Efficient Adaptive Compressive Sensing Using Sparse Hierarchical Learned Dictionaries

TL;DR

This paper introduces a hybrid adaptive compressive sensing method that leverages learned sparse hierarchical dictionaries and structured sparsity to improve signal acquisition efficiency.

Contribution

It presents a novel adaptive sensing approach combined with learned hierarchical dictionaries to exploit structured sparsity in signals.

Findings

Effective adaptive sensing for tree-structured sparse signals

Learned dictionaries improve structured sparsity representation

Enhanced signal recovery performance

Abstract

Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects possess a sparse representation in some basis. Subsequent efforts have shown that the performance of CS can be improved by exploiting the structure in the location of the non-zero signal coefficients (structured sparsity) or using some form of online measurement focusing (adaptivity) in the sensing process. In this paper we examine a powerful hybrid of these two techniques. First, we describe a simple adaptive sensing procedure and show that it is a provably effective method for acquiring sparse signals that exhibit structured sparsity characterized by tree-based coefficient dependencies. Next, employing techniques from sparse hierarchical dictionary learning, we show that representations exhibiting the appropriate form of structured sparsity can be learned from collections of training data. The combination of these techniques results in an effective and efficient adaptive compressive acquisition procedure.