This paper proposes a projection based sparse representation and nonlocal regularization deblurring and denoising image restoration algorithm.The algorithm combines sparse representation via adaptive learned dictionary and nonlocal total variation

and the proposed regularization model is divided into three projection sub problems to solve to improve the efficiency.Experimental results show that the proposed algorithm can preserve the detail information effectively

and have nice restoration results for images with different degree of degradation.The proposed algorithm achieves improvement on both visual appearance and objective indices compared with state-of-the-art methods.