Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface

Abstract

Two universal reconstruction methods for photoacoustic (also called optoacoustic or thermoacoustic) computed tomography are derived, applicable to an arbitrarily shaped detection surface. In photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample. The imaging problem consists in reconstructing the initial pressure sources from those measurements. The first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method. The pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order. In the second approach the reconstruction problem is solved by calculating the far-field approximation, a concept well known in physics, where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center. Numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms.

Three-dimensional thermographic imaging using a virtual wave concept

“…To calculate the discrete cosine transformT 0 , the time evolutionT according to Eq. (14), and the inverse discrete cosine transform to determine the surface temperature Tðr S ; tÞ ( Fig. 2(b)), a short MATLAB routine was written.…”

“…For all three reconstructions from the three detector planes, limited-view artifacts are visible and the inclusions far from the detector planes cannot be reconstructed at all. Better results could be obtained by using a single reconstruction incorporating data from all three detection surfaces, e.g., by using a time-reversal reconstruction algorithm 14 or reconstruction methods from Kunyansky. 40 However, as demonstrated in the past, simply taking the sum of the reconstructions from the three detector planes gives similar results and gives a reasonable reconstruction quality, 25 which is shown in Fig.…”

“…Both equations are second order linear partial differential equations in space and time but describe a quite different physical phenomena. While undamped acoustic waves are invariant to time reversal and therefore can be used for ultrasound image reconstruction, 14 the diffusion of heat is an irreversible process, which cannot be time-reversed. As described by Salazar,15 in contrast to an acoustic wave, "thermal waves" do not have a mean energy propagation.…”

“…The inverse transformation of the measured damped acoustic wave to the virtual wave without damping is illposed and has to be regularized in order to reconstruct acoustic images from the signals. The evolution in space and time of this virtual wave signal is described by the wave equation and, therefore, all well-known reconstruction algorithms from ultrasound imaging or from photoacoustic tomography 14,19,20 can be used to reconstruct the acoustic pressure distribution in space for earlier times. In particular, the initial pressure distribution can be reconstructed for a time just after the excitation pulse.…”

“…In particular, the initial pressure distribution can be reconstructed for a time just after the excitation pulse. One reconstruction method which directly uses the time invariance of the virtual wave signal is time-reversal reconstruction, 14,21,22 and another one which works well for planar sample surfaces is the frequency domain synthetic aperture focusing technique (F-SAFT). [23][24][25] In this work, we introduce the concept of virtual waves for thermographic image reconstruction for the case of short excitation pulses.…”