Iterative soft-thresholding for time-varying signal recovery

Recovering static signals from compressed measurements is an important problem that has been extensively studied in modern signal processing. However, only recently have methods been proposed to tackle the problem of recovering a time-varying sequence from streaming online compressed measurements. In this paper, we study the capacity of the standard iterative soft-thresholding algorithm (ISTA) to perform this task in real-time. In previous work, ISTA has been shown to recover static sparse signals. The present paper demonstrates its ability to perform this recovery online in the dynamical setting where measurements are constantly streaming. Our analysis shows that the ℓ₂-distance between the output and the target signal decays according to a linear rate, and is supported by simulations on synthetic and real data.