Comparison of l1-Minimization and Iteratively Reweighted least Squares-l p-Minimization for Image Reconstruction from Compressive Sensing

Abstract

Compressive sensing is the recent technique in data acquisition that allows to reconstruct signal form far fewer samples than conventional method i.e. Shannon-Nyquist theorem use. In this paper, we compare l1-minimization and Iteratively Reweighted least Squares (IRlS)-lp-minimization algorithm to reconstruct image from compressive measurement. Compressive measurement is done by using random Gaussian matrix to encode the image that the first be divided into number of blocks to reduce to the computational complexity. From the results, IRlS-lp and l1-minimization provided almost the same image reconstruction quality, but the IRlS-lp-minimization resulted the faster computation than l1-minimization algorithm.