Spotlight, priorsketching and Bayesian approximation error paradigms

TL;DR

This paper compares Bayesian approximation error and spotlight inversion methods for reducing computational costs and modeling errors in large-scale inverse problems, highlighting their relation and effectiveness.

Contribution

It reveals the close relationship between Bayesian approximation error and spotlight inversion, and connects them to randomized linear algebra sketching schemes.

Findings

Both methods effectively suppress clutter effects in inverse problems.

The approaches are closely related but not equivalent.

Successful examples in X-ray and electrical impedance tomography demonstrate their utility.

Abstract

A way to lower computational cost in large scale inverse problems and problems depending on poorly known model parameters is to replace the detailed model by an approximate one. Inverse problems are typically ill-posed, and the model discrepancy introduced by using approximate models often shows up in the computed solutions as disturbing artifacts or blurring. In this article, we consider two methods of addressing certain types of modeling errors, the Bayesian approximation error (BAE) method and linear algebraic spotlight inversion to suppress clutter in the computational model by orthogonal projections. Through the process of analyzing the two approaches, we show that they turn out to be closely related but not equivalent, and we highlight a connection to sketching schemes in randomized linear algebra. The similarities between the methods and their successful suppression of most of the clutter effects is elucidated with two computed examples, one addressing of X-ray tomography and the other electrical impedance tomography.