The Structure Of One Class Of Signal Compression Algorithm

Wavelet analysis is recently developed an application subject. From the angle of mathematics, it is in particular space according to the wavelet basic function to the mathematical expression with approximation. The main features of wavelet transform in the multi-resolution analysis focuses on multiscale analysis ability, and become a powerful signal analysis tool after the Fourier analysis.In order to relieve the enormous pressure that the people in a huge amount of information processing demand signal sampling, transfer and storage, recently, an emerging of compressed sensing is different from the traditional Nyquist sampling theorem. It points out that, as long as the signal in a transform domain is sparse, and then can use a transform basis without related to transform matrix from high- dimension signal to a low-dimensional space. At last by solving an optimization problem can from this small projection in high probability, reconstruct the original signal and may prove that the projection contains enough reconstructed signal. In the theoretical framework, sampling rate is not determined by the signal bandwidth, and is decided to the structure and the information in the signal.This work is based on this theory, and researches the following three problems: the first by the discrete signal sparse transform accordingly discuss continuous signal sparse transform, hence, wavelet coefficients are sparse which can be compressed sensor. The second , using multi-resolution analysis theory make the coefficients of transform processed, and mainly process the high-frequency information which human can not see clearly to approximately zero, as the low-frequency part retained to improve the compression ratio. Thirdly, through the above, we discuss the basic conditions which the constructed compression operator needs to meet and by solving linear equations reconstruct signal, estimating the original signal error.