Theory And Application Of Compressive Sensing Based On Wavelet Domain Wiener Filter

Along with the advance of information technologies, the existing systems are difficult to meet the challenges of high speed sampling, large data transmission and storage. In recent years, the emergence of compressive sensing theory has brought the revolutionary breakthrough for data collection technology. This theory employs nonadaptive linear projections to maintain the structure of signal. By solving an optimization problem, the original signal can be reconstructed accurately. This theory represents compressible signals at a sampling rate significantly below Nyquist rate, which results in broad applications of the compressive sensing theory.Sparse representation of signals, designing of the measurement matrix and reconstruction algorithm are three hot issues of compressive sensing theory. Sparse representation of signals is the basic requirement of this theory. Therefore, the studying of the sparse representation is particularly important for the compressive sensing. The main contributions of this paper are as follows:1. According to the properties of the optimal linear estimator that minimizes the mean square error of the Wiener filter, an improved signal sparse representation algorithm based on the wavelet-domain Wiener filter was proposed. Compared with the original compressive sensing reconstruction algorithm, experiment results on both one-dimensional signal and two-dimensional image showed that our proposed algorithm improved the quality of the recovered signal significantly.2. An improved signal denoising algorithm based on the wavelet-domain Wiener filter was proposed. This algorithm employed a wavelet denoising scheme based on the sparse representation of wavelet-domain Wiener filter for noise removal. Compared with hard thresholding denoising algorithm and the original denoising algorithm based on wiener filter, experiment results showed that this new denoising scheme is effective.3. A new noise speech recognition method based on the compressive sensing theory was proposed. Our method can increase the anti-noise ability of speech recognition system. According to the experiments, our proposed method achieved better recognition performance compared with the traditional recognition method.