Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing the solution of this problem in terms of the measured data, under the assumption of the constant and known speed of sound. However, almost all of these formulas require data to be measured either on an unbounded surface, or on a closed surface completely surrounding the object. This is too restrictive for practical applications. The alternative approach we present, under certain restriction on geometry, yields a theoretically exact reconstruction of the standard Radon projections of the source from the data measured on a finite open surface. In addition, this technique reduces the time interval where the data should be known. In general, our method requires a pre-computation of densities of certain single-layer potentials. However, in the case of a truncated circular or spherical acquisition surface, these densities are easily obtained analytically, which leads to fully explicit asymptotically fast algorithms. We test these algorithms in a series of numerical simulations.

Original languageEnglish (US)
Article number094004
JournalInverse Problems
Volume34
Issue number9
DOIs
StatePublished - Jul 16 2018

Fingerprint

Photoacoustic effect
Inverse Source Problem
Single Layer Potential
Thermoacoustics
Inversion Formula
Radon
Acoustic wave velocity
Wave equations
Tomography
Fast Algorithm
Wave equation
Projection
Restriction
Numerical Simulation
Closed
Interval
Series
Geometry
Alternatives
Computer simulation

Keywords

  • explicit inversion formula
  • photoacoustic tomography
  • reduced data
  • spherical means
  • thermoacoustic tomography
  • wave equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data. / Do, N.; Kunyansky, Leonid.

In: Inverse Problems, Vol. 34, No. 9, 094004, 16.07.2018.

Research output: Contribution to journalArticle

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