In order to obtain better image structure smoothness and significantly improve the quality of restored images

total variational norm and Lp norm are introduced into the existing reweighted low rank matrix restoration algorithm

and a new low rank matrix recovery algorithm is proposed and applied in image denoising. Combining the total variational norm and the Lp norm

it is possible to utilize the low rank property of natural images

enhance structural smoothness

and eliminate large sparse noise and various mixed noises. The iterative alternating direction and fast gradient projection algorithm are used to solve the challenging non-convex optimization problem smoothly.Experimental results of image denoising show that the proposed method is superior to the most advanced low rank matrix recovery method

especially for large random noise. When the random sparse noise density is 30 % and40 %

the peak signal-to-noise ratio of the image after denoising by the proposed algorithm is increased by 3. 61 d B and 7. 13 d B

compared with the existing methods.