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

In this article, we review the literature on recursive algorithms for reconstructing a time sequence of sparse signals from a greatly reduced number of linear projection measurements. The signals are sparse in some transform domain referred to as the sparsity basis, and their sparsity pattern (support set of the sparsity basis coefficients’ vector) can change with time. We also summarize the theoretical results (guarantees for exact recovery and accurate recovery at a given time and for stable recovery over time) that exist for some of the proposed algorithms. An important application where this problem occurs is dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology and MRIguided surgery, or in functional MRI to track brain activation changes.