Gradient methods for superresolution

Abstract

Conjugate gradient methods for superresolution are shown to accelerate convergence to the solution. The ill-posed nature of superresolution, combined with the fast convergence of the conjugate gradient algorithm, results in oscillatory artifacts or "null objects" which must be dealt with by regularization. We utilize a combination of Tikhonov-Miller regularization and positivity constraints as a means of regularizing the conjugate gradient algorithm.