Recovering linear images of sparse signals from indirect observations

Abstract:In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=Ax+\xi$. It is {\em a priori} known that $x\in \cX$, a given convex compact set, and that $x$ is $s$-sparse---has at most $s$ nonvanishing entries. The proposed estimates belong to a large family of recovery routines by $\ell_1$-minimization. However, unlike the classical result describing performance of such estimates, we do not make any special (and hard to check) assumptions about the sensing matrix $A$ such as nullspace or Restricted Isometry condition and the like. As a consequence, parameters of the estimates and the upper bounds on their risks are not available in a closed analytic form, but are delivered instead by efficient computation as solutions to explicit convex optimization problems.

Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2609.06182 [stat.ML]

(or arXiv:2609.06182v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.06182 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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