2 research outputs found
Discrete and Continuous-time Soft-Thresholding with Dynamic Inputs
There exist many well-established techniques to recover sparse signals from
compressed measurements with known performance guarantees in the static case.
However, only a few methods have been proposed to tackle the recovery of
time-varying signals, and even fewer benefit from a theoretical analysis. In
this paper, we study the capacity of the Iterative Soft-Thresholding Algorithm
(ISTA) and its continuous-time analogue the Locally Competitive Algorithm (LCA)
to perform this tracking in real time. ISTA is a well-known digital solver for
static sparse recovery, whose iteration is a first-order discretization of the
LCA differential equation. Our analysis shows that the outputs of both
algorithms can track a time-varying signal while compressed measurements are
streaming, even when no convergence criterion is imposed at each time step. The
L2-distance between the target signal and the outputs of both discrete- and
continuous-time solvers is shown to decay to a bound that is essentially
optimal. Our analyses is supported by simulations on both synthetic and real
data.Comment: 18 pages, 7 figures, journa