Restoration of images corrupted by mixed Gaussian-impulse noise via l1–l0 minimization

In this paper, we study the restoration of images corrupted by Gaussian plus impulse noise, and propose a l1–l0 minimization approach where the l1 term is used for impulse denoising and the l0 term is used for a sparse representation over certain unknown dictionary of images patches. The main algorithm contains three phases. The first phase is to identify the outlier candidates which are likely to be corrupted by impulse noise. The second phase is to recover the image via dictionary learning on the free-outlier pixels. Finally, an alternating minimization algorithm is employed to solve the proposed minimization energy function, leading to an enhanced restoration based on the recovered image in the second phase. Experimental results are reported to compare the existing methods and demonstrate that the proposed method is better than the other methods.

Research highlights
► A l1–l0 minimization approach is proposed for Gaussian plus impulse noise removal.
► An alternating minimization algorithm is employed to solve the proposed minimization energy function.
► The proposed algorithm combines the adaptive median filter with an effective dictionary learning method.
► Experimental results show that the proposed method is better than the other methods.