An Adaptive Bayesian Framework for Recovery of Sources with Structured Sparsity

Abstract

In oversampled adaptive sensing (OAS), noisy measurements are collected in multiple subframes. The sensing basis in each subframe is adapted according to some posterior information exploited from previous measurements. The framework is shown to significantly outperform the classic non-adaptive compressive sensing approach.This paper extends the notion of OAS to signals with structured sparsity. We develop a low-complexity OAS algorithm based on structured orthogonal sensing. Our investigations depict that the proposed algorithm outperforms the conventional non-adaptive compressive sensing framework with group LASSO recovery via a rather small number of subframes.

Oversampled Adaptive Sensing via a Predefined Codebook

“…The behavior illustrated via Fig. 1 is consistent with the prior investigations on OAS with no predefined codebooks [1]- [3]. In fact, those initial cases can be observed as a special case of OAS via a predefined codebook whose size goes to infinity.…”

“…Consider x ∈ R N containing N signal samples. We postulate 3 that the samples are independent and identically distributed (i.i.d.) with prior distribution q (x).…”

“…2) The oversampled adaptive sensing (OAS) framework [1]- [3], in which the given time frame is divided into multiple subframes. In each subframe, K observations are collected.…”