Study On With Noise Image Restoration Method Based On Sparse Low-rannk Matrix

Sparse low-rank matrix recovery problem based on Convex optimization comes fromthe compressive sensing technology,which is very popular these years for image processingand computer vision,such as face recognition systems, Robust alignment by sparse andlow-rank decomposition, low-rank texture background modeling,etc. In this dissertation,the algorithm of processing based on low-rank matrix recovery is discussed, and a newalgorithm of sparse low-rank matrix recovery and an algorithm of low-rank complete ofrecovery based on variable splitting method are proposed.Finally this new algorithms areapplied to image restoration. The main works areas follows:(1)The typical sparse low-rank matrix recovery algorithms are analyzed, and theshortages of which are pointed out, namely Low-rank matrix recovery is achieved byminimizing the nuclear norm matrix to obtain low rank solutions, however, an unstablesolution can be obtained due to the requirements for the low correlation of low rank matrix.And in the traditional low-rank matrix recovery model, due to the low rank and sparseconditions, which only sparsely distributed large error. For this reason, according to thebasic idea of Elastic net study,an improved low-rank denoising recovery model.Themethod introduces a Frobenius norm of low rank matrix as a new regular item and it is alsocombined with the original low rank nuclear norm to optimize the image denoisingproblems.Using F norm can control matrix to be restored stability,and the nuclear normcontrol the recover matrix uniqueness and sparsity,which can achieve the purpose ofremoving the noise, and can make a strong correlation between the results of a more stableimage restoration.(2) Current reduction algorithms are discussed, and the shortages of which are pointedout.Therefore,the algorithm of processing based on low-rank matrix recovery is discussedin this paper, to verify the stability and denoising capability of the presented approach,some images with noise of different types of simulation parameters are generated andprocessed using the presented method compared with the existing low rank matrixalgorithm. Performance analysis of recovery time, signal-to-noise ratio, and error rate areevaluated at the same time. A low rank image denoising algorithm is proposed based onvariable splitting method.Finally, this paper put forward a new model on the basis oflow-rank matrix recovery,which can achieve the purpose of repairing the noisy obscuredimage.(3) An augmented Lagrange multiplier method based on variable splitting is used convex relaxation of sparse recovery methods to solve the problems in complex imagerestoration, and which can also save cost.For this reason, a new model on the basis oflow-rank matrix recovery is put forward in this paper,which can achieve the purpose ofrepairing the noisy obscured image.The experimental results show that the improved modelwhile keeping the original low-rank sparse recovery has good denoising performance andexcellent stability on the strong correlation matrix and can get a higher signal-to-noise ratio.