Images sparse representations over over-complete dictionaries have a wide application in image processing due to the properties of sparsity

integrity and separability.This paper proposes a dictionary learning algorithm which is applied to image de-noising.The dictionary learning problem is expressed as a box-constrained quadratic program and a fast projected gradient method is introduced to solve it.The learned dictionary describes the image content effectively.Experimental results show that:in comparison with the wavelet-based de-noising methods

our learning-based algorithm has better de-noising ability

keep more detail image information and improve the peak signal-to-noise ratio.