Low-rank matrix recovery is a hot topic in signal processing

artificial intelligence and optimization.Convex optimization based on low-rank matrix recovery problems coming from the compressive sensing technology

which is very popular these years for image processing

computer vision

text analysis

recommendation system

etc.Low-rank matrix recovery is achieved by minimizing the nuclear norm matrix to obtain a low rank solution

however

an unstable solution can be obtained due to the requirements for the low correlation of a low rank matrix.A low rank image denoising algorithm is proposed based on variable splitting method.The method introduces a Frobenius norm of low rank matrices as a new regular item and it is also combined with the original low rank nuclear norm to optimize the image denoising.In order to solve the improved denoising model

an augmented Lagrange multiplier method based on variable splitting is used by using convex relaxation of sparse recovery methods.Finally

to verify the stability and denoising capability of the presented approach

images with different noise types and simulation parameters are generated and processed using the presented method and the results are compared with the existing low rank matrix algorithm.Performance analysis of recovery time

signal-to-noise ratio

and error rate are evaluated at the same time.The proposed method can yield superior performance compared to the traditional low rank model in terms of the test results.The experiments indicate that the improved models

while keeping the original low-rank sparse recovery

have good denoising performance and exce-llent stability on the strong correlation matrix and we can get a higher signal-to-noise ratio.