resolution image features, wherein in order to obtain more training samples, an image block at the next position has an overlapping region with a current image block, specifically, an overlapping region with the size of 6x4 is formed between an overlapping block in the horizontal direction and a previous image block, and an overlapping region with the size of 4x6 is formed between an overlapping block in the vertical direction and a previous image block. Since the low-resolution features are composed of three parts, namely horizontal features, vertical features and diagonal features, the sizes of the image blocks obtained at corresponding positions are all 6x6, and for convenience, three low-resolution image feature blocks are connected in series to form an 18x6 image block and then vectorized. In addition, in order to reduce the difficulty of dictionary training, the dimensionality of the low-resolution feature blocks subjected to vector quantization is reduced by adopting a principal component analysis method, 99.9% of energy of the low-resolution feature blocks is reserved, and a final low-resolution training sample is obtainedBook (I)
Directly vectorizing the high-resolution sample block to obtain the high-resolution sample
Thirdly, training sample clustering: because the high-resolution training samples and the low-resolution training samples are in one-to-one correspondence, only the category of each sample in the low-resolution training samples needs to be calculated, and the corresponding sample in the high-resolution training samples belongs to the same category with the low-resolution training samples. The low resolution samples are classified into K classes using a gaussian mixture model, where the value of K is obtained through a large number of experiments and is set here to 19 classes. The probability density function of a Gaussian mixture model with class K is defined as follows:
where x is an input parameter, here corresponding to a low resolution training sample
ωkIs the weight of the kth multivariate Gaussian function, fk(x) Is the kth multivariate gaussian probability density function defined as follows:
wherein muk，∑kIs the mean and covariance of the kth multivariate gaussian function.
The clustering of the Gaussian mixture model requires the calculation of the parameters and weights of each multivariate Gaussian function, i.e. solving for (omega)k,μk,∑k) Is solved by the expectation maximization algorithm, the weight of each class is firstly set as
Mean value is randomAnd initializing, and setting the covariance matrix as an identity matrix. According to the formula
The posterior probability of the weights is calculated, and then the weights, mean and covariance matrices are updated using the following equations,
repeatedly using the formula to carry out iterative solution, and when the error between two iterations is less than 10-4Stopping iteration to obtain final K groups of parameters (omega)k,μk,∑k). Calculating the probability value of each low-resolution sample on all multivariate Gaussian functions, selecting the sample with the maximum probability value as the class of the sample, wherein the corresponding high-resolution sample also belongs to the same class, and finally dividing the N training samples into K classes.
Fourthly, dictionary learning: and learning the mapping relation between the K groups of high-resolution and low-resolution sample pairs obtained in the third step by using a dictionary. Calculating corresponding overcomplete dictionary D of each group of low-resolution samples by using K-SVD algorithmlAnd sparse representation coefficient Q, corresponding high resolution dictionary DhIt can be calculated by the following formula:
Dh＝PhQT(QQT)-1
wherein P ishEach column in the set is composed of a high resolution training sample vector in the class.
Fifthly, super-resolution reconstruction: for an input low resolution picture X to be super-resolved reconstructedLRFirstly, the first two steps are utilized to obtain a reconstruction image to be super-resolvedImage feature block set
Computing sparse representation coefficients α under K low resolution dictionaries using Orthogonal Matching Pursuit (OMP) for each low resolution image feature blockijAnd finally, reconstructing a high-resolution feature block by using the following formula, wherein the range of i is 1-M, and the range of j is 1-K:
wherein gamma isijA posteriori probability of the weight of the ith low resolution image block calculated in the third step belonging to the jth class, wherein
Is a high resolution dictionary in class j.
Calculating all high-resolution image characteristics by the formula
Then, the high-resolution characteristic image is combined into the whole high-resolution characteristic image according to the position of the block, wherein the pixel value of the overlapping area is the average value which is taken as the final pixel value, because the high-resolution characteristic is the residual characteristic, the image X after the final reconstruction can be obtained by adding the high-resolution characteristic to the image to be reconstructedHR。
Sixthly, global optimization: further optimizing the image reconstructed in the fifth step, as shown in fig. 4, in the whole process, firstly performing bilateral filtering on the image reconstructed in the fifth step to obtain a preliminary optimized image X (0), and then iterating the image subjected to bilateral filtering until the algorithm converges, specifically including the following steps:
t starts from 1 for the t-th iteration
(1) Image up-sampling: for the last iteration image X (t-1), firstly amplifying by twice by using bicubic interpolation to obtain Xup(t)。
(2) Simulating image degradation: for the up-sampled image X in (1)up(t), down-sampling to the size of the original image by using bicubic interpolation, and finally performing Gaussian filtering on the image to obtain a low-resolution image X of a simulated image degradation modeldown(t)。
(3) And (3) calculating an error: image X obtained by calculating analog image degradation modeldown(t) and the true low resolution image X to be reconstructed in the fifth stepLR(t) difference X betweendiff(t)＝XLR-Xdown(t)。
(4) Projection error: comparing the difference X calculated in (3)diff(t) adding the image X (t-1) obtained in the last iteration to obtain the optimized image X (t) of the current iteration X (t) -X (t-1) + Xdiff(t)。
(5) Judging whether convergence occurs: the current error calculation method is as follows:
where norm is the norm of matrix 2, when ≦ 10-5And when t is t +1, continuing the iteration, otherwise, exiting the iteration.
Claims (5)
1. A multi-dictionary image super-resolution method based on a Gaussian mixture model is characterized by comprising the following steps:
firstly, extracting image features; performing primary wavelet transformation on the low-resolution image to obtain high-frequency sub-bands in the horizontal direction, the vertical direction and the diagonal direction as the characteristics of the low-resolution image, and using the residual error between the high-resolution image and the low-resolution image as the characteristics of the high-resolution image for the high-resolution image;
secondly, obtaining a training sample; overlapping sampling is carried out on the extracted low-resolution training sample characteristic diagram according to corresponding positions, vectorization is carried out on the sampled training sample blocks, and the dimension reduction is carried out on the low-resolution characteristic vector by using a principal component analysis method;
thirdly, training sample clustering; clustering training sample vectors by using a Gaussian mixture model, and reserving parameters of each type;
fourthly, learning a dictionary; training the dictionaries by utilizing a K-SVD algorithm on the training samples of the plurality of categories obtained in the third step, so that each group of training samples can obtain a group of high-resolution and low-resolution dictionary pairs;
fifthly, super-resolution reconstruction; performing image feature extraction and blocking on an input low-resolution picture to be subjected to super-resolution reconstruction, and reconstructing a high-resolution image by utilizing a plurality of dictionaries learned in the previous step;
sixthly, global optimization is carried out; and further optimizing the image reconstructed in the fifth step by using a modified iterative back projection algorithm.
2. The multi-dictionary image super-resolution method based on the Gaussian mixture model according to claim 1, wherein the feature extraction process is as follows:
and performing primary haar stationary wavelet transform on the low-resolution image, acquiring high-frequency sub-bands in the horizontal direction, the vertical direction and the diagonal direction as the characteristics of the low-resolution image, and using the residual error between the high-resolution image and the low-resolution image as the characteristics of the high-resolution image for the high-resolution image.
3. The Gaussian mixture model-based multi-dictionary image super-resolution method according to claim 1, wherein the multi-dictionary training process is as follows:
firstly, learning parameters of a K-class Gaussian mixture model by using low-resolution training samples, calculating probability values of each low-resolution sample on all multivariable Gaussian functions in the Gaussian mixture model, selecting the sample with the maximum probability value as the class of the sample, and considering the corresponding high-resolution sample as the same class;
after K groups of high-resolution and low-resolution sample pairs are obtained, K-SVD algorithm is used for calculating corresponding overcomplete dictionary D of low-resolution samples in each grouplAnd sparse representation coefficient Q, corresponding high resolution dictionary DhCalculated using the following formula:
Dh＝PhQT(QQT)-1
wherein P ishEach column in the set is composed of a high resolution training sample vector in the class.
4. The multi-dictionary image super-resolution method based on the Gaussian mixture model according to claim 1, wherein the super-resolution reconstruction process is as follows:
for an input low resolution picture X to be super-resolved reconstructedLRFirstly, utilizing first-level haar stationary wavelet transform, then overlapping and sampling high-frequency sub-bands to obtain characteristic block set of image to be super-resolution reconstructed
Computing sparse representation coefficients α under K low resolution dictionaries using an orthogonal matching pursuit algorithm (OMP) for each low resolution image feature blockijAnd finally, reconstructing a high-resolution feature block by using the following formula, wherein the range of i is 1-M, and the range of j is 1-K:
wherein gamma isijA posteriori probability of the weight of the ith low resolution image block calculated in the third step belonging to the jth class, wherein
Is a high resolution dictionary in class j;
calculating all high-resolution image characteristics by the formula
And combining the high-resolution characteristic images into a whole high-resolution characteristic image according to the positions of the blocks, wherein the pixel value of the overlapping area is the average value which is taken as the final pixel value, and finally adding the high-resolution characteristic to the image to be reconstructed to obtain the reconstructed image.
5. The multi-dictionary image super-resolution method based on the Gaussian mixture model according to claim 1, wherein the global optimization process is as follows:
firstly, carrying out bilateral filtering on a reconstructed image to obtain a preliminary optimized image X (0), and then iterating the X (0) until an algorithm converges, wherein the method specifically comprises the following steps:
t starts from 1 for the t-th iteration
(1) Image up-sampling: for the last iteration image X (t-1), firstly amplifying by twice by using bicubic interpolation to obtain Xup(t)；
(2) Simulating image degradation: for the up-sampled image X in (1)up(t), down-sampling to the size of the original image by using bicubic interpolation, and finally performing Gaussian filtering on the image to obtain a low-resolution image X of a simulated image degradation modeldown(t)；
(3) And (3) calculating an error: image X obtained by calculating analog image degradation modeldown(t) and the true low resolution image X to be reconstructed in the fifth stepLR(t) difference X betweendiff(t)＝XLR-Xdown(t)；
(4) Projection error: comparing the difference X calculated in (3)diff(t) adding the image X (t-1) obtained in the last iteration to obtain the optimized image X (t) of the current iteration X (t) -X (t-1) + Xdiff(t)；
(5) Judging whether convergence occurs: the current error calculation method is as follows:
where norm is the norm of matrix 2, when ≦ 10-5And when t is t +1, continuing the iteration, otherwise, exiting the iteration.
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