Sparse Representation Modeling Based Image Super-Resolution Reconstruction

To improve the resolution of image is the tireless pursuit of the scientific researchand engineering application with image, thus leading to a substantial growth of thecomplexity and the total weight of the system somehow. Among numerous imagedevelopment and application, it is very urgent to restore or reconstruct potential highresolution (HR) image based on existing capture devices and observed low resolution(LR) one. Image super-resolution reconstruction (SRR) technique, which utilizes theimage prior on degradation procedure or representation model, just can generate verysatisfactory HR image. Mathematically, image SRR task is a typical inverse problem.For making the solution stable and unique, the important and feasible strategy is to addthe priori knowledge on imaging process and data into the reconstruction formula.Using the synthesis principle of different frequency components, this workresearches the SRR of single-frame image. Accordingly, we propose one type of fastquasi-bilinear interpolation method and image super-resolution technique based onsparse representation modeling, towards low and high components respectively. Withthe sparse representation modeling of image data as a main clue, the sparserepresentation theory of signal, including the construction of over-complete dictionary,signal sparse decomposition with respect to given dictionary, and the application of thistheory in image reconstruction is explored. It mainly includes:1. Sparse representation theory of image and its application are introduced,including the sparse representation modeling, the dictionary building of sparserepresentation theory, and the sparse decomposition algorithm. Image processingapplications based on sparse representation is briefly stated. This work derives andestablishes a correspondence between compressed sensing theory and image SRR,namely the relation of theory and application.2. For the interpolation amplification task of the H.264coded image, we provide acurvature-driven fast linear interpolation method. Two-dimensional coordinates of theimage and gray value of its pixel are modeled as a space of three-dimensional surface.Then, the profile curvature of the specified direction is treated as determination basis of the geometry type of the edge. Last, the curvature information drives the fastinterpolation of four pixels.3. For image reconstruction with off-line dictionary, the principle of image SRRbased on sparse representation under over-complete dictionary is analyzed. Thus the keyaspects of reconstruction include dictionary learning and sparse representation. The HRdictionary is numerically calculated by the LR dictionary learned with off-line pattern,reducing the computational complexity of the coupled dictionary learning. We supposeto apply regularized orthogonal matching pursuit algorithm to achieve sparserepresentation of LR image.4. In view of the possible deviation between the given image and the images set tobe learned, we propose that only given LR image is used to construct dictionary pairduring image reconstruction with on-line pattern. Consequently, due to small samplesize and limited structure type, the learned dictionary atoms have reduced ability torepresent. Accordingly, the fixed sparsity information is not reliable. With theaforementioned factors, we propose to apply sparse representation with blind sparsity torealize image reconstruction using sparse model.5. In the image reconstruction with dictionary cascaded, considering possiblestructure deviation used off-line dictionary and the restricted number of samples usedon-line one, the off-line dictionary pre-learned is cascaded by the on-line one learnedwith the current LR image, which constitutes an efficient over-complete dictionarycontaining diversified image structure for the given image. In view of low accuracy andhigh complexity problem occurred in existing sparse representation algorithms, wepropose that sparse representation with an approximatel0norm method should beapplied to achieve higher accuracy and fast sparse decomposition of the given image.Finally, this dissertation heuristically shows discussion on the sparse decompositionand its key issues such as how to effectively build the over-complete dictionary forsparse representation and how to design image sparse decomposition under establisheddictionary. It provides a theoretical foundation for real applications, and also paves theway for future research work.