Mathematical Modeling in Photoacoustic Imaging of Small Absorbers

Abstract

This paper is devoted to mathematical modelling in photo-acoustic imaging of small absorbers. We propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal. We also show the focusing property of the backpropagated acoustic signal. Indeed, we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal. The first method consists of a MUltiple Signal Classification (MUSIC) type algorithm and the second one uses a multi-frequency approach. We also show results of computational experiments to demonstrate efficiency of the algorithms.

Transient Wave Imaging with Limited-View Data

“…In the recent works [5,3,4], we have investigated the imaging of small anomalies using transient wave boundary measurements. We have designed different approaches for locating them and reconstructing some information about their sizes and physical parameters.…”

“…For simplicity, we model here the small anomalies as point sources or dipoles. We refer the reader to [5,3,4] for rigorous derivations of these approximate models and their higher-order corrections. It is worth mentioning that in order to model a small anomaly as a point source or a dipole, one has to truncate the high-frequency component of the transient incident and reflected waves.…”

Microwave Imaging by Elastic Deformation

“…Since [24], internal energies have been used to provide efficient imaging procedures, see [3,6,5,14,21,28].…”

“…Multi-wave systems are capable of high-resolution and high-contrast imaging [1]. A few particular examples of emerging modalities are of great current interest in the biomedical imaging community and will be investigated in detail: magnetic resonance electrical impedance tomography (MREIT) [24,29], [28], magnetic resonance elastography (MRE) [7], impedance-acoustic tomography [21], photo-acoustic [33,25,4] and acousto-optic imaging [14], magneto-acoustic imaging [6], and vibro-acoustography [19].…”

Mathematics of Photoacoustic and Thermoacoustic Tomography

“…However, the normal derivative is not measured by transducers and thus needs to be either found mathematically or measured in a different experiment. Thus, feasibility of techniques [13,28] relying on full Cauchy data requires further mathematical and experimental study.…”