Exact series reconstruction in photoacoustic tomography with circular integrating detectors

Abstract

A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of circular integrating detectors are used to reconstruct the circular projection of the source distribution. In the second step the inverse circular Radon transform is applied. In this article we establish inversion formulas for the first step, which involves an inverse problem for the axially symmetric wave equation. Numerical results are presented that show the validity and robustness of the resulting algorithm.

Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equations

“…(22) Unfortunately, our approach is not available for (22). Currently this problem is of our interest, and it should be addressed elsewhere.…”

“…the formula provides a more stable way to reconstruct the initial data. This issue for photoacoustic tomography and photoacoustic tomography with circular detectors are discussed in [10] and [22], respectively.…”

Photoacoustic tomography with direction dependent data: an exact series reconstruction approach

“…Among these formulas so-called series expansion formulas provide very fast and accurate reconstructions. They give an expansion of the initial pressure in terms of eigenfunctions of the Laplacian [1,11,15,17,31].…”

Thermoacoustic Tomography with circular integrating detectors and variable wave speed

“…The case of point-wise measurements with constant and variable wave speed in the region of interest has been studied extensively [7,10,15]. Other methods of measurement of the ultrasonic waves include measurements with linear integrating detectors [6], planar integrating detectors [2,11] and circular integrating detectors or cylindrical stacks of circular integrating detectors [16,17]. Circular integrating detectors have a few advantages over linear integrating detectors and planar integrating detectors, including compactness of the experimental setup [16].…”

“…The case of planar integrating detectors was studied in [11], and that work focused on the problem with a smooth, variable wave speed. The case of circular (and cylindrical) integrating detectors with constant wave speed has been studied in [16,17]. In those works, explicit formulae are given for reconstruction of an initial pressure density using full measurements, i.e.…”