Based On Signal Sparse Representation Dictionary Design

Both the image signal and the speech signal are the medium by which we perceiving the world. And the way of effective representation is the basic problem of the image processing. Sparse Representation of image aims at capturing the characteristic of the image signal, it also means that only little and important information appeals to us. sparse representation modeling of data describes the signals as liner combinations of a few toms, which is from a pre-specified Dictionary, so the choice of the dictionary is the key for the sucsess of sparsifying the signals based on this model. In general, we have two ways to choose the dictionary: the analytic dictionary based on the fixed structure and the adaptive learnt dictionary. Each of them has the superiority and the weakness, and the combination of both the advantages and character has been the research direction for many scholars.This paper’s major work is based on the analytic dictionary and the learnt dictionary:1. After introduced the theoretical background of the sparse representation, we research on the orthogonal complete dictionary and the over-complete redundant dictionary. Firstly, we realize the compressed sensing(CS) algorithm for the image signal based on analytic dictionary. We compare the reconstruction effect of image signal based on different analytic dictionary, in order to explore the sparse representation ability of analytic dictionary. Then an improved compressed sensing algorithm has been presented. Compared with the classical algorithm, which the PSNR improvement of the proposed algorithm is about0.5-0.8dB for different measurement length.For over-complete redundant learnt dictionnary, its adaptive ability is much better than analytic dictionary. In general, we can get better sparse representation based on the Training dictionary model, but also, the algorithm is more complex. And another work of this paper is based on the popular algorithm—K-SVD:Both the multi-scale K-SVD algorithm based on analytic dictionary and the K-SVD algorithm based on wavelet tree is realized. A new K-SVD algorithm based on wavelet tree is presented. It has better reconstruction effect in low PSNR than classical K-SVD algorithm for some pictures, and it fully squeezes the spatial redundancy of in the wavelet domain by combining the advantages of analytic dictionary when reorganizing the training data. Compared with the classic K-SVD algorithm, the new algorithm can process the image of bigger size; and the learnt dictionary is more adaptive in image sequence processing, while ensuring the denoising performance.