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- W4297813542 abstract "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." @default.
- W4297813542 created "2022-10-01" @default.
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- W4297813542 date "2014-05-06" @default.
- W4297813542 modified "2023-09-30" @default.
- W4297813542 title "Discrete and Continuous-time Soft-Thresholding with Dynamic Inputs" @default.
- W4297813542 doi "https://doi.org/10.48550/arxiv.1405.1361" @default.
- W4297813542 hasPublicationYear "2014" @default.
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