Image super resolution using compressed sensing observations

Abstract

Compressed Sensing (CS) is a new technology that simultaneously acquires and compresses images reducing acquisition time and memory requirements to process or transmit them. It es- tablishes that a sparsely representable image/signal can be recovered from a highly incomplete set of measurements or projections of the image. Image Super Resolution (SR) is an important post-processing technique where multiple input images are super resolved to obtain one or more images of higher resolution and better quality. SR necessitates a good image registration procedure in order to obtain a High Resolution (HR) image of enhanced quality. Such quality should overcome image degradation due to system hardware, optical and spatial limitations. In this dissertation we propose a novel framework to obtain HR images from CS imaging systems capturing multiple Low Resolution (LR) images of the same scene. The assumption that when an image admits a sparse representation in a transformed domain, a blurred version of it will also be sparse in the transformed domain allows us to recover blurred images from CS observations Similarly, a warped, blurred, and down-sampled LR image is expected to be also sparse in a transformed domain and hence can be reconstructed from the corresponding CS observation. The proposed Compressed Sensing Super Resolution (CSSR) approach, combines existing CS reconstruction algorithms with an LR to HR approach based on the use of a new robust sparsity promoting prior based on super Gaussian regularization.