Optimal combination of data modes in inverse problems: maximum compatibility estimate

TL;DR

This paper introduces the maximum compatibility estimate (MCE), an optimal strategy for weighting different data modes in inverse problems, which is independent of noise levels and data scale factors, demonstrated through a shape reconstruction case study.

Contribution

The paper proposes the MCE method for optimally combining multiple data modes in inverse problems, avoiding dependence on noise and scale parameters.

Findings

MCE provides a robust weighting scheme for data modes.

MCE is applicable without explicit knowledge of noise levels.

Successful shape reconstruction case study demonstrates effectiveness.

Abstract

We present an optimal strategy for the relative weighting of different data modes in inverse problems, and derive the maximum compatibility estimate (MCE) that corresponds to the maximum likelihood or maximum a posteriori estimates in the case of a single data mode. MCE is not explicitly dependent on the noise levels, scale factors or numbers of data points of the complementary data modes, and can be determined without the mode weight parameters. As a case study, we consider the problem of reconstructing the shape of a body in $\R^3$ from the boundary curves (profiles) and volumes (brightness values) of its generalized projections.