- Sparse Signal Reconstruction via Iterative Support Detection Yilun Wang (yilun.wangrice.edu) Wotao Yin (wotao.yinrice.edu) Abstract: We present a novel sparse signal reconstruction method ISD'', aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical l_1 minimization approach. ISD addresses failed reconstructions of l_1 minimization due to insufficient measurements. It estimates a support set I from a current reconstruction and obtains a new reconstruction by solving the minimization problem min{\sum_{i\not\in I}|x_i|:Ax=b}, and it iterates these two steps for a small number of times. ISD differs from the orthogonal matching pursuit (OMP) method, as well as its variants, because (i) the index set I in ISD is not necessarily nested or increasing and (ii) the minimization problem above updates all the components of x at the same time. We generalize the Null Space Property to Truncated Null Space Property and present our analysis of ISD based on the latter.We introduce an efficient implementation of ISD, called threshold--ISD, for recovering signals with fast decaying distributions of nonzeros from compressive sensing measurements. Numerical experiments show that threshold--ISD has significant advantages over the classical l_1 minimization approach, as well as two state--of--the--art algorithms: the iterative reweighted l_1 minimization algorithm (IRL1) and the iterative reweighted least--squares algorithm (IRLS). MATLAB code is available for download from http://www.caam.rice.edu/~optimization/L1/ISD/ Keywords: compressed sensing, l1 minimization, iterative support detection, basis pursuit Category 1: Applications -- Science and Engineering Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Rice CAAM Technical Report TR09-30 Download: [PDF]Entry Submitted: 09/14/2009Entry Accepted: 09/14/2009Entry Last Modified: 07/05/2010Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.