NonConvex Iteratively Reweighted Least Square Optimization in Compressive Sensing Madhuparna Chakraborty 1, a , Alaka Barik 2, b , Ravinder Nath 3, c , Victor Dutta 4, d 1 Asst Prof., EEE Dept., S.M.I.T, Sikkim Manipal University, Sikkim, India 2 Asst Prof., ECE Dept., I.T.E.R, Siksha ‘O’ Anusandhan University, Bhubaneswar, Orissa, India 3 Associate Prof., EE Dept., NIT Hamirpur, Hamirpur, Himachal Pradesh, India 4 Asst Prof., EEE Dept., S.M.I.T, Sikkim Manipal University, Sikkim, India a madhu_parna@yahoo.com, b abarik.nith@gmail.com, c nath@nith.ac.in, d dutt.victor@gmail.com Keywords: Compressive sensing, regularization, optimization Abstract. In this paper, we study a method for sparse signal recovery with the help of iteratively reweighted least square approach, which in many situations outperforms other reconstruction method mentioned in literature in a way that comparatively fewer measurements are needed for exact recovery. The algorithm given involves solving a sequence of weighted minimization for nonconvex problems where the weights for the next iteration are determined from the value of current solution. We present a number of experiments demonstrating the performance of the algorithm. The performance of the algorithm is studied via computer simulation for different number of measurements, and degree of sparsity. Also the simulation results show that improvement is achieved by incorporating regularization strategy. Introduction The pioneer works by Donoho [1], Candes, Romberg and Tao [2] brought to notice the new field of compressive sensing. Many situations arise where the number of measurement is less for recovery of data. For instance in astronomical imaging or medical imaging the number of data collected is less compared to the original number of pixels, yielding in lesser number of measurements. For recovering the data from those few measurements results in underdetermined situation. Underdetermined kind of situations cannot be solved easily as it results in infinite number of possibilities and the correct solution out of the possibilities is not easy to judge. In Compressive sensing (CS) the analog signals are digitized for processing not via uniform sampling but via measurements using more general even random test functions. To make this possible compressive sensing relies on two properties sparsity and incoherence. Sparsity depends on the fact that many types of signal or image can be represented, by only a small number of non-zero coefficients [3]. In signal processing, one can sample signals which are known to be sparse or after the signals have been transformed to proper basis. Since we are interested in highly undersampled case, the linear system describing the measurements is underdetermined and therefore has infinitely many solutions [4]. The key idea is that the sparsity along with incoherence helps in isolating the original vector. Another important feature of compressive sensing is that practical reconstruction can be performed by using efficient algorithms [5]. Let denote an unknown signal and represent a set of m linear projection of . The approach for a recovery is to search for the sparsest vector which is consistent with the measurement vector . The optimization problem for recovering such signals can be done by following way: The norm: , such that with being the degree of normalization having value of 0, 1, 2. Putting we get the norm which gives fast but incorrect results. The norm is not of much use as its solution involves some intractable combinatorial search. The norm gives a correct reconstruction also the norm is a Advanced Materials Research Vols. 341-342 (2012) pp 629-633 Online: 2011-09-27 © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.341-342.629 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 69.26.46.21, Sikkim Manipal University, Sikkim , India-19/08/15,13:26:46)