Determining the regularization parameters for super-resolution problems

We derive a novel method to determine the parameters for regularized super-resolution problems, addressing both the traditional regularized super-resolution problem with single- and multiple-parameters and the simultaneous super-resolution problem with two parameters. The proposal relies on the joint maximum a posteriori (JMAP) estimation technique. The classical JMAP technique provides solutions at low computational cost, but it may be unstable and presents multiple local minima. We propose to stabilize the JMAP estimation, while achieving a cost function with a unique global solution, by assuming a gamma prior distribution for the hyperparameters. The resulting fidelity is similar to the quality provided by classical methods such as GCV, L-curve and Evidence, which are computationally expensive. Experimental results illustrate the low complexity and stability of the proposed method.