Subgradient projection for sparse signal recovery with sparse noise

Recovering sparse signals from a few linear measurements with sparse noise is attracting growing attention. Such a problem has appeared in a diverse set of fields such as super-resolution, image inpainting and face recognition. A new model for this problem on learning the sparsity of the signal is presented. A corresponding algorithm is also presented by combining the subgradient method and the hard thresholding pursuit strategy. Numerical results demonstrate the efficiency of the model and algorithm.