Sparse Decomposition Based On Cascade Dictionary And Its Application

The sparse decomposition is a method that decomposes signal in a group of over-complete dictionary, and then represent the signal a series of atomic.This way can obtain natural characteristics and sparse decomposition of the signals as the form of expressing the input signal as the signal components with clearly features under the certain precision conditions, so this signal decomposition method can express the overall and partial characteristics of the signals flexible, and get more presentation of the signal concise and flexible, it provides more convenience for the signals in further use.But, there has some limitations about using a single atomic library to express complex signal because of the current sparse decomposition research mainly focus on a single atomic library; the cascade atomic library has a natural advantage for complex atomic library multi-component signal and image, because it contains a lot of atomic libraries with different characteristics. Therefore, this paper researches the cascade atomic library of sparse decomposition, and construct three different cascade atomic libraries, and then, use them separately in radar emitter signals decomposition, harmonic analysis, and recognition of palm print. Expand the range of sparse decomposition in application, and provides some reference and application about building the cascade atomic library in further study about cascade atomic sparse decomposition. The major work and research results are as follows:1,The evolutionary algorithm of DNA is introduced to the matching pursuit. It greatly reduces the count of matching pursuit in calculation. Introduce the evolutionary algorithm of DNA to measure the diversity of the population, execute the catastrophe operations according to the diversity of evolution population, improve the optimization ability of DNA evolutionary algorithm. This paper analysis the characteristics of the library such as Chirplet, Laplace and Gabor, and the results is used to construct their cascade atomic library. It also is used in radar emitter signal decomposition multi-component to obtain similarity and attenuation rate better than single atoms library;and the reconstruction time-frequency diagrams can accurate characterization of multi-component radar emitter signal characteristics of each signal components.2,The cascade dictionary is built by the cosine dictionary of atoms and the dirac dictionary which is suitable for the signals to decompose the harmonic signal;it is applied to the harmonic analysis, harmonic and impulse noise will be separated under the large impulse noise condition.Avoid the influence coming from high frequency harmonic and impulse noise to affect each other, thus get the amplitude and phase of the harmonic accurately,.3,The cascade dictionary which is suitable for the decomposition of palmprint is construct by training palmprint and the dirac dictionary, and it is applied to palmprint recognition. It obtain a good recognition rate much better than principal component analysis and two-dimensional principal component analysis by comparing with them in different contents of experiment, respectively salt-pepper noises, gaussian noise, multiplicative noise. Additionally, the results of experimental under the different proportions of occlusion show that this method can obtain good recognition rate much better than principal component analysis and two-dimensional principal component analysis.This work is supported partially by the National Natural Science Foundation of China (60702026), the Scientific and Technological Funds for Young Scientists of Sichuan (09ZQ026-040) and the open Research Fund of Key Laboratory of Signal and Information Processing, Xihua University (SZJJ2009-003).