Performance Bounds For Co-/Sparse Box Constrained Signal Recovery

Universal Measurement Bounds for Structured Sparse Signal Recovery

Standard compressive sensing results state that to exactly recover an s sparse signal in R, one requires O(s · log p) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also exhibit structure in the sparsity pattern. We focus on group-structured patterns in this paper. Under this model, groups of signal coefficients are active (or i...

Performance Bounds for Sparse Signal Reconstruction with Multiple Side Information

In the context of compressive sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information (SI). To address this problem, we propose a reconstruction algorithm with multiple SI (RAMSI) that solves a general weighted n-`1 norm minimization. The proposed RAMSI algorithm takes advantage of both CS and th...

Algorithms and Lower Bounds for Sparse Recovery

We consider the following k-sparse recovery problem: design a distribution of m× n matrix A, such that for any signal x, given Ax with high probability we can efficiently recover x̂ satisfying ‖x− x̂‖1 ≤ C mink-sparse x′ ‖x− x‖1. It is known that there exist such distributions with m = O(k log(n/k)) rows; in this thesis, we show that this bound is tight. We also introduce the set query algorithm,...

Lower Bounds for Adaptive Sparse Recovery

We give lower bounds for the problem of stable sparse recovery from adaptive linear measurements. In this problem, one would like to estimate a vector x ∈ R from m linear measurements A1x, . . . , Amx. One may choose each vector Ai based on A1x, . . . , Ai−1x, and must output x̂ satisfying ‖x̂− x‖p ≤ (1 + ) min k-sparse x′ ‖x− x‖p with probability at least 1−δ > 2/3, for some p ∈ {1, 2}. For p = ...

Sparse Sampling of Signal Innovations: Theory, Algorithms and Performance Bounds