Optimal incorporation of sparsity information by weighted ${\ell }_1$ optimization

Abstract

Compressed sensing of sparse sources can be improved by incorporating prior knowledge of the source. In this paper we demonstrate a method for optimal selection of weights in weighted $L_1$ norm minimization for a noiseless reconstruction model, and show the improvements in compression that can be achieved.

5 pages, 2 figures, to appear in Proceedings of ISIT2010

References in corpus (4)

• Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
• A typical reconstruction limit of compressed sensing based on Lp-norm minimization
• On-Off Random Access Channels: A Compressed Sensing Framework
• Breaking through the Thresholds: an Analysis for Iterative Reweighted ${\ell }_1$ Minimization via the Grassmann Angle Framework

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• On Sparse Vector Recovery Performance in Structurally Orthogonal Matrices via LASSO
• Matrix Completion with Prior Subspace Information via Maximizing Correlation
• Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
• RLS Recovery with Asymmetric Penalty: Fundamental Limits and Algorithmic Approaches