Nonlinear least squares and super resolution

Abstract

Digital super resolution is a term used to describe the inverse problem of reconstructing a high resolution image from a set of known low resolution images, each of which is shifted by subpixel displacements. Simple models assume the subpixel displacements are known, but if the displacements are not known then nonlinear approaches must be used to jointly find the displacements and the reconstructed high resolution image. Furthermore, regularization is needed to stabilize the inversion process. This paper describes a separable nonlinear least squares formulation and a solution scheme based on the Gauss-Newton method. In addition, an approach is proposed to choose appropriate regularization parameters at each Gauss-Newton iteration. © 2008 IOP Publishing Ltd.