Research And Application Of Non-convex Compressed Sensing Reconstruction Algorithm

Compressed sensing technology proposed in recent years can realize high-probability reconstruction of the original signal with only a few measurements,so it has attracted extensive attention since it was proposed.Compressed sensing mainly includes three aspects:sparse representation of signal,selection of observation matrix and signal reconstruction,among which signal reconstruction is the most critical one.Therefore,this paper studies the current mainstream signal reconstruction algorithms,and proposes new signal reconstruction algorithms in view of their shortcomings.In this paper,the basic framework of compressed sensing is introduced.The current mainstream greedy algorithm,minimum ₀l norm method and minimum l_p norm method are mainly studied,and the main advantages and disadvantages of these reconstruction approaches are analyzed.First,the shortcomings of greedy algorithm in the process of atom matching and selection are studied,and the reasons for these shortcomings are analyzed.Based on this,a new method of atom matching and selection is proposed and employed in classical greedy algorithm.Second,a new smoothed symmetric composite trigonometric function to approach the l₀ norm,a new reweighted function to promote sparsity,the Tikhonov regularization mechanism to improve the anti-noise performance in signal reconstruction and an optimization method to approximate the optimal solution of sparse signal are studied based on the current shortcomings of the minimum ₀l norm method in signal reconstruction accuracy and anti-noise performance,and then the RRCTSL0 algorithm is proposed.Then,a maximum entropy function for approximating l_p norm and the regularization mechanism for improving the anti-noise performance are studied based on the current shortcomings of the minimum l_p?0?27?p?27?1?norm method in signal reconstruction accuracy,reconstruction speed and anti-noise performance.Further,the RMEF minimization algorithm is proposed.In addition,the feasibility and convergence of the RMEF minimization algorithm are theoretically deduced and analyzed in this paper,thus providing theoretical support for the application of this algorithm.Finally,the compressed sensing theory is applied to recovery the magnetic resonance image.The three algorithms proposed in this paper are employed to magnetic resonance image recovery,and compared with other mainstream compressed sensing reconstruction algorithms.This verifies the excellent performance of the three proposed algorithms in magnetic resonance image restoration,and lays a foundation for their practical application in other fields.