Abstract:

In terms of sparse representations of the underlying image in an over-complete dictionary, a sparsity regularized convex variational model for multi-frame image super-resolution is proposed. The regularization term constrains the underlying image to have a sparse representation in a proper over-complete dictionary. The fidelity term restricts the consistency with the measured image in terms of the data degradation model. Furthermore, by replacing the regularization term with its Bregman distance and linearizing the fidelity term, this convex variational problem is decoupled and a fast two step numerical iteration algorithm is proposed to solve it in terms of the linearized Bregman method. The first step is threshold shrinkage with respect to only the regularization term and the second step is to use the gradient descent dealing with only the fidelity term, thus the numerical complexity is decreased rapidly and is robust to noise. Numerical results for optics images demonstrate that only a few iterations can obtain very well results, thus both our super-resolution model and numerical algorithm are effective.