Signal Reconstruction Algorithms Based On Compressed Sensing Sampling Architecture

Compressed sensing breaks the bottleneck of traditional signal processing and permits sub-Nyquist sampling and signal recovering,which makes that signal sampling is no longer limited to the highest cut-off frequency,but depends on its own information content.The main techniques of the theory include sparse representation of signals,design of the measurement matrix and reconstruction algorithms.The selection and optimization of the reconstruction algorithm is the key step in the compressed sensing,and the focus of the research and attention in the thesis.In this thesis,an improved SAMP algorithm is proposed based on sparsity adaptive matching pursuit(SAMP)algorithm by adding a denoising module.SAMP is a kind of greedy algorithm,with no need of signal's prior sparsity information.The denoising module is based on the first significant jump point theory,and it detects the first fast jumping point from all the nonzero frequency coefficients returned by SAMP and filters out the clutter frequency components below the jump point.We simulate the performance of SAMP,the improved SAMP and the commonly used algorithm under the selected sampling framework in the MATLAB environment.The results show that the improved SAMP algorithm has higher mean output signal-to-noise ratio(SNR)than SAMP,having an improvement of almost lOdB.And for improved SAMP,the spectrum support set has a larger successful recovery percentage at low sampling ratios.This thesis also studies the iterative support detection(ISD)algorithm,and proposes an improved ISD algorithm by adding a support correction module and a denoising module.The implementation of ISD has no necessity of signal's prior sparsity information.It solves the truncated L1 norm minimization problem,and finds the spectrum support set in an iterative way.In this thesis,the support correction module is proposed,and the "residual signal to noise ratio(SNR)" is defined as the decision condition for the module's implementation.The denoising module filters out the frequency clutter generated during the last iteration of ISD,and optimizes the reconstruction performance.Simulations are made for signal's recovery performance using ISD,improved ISD and the commonly used algorithm under the selected sampling architecture.The results show that the improved ISD algorithm increases the robustness of signal reconstruction at low sampling ratios.And the improved one makes the "cliff point" in the mean output SNR performance curve with sub-sampling ratios shift left.Compared with the ISD algorithm,the improved one makes an improvement of 5-10dB in output SNR.