Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model
Author(s)Misra, Sidhant; Parrilo, Pablo A
MetadataShow full item record
Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted ℓ₁-minimization with suitable choice of weights has been shown to improve performance in the so-called non-uniform sparse model of signals. In this paper, we consider a full generalization of the non-uniform sparse model with very mild assumptions. We prove that when the measurements are obtained using a matrix with independent identically distributed Gaussian entries, weighted ℓ₁-minimization successfully recovers the sparse signal from its measurements with overwhelming probability. We also provide a method to choose these weights for any general signal model from the non-uniform sparse class of signal models.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Misra, Sidhant, and Parrilo, Pablo A. “Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Modell.” IEEE Transactions on Information Theory 61, 8 (August 2015): 4424–4439 © 2015 Institute of Electrical and Electronics Engineers (IEEE)