Quasi-Optimal Filtering in Inverse Problems

TL;DR

This paper introduces a quasi-optimal nonlinear filtering method for inverse problems that is stable, efficient, and does not rely on Bayesian assumptions, based on the statistical approach to inverse theory.

Contribution

It proposes a new quasi-optimal filtering technique that approximates the Kolmogorov-Wiener filter without Bayesian assumptions, utilizing the internal resources of inverse theory.

Findings

Provides an exact representation of the feasible region for inverse solutions.

Demonstrates stability and efficiency of the proposed filter.

Offers a non-Bayesian approach to inverse problem filtering.

Abstract

A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces stable and efficient solutions by relying solely on the internal resources of the inverse theory. The exact representation is given of the Feasible Region for inverse solutions that follows from the statistical consideration.