aiqbench analysis
This research advances sparse signal recovery by removing restrictive assumptions on sensing matrices, such as the Restricted Isometry Condition, typically required in classical $\ell_1$-minimization frameworks. Instead of closed-form analytic bounds, the study delivers risk parameters and performance guarantees through efficient solutions to explicit convex optimization problems. This methodological shift offers more robust theoretical foundations for inverse problems in imaging and data science without relying on hard-to-verify matrix properties.
Recovering linear images of sparse signals from indirect observations
arXiv:2609.06182v1 Announce Type: cross 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.
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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