Research On Energy Based Sparse Reconstruction And Multiscale Compressed Sensing

Facing with the growing demands for data, the signal processing framework based on the Shannon-Nyquist sampling theorem has brought great challenges to signal processing capabilities and hardware implementation of information system inevitably. In recent years, compressed sensing, a new signal acquisition and compression theory making full use of the prior feature that the signal is sparse or compressible, is proposed and receives widespread attentions in academic and industrial fields. In the compressed sensing framework, the sampling frequency which is applied to sample the prior sparse or compressible signal is much lower than the traditional Nyquist rate. It can accomplish the sampling and compression simultaneously and effectively reduce the amount of transmitted data and storage capacity. Compressed sensing theory involves the sparse signal reconstruction algorithms, sparse representation and the design of observation matrices. The signal reconstruction algorithms focus on fast and accurate reconstruction. The goal of sparse representation is to find a suitable base, in which a small number of coefficients can reveal the useful information of signals. The design of measurement matrices aims to meet the requirements of restricted isometry property and non-coherent characteristic. Focusing on compressed sensing, this paper researches on signal reconstruction under blind sparsity level and on the combination of compressed sensing with the contourlet. The major contributions and innovations are as following:(1) Variable Stepsize Stagewise Adaptive Matching Pursuit algorithmConsidering that the sparsity level of signals can not be known in adcance in recovering unknown signals, some researches on signal reconstruction under blind sparsity level are done. This paper systematically summarizes the matching pursuit algorithms and intensively analyzes them with back-tracing idea. The step size of sparsity adaptive matching pursuit algorithm is sensitive to the image reconstruction, thus variable stepsize stagewise adaptive matching pursuit algorithm is proposed. According to four to one rule, the controlling factor is proposed to govern the estimated sparsity level in current iteration. If the estimated size of signal is small in current iteration, then a variable and big step size is applied; if the estimated size in current iteration is big enough, a fixed step size is used in the next iterations. As the iterations move on, the estimated sparsity level will gradually approach the true value. The simulation results show that the proposed algorithm not only overcomes the impact of step size on reconstruction, but also improves the peak signal to noise ratio of images. (2) Energy-based adaptive matching pursuit algorithm with fixed step sizeFor the matching pursuit algorithms always obtain low successful reconstruction frequency when recovering the binary sparse signals, the energy relationship between measurement and original signal is proved, based on which the energy-based adaptive matching pursuit algorithm with fixed step size (EAMP-FSS) is proposed, in which the energy of measurement vector is introduced into signal reconstruction process. In order to let the estimated sparsity level gradually approach the true value through the iterations, the proposed algorithm utilizes the energy comparison between measurement vector and the candidate signals to determine whether the step size should be applied to increase the current estimated sparsity level. The simulation experiments show that the proposed algorithm can obtain higher successful reconstruction frequency and fewer processing time with less iteration number than other matching pursuit algorithms for binary sparse signal reconstruction.(3) Energy-based adaptive matching pursuit algorithm with adaptive step sizeIn order to improve the adaptability of the energy-based adaptive matching pursuit algorithm with fixed step size algorithm, the adaptive matching pursuit algorithm with adaptive step size (EAMP-ASS) is proposed from the energy point of view. According to the current energy relationship between the candidate signal and the measurement vector, the reconstruction process is divided into three stages and the energy between the candidate and the measurement are compared to automatically choose the step size used in each iteration. From the frequency of successful reconstruction, processing time and iteration number, the simulation results show that EAMP-ASS is better than other matching pursuit algorithm. Two properties are proved form mathematical knowledge. One is the relationship between the step size and the sparsity level. And the other is the completeness and orderliness of the reconstruction stages. The EAMP-ASS algorithm further expands the application scope of matching pursuit algorithms.(4) Image Compressed Sensing based on Wavelet transform in Contourlet domainBoth a large random measurement matrix and a great amount of transmission are required for sampling two-dimensional signals by using traditional compressed sensing model, so the combination of compressed sensing with contourlet belonging to multi geometry analysis is proposed and multi-scale compressed sensing scheme based on wavelet transform in contourlet domain is designed to achieve better image reconstruction quality. In order to compress the subimage in contourlet domain, the wavelet transform is introduced into contourlet domains. The transformation makes the number of coefficients and the size of measurement matrix reduced. Then the cost of transmission, computation and storage is reduced and the quality of image reconstruction is improved. By comparing the scheme based on multi-scale compressed sensing in curvelet domain, the experimental simulation results showed that:the proposed scheme not only reduces the amount of transmission and the size of the measurement matrix, but also improves the reconstruction quality. By comparing the proposed scheme with the scheme based on multi-scale compressed sensing in wavelet domain, the experiment result verifies the validity of the proposed scheme and gives the motivation of the proposed scheme.(5) NSCT based CS Reconstruction for Noisy ImageConsidering the non-subsampled Contourlet can effectively remove the image noise, NSCT based CS reconstruction is proposed for noisy imge. The proposed algorithm not only uses the smoothed projected landweber (SPL) to recover the image, but also applies the threshold operation in nonsubsampled contourlet domain to remove noise. And then the non-local means filter is introduced to denoise the recovered image. Simulation results show that the algorithm has better reconstruction performance and denoising ability than the SPL based on contourlet domain.