Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review

TL;DR

This review discusses recursive algorithms for reconstructing time sequences of sparse signals from compressive measurements, focusing on applications like dynamic MRI and CT where signals evolve gradually over time.

Contribution

It provides a comprehensive overview of existing methods for recursive sparse signal recovery in dynamic settings, highlighting their design and analysis.

Findings

Algorithms effectively track changing sparsity patterns.

Applications include real-time medical imaging.

Gradual signal changes improve reconstruction accuracy.

Abstract

In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change with time, although, in many practical applications, the changes are gradual. An important class of applications where this problem occurs is dynamic projection imaging, e.g., dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology, or dynamic computed tomography.