The Research Of Nonlocal Group Sparsity Model In Image Restoration

Image plays an important role as a form of information storage in daily life. With the popularization of computers and electronic equipments, images can be found everywhere in working life and are widely used in satellite TV, magnetic resonance imaging, geographic information systems, astronomy and other fields. People can understand and express information more intuitively by observing images. However, image distortion often happens in the process of image acquisition, conversion and transfer because of the effects of light and sensor equipments. Great contributions with a wide range of views for solving this defect were made in the past five decades. Such as spatial adaptive filters, stochastic analysis, partial differential equations, transform domain method, splines, morphological analysis, differential geometry, order statistics and more probing in the direction are also proposed to solve this problem.It is a challenging and meaningful subject to reduce the dimension of data with less information loss. It has been proved that the sparse representation can represent high-dimensional data effectively. In recent years, the non-local property of the images is widely used in various image-processing fields and help us to achieve better results due to its good protection for details. Based on the non-local group sparse model, we proposed sparse model from synthesis and analysis aspects for image restoration respectively. Main works of this paper are the following three points:(1) Focused on solving the K-SVD algorithm for random selection of initial dictionary, we considered the highly correlation of sparse coding and geometric similarity in images. A dictionary learning method based on sparse representation after image classification was proposed. The method clusters patches firstly and learns out each dictionary in rapid sequence. The results in this paper show that our method can get better results in image denoising.(2) Considering the sparse coefficients existing some correlations between non-zero elements, the structural correlations between non-zero elements usually exist in different gradient of the image analysis field. We present a group sparsity model in the gradient analysis field. The model minimizes the l2 norm of the vectors with similar non-zero elements for image denoising and edge detecting. Experimental results show that our method could achieve remarkable results.(3) Similar to (2), we divide image into a cartoon part and a texture part, and create model using group sparse l2 type regularizer. We propose a fast approximation algorithm combined with the ADMM algorithm for settling the relevant model and the key sub-problems in the process. The model performs well in terms of image decomposition and image inpainting.