A robust image reconstruction based on convex combination of criteria

In this paper we propose a novel regularization method for robust image reconstruction against noise, based on convex combination of the least squares and least absolute deviations. Unlike conventional regularization methods with an assumption of Guaussian noise, the proposed regularization method can deal with Gaussian noise and non-Gaussian noise. To overcome difficulty of the non-smooth objective function, we develop an efficient sub-gradient algorithm. Computed examples with an application to MR images show that the proposed subgradient algorithm can give better reconstruction quality than the conventional reconstruction regularization algorithms in various noise.