Application of a nudging technique to thermoacoustic tomography

TL;DR

This paper introduces a novel back and forth nudging algorithm for thermoacoustic tomography, demonstrating its convergence and effectiveness through numerical experiments and comparisons with existing methods.

Contribution

The paper adapts the back and forth nudging algorithm to TAT, providing theoretical convergence analysis and practical validation with improved results.

Findings

BFN algorithm converges geometrically for TAT

Numerical experiments show BFN outperforms traditional methods

Comparison indicates BFN offers faster convergence and better accuracy

Abstract

ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to correct the state of an evolution model, the \emph{back and forth nudging} (BFN), for the TAT inverse problem. We show that the flexibility of this algorithm enables to consider a quite general framework for TAT. The backward nudging algorithm is studied and a proof of the geometrical convergence rate of the BFN is given. A method based on Conjugate Gradient (CG) is also introduced. Finally, numerical experiments validate the theoretical results with a better BFN convergence rate for more realistic setups and a comparison is established between BFN, CG and a usual inversion method.