Research On Signal Sparse Representation

With the continuou development of information technology recentlly, the demandon the information becomes much bigger.There is a problem that a large amount of highcomplexity calculating produced in the traditional signal decomposition process appearsvery prominent,and restricting signal processing and transmission. The resrarchers havebeen looking for a simple, efficient method of signal representation, signal sparserepresentation algorithm is one of the methods which is commonly used. Therefore, thisthesis does some reach about problems of the inner product and vector decomposition insparse signal representation.Aiming at the large number of inner product problem in sparse decomposition, a fastcomputation method for sparse decomposition based on the cross-correlation calculationis proposed in this thesis. The main idea of the algorithm is as fellow:It uses a fast jumppoint computation method instead of a large number of inner product operation at eachstep of iterative operation to find out the best atomic. Simulation results show that theimproved algorithm can be used to reconstruct the orginal signal well. Compared withthe matching pursuit algorithm, the computation of the improved algorithm issignificantly reduced, the calculation speed is improved, and has a better convergence.Considering the issue of a large number of computing and storge in the process offormating Over-complete dictionary,in this paper,STF algorithm is applied to theformation of the framework based on the introduction of the theory of frame to obtain asparse frame,and the sparerepresentation of signal is processed by sparse frame insteadof over-complete dictionary.The results of simulation by software shows that thereconstructed signal which is decomposition by sparse frame can represent the mainfeatures of original signal well to some extent.Compared with the sparerepresentation ofsignal by over-complete dictionary,the number of atoms of constituting a spare frame ismuch smaller,and this approach greatly simplifies computing and storage during theformation of the atom library, and reduces the computational time and improvescomputing efficiency.