On the stability of some imaging functionals

TL;DR

This paper analyzes the stability and resolution of various imaging functionals in complex media, providing asymptotic estimates of signal-to-noise ratios considering different physical parameters and media properties.

Contribution

It introduces simplified models for imaging functionals and derives optimal asymptotic estimates in complex environments with diverse media correlations.

Findings

Optimal asymptotic SNR estimates depending on physical parameters

Stability analysis for both linear and quadratic wavefield functionals

Applicability to media with long-range dependence and varying correlation lengths

Abstract

This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using simplified measurement settings and reduced functionals that retain the main features of functionals used in practice, we obtain optimal asymptotic estimates of the signal-to-noise ratios depending on the main physical parameters of the problem. We consider random media with possibly long-range dependence and with a correlation length that is less than or equal to the central wavelength of the source we aim to reconstruct. This corresponds to the wave propagation regimes of radiative transfer or homogenization.