Recent results in compressive sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of linear observations, provided that the objects possess a sparse representation in some basis or dictionary. Subsequent efforts have shown that the performance of CS techniques can be improved by either exploiting higher-order structure that may exist in the sparse representation of the object being acquired, or by online sequential adaptation of the sensing process. Here we discuss a powerful hybrid of these two notions. We describe a simple adaptive sensing procedure for acquiring objects that exhibit a form of sparsity characterized by tree-structured coefficient dependencies, and demonstrate that representations exhibiting this form of structured sparsity can be learned from collections of training data using recently developed techniques from sparse hierarchical dictionary learning. The result is an effective and resource-efficient data-driven adaptive CS procedure, which we demonstrate in the context of a noisy compressive imaging application.
Copyright. All Rights Reserved.