Research On Image Super Resolution Methods With Sparse Representation

In the field of digital imaging applications, effected and limited by various kinds of factors, the images or image sequences we captured are often low-resolution (LR) and degraded and cannot meet the demand of real applications. To solve the lack of imaging device and the limitation of imaging qualification, some post-process software techniques are proposed to improve the image spatial resoltion based on the existing imaging device and currently observed images. These techniques are specifically referred to as super-resolution reconstruction (SRR). By modeling the image degeneration processing and using the signal processing methods with image prior information, SRR techniques try to retrieve the lost high freguency components from several observed LR images or a single image, thereby obtaining the high-resolution (HR) images with lowest cost. The SRR techniques have been broadly and thoroughly researched by many reaearchers at home and abroad because of its wide application foreground.The theory of signal sparse reparesentation brings new opportunity and application for the learning-based SRR techniques. It's the hotspot research problem in the fields of SRR. Based on the signal sparse reparesentation theory, this thesis lean the prior knowledge from image sample patches by using machine leanrning methods. By combing the example learing-based and the regularization reconstruction-based SRR approaches, this thesis research the key problems the SRR confronted for single image. The key problems are the SRR model constructing, the problem of the sparse coding precision, the unit sparse representation for local and non-local prior, and the fast SRR methods, etc. In summary, the major research contributions and innovation this thesis makes are as the following.1. The robust single image SRR model and numerical method in sparse domain are proposed. The modeling theory of image prior regularization term in the reconstruction-based SRR approaches is unionized to the sparse representation SRR framework. Complemented with the advantage of the example learning-based methods for its good results in retrieve the high freguency components, the unifying SRR model in sparse domain with the image prior regularization term is proposed. The robust SRR model is constructed which can suppress the noise (or the sparse coding fidelity) effectively. For the LR dictionary the SRR needed, the property of the Hadamard product for matrix is used to the process of the K-SVD dictionary learning method, and both the sparse coding precision and dictionary learning speed are impoved. The HR dictionary learning is modeled by the optimization object function, by utilizing the LR dictionary and training examples, the least norm solution of the function can be obtained directly. In the reconstructing step, the global and local reconstruction constraints are enforced to the object function. The global constrain is to minimize the fidelity which is defined by LI-norm between the reconstruction image and the initial interpolation result and the local constrain is to enforce the fidelity between the image patch and its sparse representation to be minimized. Extensive experiment is perfomend with various kinds'images and the results demonstrate the validity of the proposed method.2. At the present time, the representation fedility of the sparse domain SRR model is measured by the L2-norm or L1-norm. Such a sparse coding model may not be accurate enough to the SRR model in practice. To solve this problem, the mixture Gaussian sparse coding model for SRR is proposed. From the viewpoint of maximum likelihood estimation principle, the mixture Gaussian sparse coding model is constructed according to the probability density function of the coding residual. To solve it, the model is transformed to the weighted norm approximation problem and the weight matrix is designed to adapt to the image SRR problem. The interior-point method for large-scale L1-regularized least squares is used to solve the model. With the mixture Gaussian sparse coding method, the sparse isomorphic coupled LR/HR dictionary for SRR is learned offline. The input LR image patches are coded one by one, using the mixture Gaussian sparse coding method with the LR dictionary. At last, the estimated HR image patch can be represented as a sparse linear combination of the coding coefficients and the HR dictionary, and the overall image is updated gradually by the image patch. The proposed model enhances the quality of the SRR image.3. For the special face image SRR, the face hallucination method is proposed combined the local and non-local sparse representation. The face image is represented by the local and non-local sparse property respectively to retrieve their lost information. The reconstruction processing can be devided into two steps. In the first step, the sparse non-negative matrix factorization eigenface model is proposed. The global eigenface is obtained by solving the model using the online dictionary learning algorithm. In the second step, the non-local self-similarity of the face image is taken into account, the over-complete redundant dictionary is replaced by the clustering sub-dictionaries learned by PCA to represent different face image patches with variouse structure character. In the reconstructing process, to further reduce the sparse coding noise, the centralized sparse approximating constrain term defined by the cluster centroid is added to the coding model. Therefore, the sparse representation coefficient is approximated to the original face image closely, and the better results with fewer visual artifacts can be obtained.4. In practical application, the bottleneck for SRR algorithms is their slow speed. Aiming at the low efficiency of the SRR algorithms with large scale, the fast SRR method based on the local self-similarity match and multilscale sample filters is proposed. With reducing the searching and matching example space and the input image patches, the method utilize the scale invariance feature, i.e., a singular structure in the upper scale image will has a similar structure in its origin location on the lower spatial scale. For the many patches in the smooth region which have little structure information, singular value decomposition is performed on the gradient matrix of the image patch to differentiate smooth and textured regions. As a result, the input image patches to be processed with our method is reduced, the speed can be improved with preserving the SRR result.By solving the above-mentioned problems, the limitatios of the existing methods confronted can be overcomed effectively; both the SRR result and the algorithm efficiency can be improved. On the one hand, the research work can lay foundations for the SRR techniques based on newly sparse theory to be applied in practical. On the other hand, it's helpful to understand the essence of the new signal sparse representation theory and its application in image processing, and it's also has the reference value for the similar ill-posed image processing problem, such as the image denoising, inpainting and deblurring, etc.