Study Of Sparse Decompression Of The Signal Based On MP Algorithm

Sparse decomposition of audio signals have been a very important use in the analysis and applications of audio signals, such an audio composition, audio recognition and de-noising. It is a new method of audio signals of decomposition. It can be express audio signal simply. Sparse decomposition of signal is a typical NP problem, that the computational complexity is very huge. In most of the studies currently, matching pursuit (MP) algorithm is used to decompose signals generally, which is an iteration algorithm. MP algorithm is not reconstruct a signal exactly, but the approximation can be get. Compared with another sparse decomposition, MP algorithm is easy to be understood and implemented, also resolve the NP program. But there are the problems that have large memory capacity and huge computational complexity in MP algorithm. The problems will be studied and resolved in this paper.This paper focuses on the sparse decomposition of audio signal, and resolves the problem of large storage and huge computational complexity which is caused by the long signal. This paper will introduce the basic theory of the signal decomposition and the sparse signal decomposition first. Then the application of the sparse decomposition of audio signals in MP algorithm will be mentioned. To resolve the problem of large storage and huge computational complexity, the algorithm will be improved. Based on the characteristics of atoms in dictionary, the atoms in dictionary will be stored by the unpacking method. Each atom will be cut off at that the data is effective. This paper just save the position of atom, the position of the beginning of the effective data and the effective data. It will reduce the length of the atom and the complexity. Though the equivalent condition of the transfer and phase of the atoms in dictionary, the set will be divided into the unequal set of the atoms, that reduce the size of the storage of the atoms again. The last is that the common computer can not deal with the too large signal effectively. Based on the cutting off the atoms, the method is proposed to resolve this problem in this paper. It is that the signal will be cut off to the rank of the signal resolving in common computer, then the best atoms of the dictionary will be found. That resolved the problem of long signal and many atoms in dictionary.The process of the division in dictionary is not to generate the approximation atom, but the process of the cutting generates the approximations. The result of the cutting will have errors compared to the original signal. But it have a big advantage to reduce the storage and compute complexity. In the signal analysis of cutting off, it will cause the problem of not the best matching, because of the reducing of the atoms in dictionary.