On Polyhedral Estimation of Signals via Indirect Observations

TL;DR

This paper introduces a new polyhedral estimation method for recovering signals from indirect noisy observations, offering near-optimal performance under broad conditions and providing computationally efficient design and analysis techniques.

Contribution

It presents a novel nonlinear polyhedral estimator that is computationally feasible and provably near-optimal in minimax sense under less restrictive assumptions.

Findings

Estimator is near-optimal in minimax sense

Method is computationally efficient

Applicable under broad conditions

Abstract

We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear in observations "polyhedral" estimate along with computation-friendly techniques for its design and risk analysis. We demonstrate that under favorable circumstances the resulting estimate is provably near-optimal in the minimax sense, the "favorable circumstances" being less restrictive than the weakest known so far assumptions ensuring near-optimality of estimates which are linear in observations.