Research On Compressed Sensing Signal Reconstruction Algorithm Based On Cosparse Analysis Model

Compressed Sensing(CS),as a new signal processing technology,breaks the limit of Nyquist's theorem on signal sampling rate,and can combine signal sampling and singal compression.CS can completely reconstruct the original signal from a small number of measurements by using the characteristic of signal sparsity.To achieve this goal,we must make full use of the prior information of the sparse representation of the signal.The main research models in the field of signal sparse representation are the synthetic sparse model(SSM)and the cosparse analysis model(CAM).CAM has been introduced as an attractive alternative for the SSM.It provides a new signal processing paradigm for recovering cosparse signals with respect to an analysis operator from the undersampled linear measurements in the context of emerging theory of CS.The analysis pursuit problem is a key one brought up by this new paradigm.Inspired by iterative support detection(ISD)for SSM,this thesis presents a new family of analysis pursuit algorithms for the cosparse recovery problem when the signals obey the cosparse analysis model,named iterative cosupport detection estimation(ICDE).ICDE is an algorithmic framework,which alternates between detecting a cosupport set of the unknown true signal and estimating the underlying signal by solving a truncated analysis pursuit problem on the detected cosupport.Under this algorithm framework,the ICDE-L1 algorithm was proposed.The algorithm realized the cosupport detection via an effective non-descending or nested thresholding strategy.Based on the cosupport detection,the signal estimation was carried out by solving the truncated analysis basis pursuit problem.Experimental results show that the reconstruction results of ICDEL1 algorithm match the original signal characteristics completely,and the reconstruction performance of ICDE-L1 algorithm is significantly better than that of ABP algorithm,which requires fewer measured values compared with ABP algorithm to achieve accurate reconstruction.The threshold parameters in the cosupport detection strategy have a positive impact on the reconstruction quality of the algorithm,and ICDE-L1 algorithm has obvious competitiveness compared with other advanced cosparse signal reconstruction algorithms.To alleviate the high computational complexity of ICDE-L1 algorithm,this thesis proposes the ICDE-L2 algorithm,which uses the least squares negative gradient algorithm as the reference for the iterative detection of cosupport,and truncated least squares problem as the signal estimation algorithm.The experimental results show that the reconstruction performance of ICDE-L2 algorithms is better than the current optimal similar algorithms.The ICDE-L2 algorithm is applied to the Shepp-Logan image reconstruction problem,and the algorithm achieves complete image reconstruction with a lower number of ray samples,which can achieve a 20% performance advantage compared with other reconstruction algorithms.