Application Of Compressed Sensing In Image Recovery

Compressed sensing theory has been studied by many scholars in recent years.It is mainly used to solve the problem of sparse signals and image restoration.This paper gives the sufficient condition of modified iterative hard thresholding pursuit algorithm to recover sparse signals under the condition of known partial support,and proposes a modified conjugate gradient hard thresholding pursuit algorithm based on compressed sensing theory.The main work is as follows:First,under the condition of known partial support,the sufficient condition of the modified iterative hard thresholding pursuit algorithm to recover sparse signals are studied.Theoretical proof of stable recovery of sparse signals is given.Compared with the traditional hard thresholding pursuit algorithm,it shows that in the case of known partial support,sparse signals can be recovered through fewer measurements,and the constraint conditions on the restricted isometric constant are weak.Finally,numerical experiments verify that the performance of sparse signal recovery is better under the condition of known partial support.Second,the hard thresholding pursuit algorithm in compressed sensing theory is used to recover sparse signals.Since the algorithm is simple and fast,it has been widely used.However,compared with other algorithms in compressed sensing,the hard thresholding pursuit algorithm is not better than others.The conjugate gradient method in the optimization algorithm is widely used to solve the unconstrained optimization problem because of its good convergence.This paper combines the conjugate gradient method to propose a modified conjugate gradient hard thresholding pursuit algorithm,and gives a theoretical proof of the convergence of the algorithm.Finally,numerical experiments such as signal recovery and image recovery verify the effectiveness of the algorithm.