Image Super-resolution Reconstruction Via Sparse Representation

The sparse and over-complete representations of images are a new image model, image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary, which can represent images in a compact and efficient way most atom coefficients are zero, only few coefficients are big, and the nonzero coefficients can reveal the intrinsic structures and essential properties of images. Besides, redundant systems are also robust to noise and error. At the same time, sparse representation model can effectively match the sparse coding strategy in the primary visual cortex of mammal. At present it is a research hotspot problem.Super-resolution reconstruction is the typical pathological inverse problem, introduce appropriate regularization is the key to solve the problem. Based on a complete model of sparse representations, usually use sparse solution priori restraint as the regularization items, but it does not take into consideration of the image prior information. How to structure sparse solution in the sparse representation model, based on image prior information of regularization, is the key to improve the super-resolution reconstruction effect. Structured sparse solution is the key problem in this paper to solve.This paper focus on the theory of image sparse representation in the complete image sparse representation model and the application of the model in image super-resolution reconstruction. This paper focus on the two aspects and in-depth research, this paper mainly innovation points include:(1) Based on the complete sparse representation theory thought, established new sparse model of the solution of the regularized image sparse representation. The image sparse regularization constraint coefficient represents sparsity, fidelity term is accord with visual perception structure similarity measure. The experiment shows that the model can better keep signal structure, to get a better image visual effect, and the algorithm is better than the traditional algorithm and more comprehensive.(2) Based on the model of complete sparse representation, we established the sparse constraint of super-resolution reconstruction model, which usually use reconstruction square error as fidelity term. This method is not efficient reconstruct the local geometrical structure of image such as the edge, outline and texture and so on. This is adverse in the recovery of reconstruction the geometric structure of image. This paper consider the human visual model as the basis of geometric structure of prior image, based on structured sparse regularization to establish structure similarity model, which can better restore the local geometrical features of super-resolution reconstruction images of the edge, outline and texture.