Scale Space and Variational Methods in Computer Vision

Abstract

We propose a novel image resolution enhancement method for multidimensional images based on a variational approach. Given an appropriate down-sampling operator, the reconstruction problem is posed using a deconvolution model under the assumption of Gaussian noise. In order to preserve edges in the image, we regularize the optimization problem by the norm of the total variation of the image. Additionally, we propose a new edge-preserving operator that emphasizes and even enhances edges during the up-sampling and decimation of the image. Furthermore, we also propose the use of the Bregman iterative refinement procedure for the recovery of higher order information from the image. This is coarse to fine approach for recovering finer scales in the image first, followed by the noise. This method is demonstrated on a variety of low-resolution, natural images as well as 3D anisotropic brain MRI images. The edge enhanced reconstruction is shown to yield significant improvement in resolution, especially preserving important edges containing anatomical information.