Image super-resolution from compressed sensing observations

In this work we propose a novel framework to obtain High Resolution (HR) images from Compressed Sensing (CS) imaging systems capturing multiple Low Resolution (LR) images of the same scene. The proposed CS Super Resolution (SR) approach combines existing CS reconstruction algorithms with an LR to HR approach based on the use of a Super Gaussian (SG) regularization term. The reconstruction is formulated as a constrained optimization problem which is solved using the Alternate Direction Methods of Multipliers (ADMM). The image estimation subproblem is solved using Majorization-Minimization (MM) while the CS reconstruction becomes an l₁-minimization subject to a quadratic constraint. The performed experiments show that the proposed method compares favorably to classical SR methods at compression ratio 1, obtaining excellent SR reconstructions at ratios below one.