Sparse Representation For Image Restoration

In recent year, with the development of compressed sensing, the capacity of sparse recovery is fully analysed in theory. In signal processing, such as image processing, since the large data (e.g., image patch) set may include largely redundant information, the assumption that the signal admit a sparse representation over an over-complete dic-tionary is reasonable. Moveover, in practical application, the sparsity leads to excellent performances. However, how to design an effective algorithm for learning a proper over-complete dictionary and sparse representations becomes an important work at-tracting lots of researches. To achieve sparse representations, many approaches have been developed, e.g., sparse PCA, sparse NMF. One of the most typical methods is sparse coding, which has received a lot of attention in machine learning, signal pro-cessing and neuroscience.In this paper, my work mainly deals with sparse representation-based image de-noising and image super-resolution problem in image processing. Some works have been studied to handle these problem and obtained state-of-the-art performances. How-ever,1) In image denoising, traditional sparse coding algorithm doesn’t take into con-sider the noise information, and may lead to the noise access into the learned dictio-nary, which effects the denoising performance. The proposed idea is to take advantage of the noise information for designing a sparse coding algorithm, which effectively suppresses the noise influence for learning an over-complete dictionary. Experimental results demonstrate that the proposed method yields excellent performance and surpass the similar method.2) In image super-resolution, most of the existing approaches to sparse coding fail to consider the geometrical structure of the data (image patch) set. Similar patches sometimes admit very different estimates due to the potential instability of sparse decompositions, which can result in practice in noticeable reconstruction ar-tifacts. In this paper, a novel cluster-based sparse coding algorithm is proposed, which takes into consider the geometrical structure of the data set. By using cluster as a smooth operator, the sparse decompositions becomes robust. Furthermore, to utilize the proposed sparse coding algorithm effectively for image super-resolution, a novel dictionary-pair learning method is also proposed. Extensive experiments are carried out on a large set of images, and the results clearly demonstrate the proposed algorithm can obtain state-of-the-art performance.