Image smoothing method under strength and gradient sparsity constraint

The invention relates to an image smoothing method under strength and gradient sparsity constraint. The method is characterized by constructing a least square model of an original image and a smooth image by establishing an image smoothing constraint function based on the pixel strength and gradient of the original image; adding the constraint function to the least square model to establish a smoothing energy objective function; introducing two auxiliary variables which are used for substituting for the strength and the gradient in the objective function respectively, adding two error penalty terms to establish an image smoothing minimized model; by computing the values of the two auxiliary variables of the minimized model, computing the analytic solution S of the minimized model to obtain a smooth image matrix. The image smoothing method under strength and gradient sparsity constraint comprehensively utilizes the global characteristic and the local characteristic of an image, and a relation between the global characteristic and the local characteristic, and achieves purposes of improving accuracy and robustness and decreasing computing amount.