Instability of the linearized problem in multiwave tomography of recovery both the source and the speed

TL;DR

This paper demonstrates that the linearized problem of recovering both sound speed and thermal absorption in thermoacoustic and photoacoustic tomography is inherently unstable across all Sobolev space scales.

Contribution

It establishes the fundamental instability of the joint reconstruction problem in multiwave tomography, highlighting limitations in current inversion approaches.

Findings

The problem is unstable in all Sobolev spaces.

Joint recovery of speed and absorption is fundamentally ill-posed.

Implications for the design of stable reconstruction algorithms.

Abstract

In this paper we consider the linearized problem of recovering both the sound speed and the thermal absorption arising in thermoacoustic and photoacoustic tomography. We show that the problem is unstable in any scale of Sobolev spaces.