Multi-Image Super Resolution Using Compressive Sensing and a Normalized Transpose Initial Guess

Abstract

Multi-Image Super Resolution (MISR) is the problem of recovering a high-resolution (HR) image from multiple overlapping low-resolution (LR) images. Much recent progress in MISR has investigated the use of compressive sensing (CS) as a method for reconstructing the HR image as an under sampled sparse linear system. However, older techniques for MISR have used iterative optimization from a traditional initial guess of simply averaging the overlapping images based on their fractional pixel contributions. In this work, we integrate this traditional initial guess with CS as an initial solution to the under determined linear system. We show that this initial guess is analogous to crudely ?inverting? a non-orthogonal matrix via it'stranspose. The proposed approach does not make a global sparsity assumption, as typically required by compressive sensing. Rather, we assume sparsity only for the deviation between the high-resolution image and the normalized transpose initial guess. This initial guess is then refined using Matching Pursuit (MP) to super-resolve the HR image assuming k-sparsity. We empirically evaluate the ability for the initial guess-based CS with the traditional wavelets-based CS for MISR. We compare the results in both the native pixel basis and a wavelet basis spaces with and without the traditional initial guess. The results are compared in terms of the PSNR values of the final super-resolved images, effect of initial guess on convergence of the MP algorithm and the difference in the running time of MP algorithm with and without initial guess.