Sparse Recovery of Streaming Signals Using L1-Homotopy

Understand

Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm minimization program is solved for the reconstruction.

• However, the same representation and reconstruction framework is not readily applicable in a streaming system: the unknown signal changes over time, and it is measured and reconstructed sequentially over small time intervals.
• In this paper, we discuss two such streaming systems and a homotopy-based algorithm for quickly solving the associated L1-norm minimization programs: 1) Recovery of a smooth, time-varying signal for which, instead of using block transforms, we use lapped orthogonal transforms for sparse representation.
• 2) Recovery of a sparse, time-varying signal that follows a linear dynamic model.