This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown priori. We first introduce nonconvex penalty function, where the partition is adapted signal of interest by minimizing mixed $\ell _{2}/\ell _{1}$</...

Abstract In this paper, we discuss application of iterative Stochastic Optimization routines to the problem sparse signal recovery from noisy observation. Using Mirror Descent algorithm as a building block, develop multistage procedure for solutions under assumption smoothness and quadratic minoration on expected objective. An interesting feature proposed is linear convergence approximate solut...

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy BAYESIAN SPARSE SIGNAL RECOVERY By Xing Tan December 2009 Chair: Jian Li Major: Electrical and Computer Engineering Sparse Bayesian learning (SBL) was first proposed in the machine learning literature and later applied to sparse signal r...

We study the heavy hitters and related sparse recovery problems in the low-failure probability regime. This regime is not well-understood, and has only been studied for non-adaptive schemes. The main previous work is on sparse recovery by Gilbert et al. (ICALP’13). We recognize an error in their analysis, improve their results, and contribute new non-adaptive and adaptive sparse recovery algori...

Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty (MMU). Here the MMU is modeled as a bounded additive error. An anti-uncertainty constraint in the form of a mixed 2  and 1  norm is deduced from the sparse ...

In this paper, we investigate conditions for the unique recoverability of sparse integer-valued signals from few linear measurements. Both the objective of minimizing the number of nonzero components, the so-called l0-norm, as well as its popular substitute, the l1-norm, are covered. Furthermore, integer constraints and possible bounds on the variables are investigated. Our results show that th...