Image Super-Resolution Via Over-Complete Sparse Regularization

Sparse representation is a widely used model of image representation, imagescan be well-represented as a sparse linear combination of atoms from an appropriatelyover-complete dictionary. By using the completeness of the dictionary, we can capturethe mainly information and internal geometry of an image. And it is not affected byaffine transformation, and more robust to noise and error.The super-resolution of image reconstruction is a typical ill-conditioned inverseproblem in image processing. An effective way to solve this kind of problemis to introduce appropriate regularization. This paper mainly focuses on constructionof the over-complete dictionary, the application of sparse regularization in imagesuper resolution reconstruction and using the non-local self-similarity as a prioriinformation in image super resolution. The mainly contents of the paper include:1) The paper introduces the basic concepts, mathematical model and theapplication of sparse representation and image super resolution.2) Consider the construction of over complete dictionary, based on K-SingularValue Decomposition, study a new method that use structural similarity as themeasurement of fidelity of the information, meanwhile, consider the human visualcharacteristics for the construction of redundant dictionary. So that we can design amore applicable dictionary to retain the feature while reduce the redundancy.3) To the image super resolution via sparse representation, using the overcomplete dictionary based on structure similar. So that we can improve the effectiveof construction in edge, contour, texture and so on.4) Introduce the non-local self-similarities as priori information in the imagesuper resolution based on the structural dictionary, and further, improve the quality ofimage reconstruction.