Sparse Recovery of Fusion Frame Structured Signals

TL;DR

This paper explores the recovery of signals structured by fusion frames using a block sparsity model, demonstrating improved reconstruction methods via mixed norm minimization under certain incoherence conditions.

Contribution

It introduces a novel approach for sparse signal recovery in fusion frames, leveraging incoherence properties to enhance reconstruction performance over traditional block sparsity methods.

Findings

Recovery is possible using mixed l1/l2 norm minimization.

Incoherence assumptions improve reconstruction accuracy.

Fusion frame structure generalizes classical compressed sensing techniques.

Abstract

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from a fusion frame. We use a block sparsity model for fusion frames and then show that sparse signals under this model can be compressively sampled and reconstructed in ways similar to standard Compressed Sensing (CS). In particular we invoke a mixed l1/l2 norm minimization in order to reconstruct sparse signals. In our work, we show that assuming a certain incoherence property of the subspaces and the apriori knowledge of it allows us to improve recovery when compared to the usual block sparsity case.