Photoacoustic tomography with spatially varying compressibility and density

Abstract

This paper investigates photoacoustic tomography with two spatially varying acoustic parameters, the compressibility and the density. We consider the reconstruction of the absorption density parameter (imaging parameter of Photoacoustics) with complete and partial measurement data. We investigate and analyze three different numerical methods for solving the imaging problem and compare the results.

Quantitative photoacoustic imaging in the acoustic regime using SPIM

“…More sophisticated models take into account spatially varying sound speed, but assume the sound speed to be known from measurements of other modalities (like for instance elastography and ultrasound experiments). PAI which takes into account given spatially varying sound speed and elasticity parameters has been considered in [1,14,13,22,24,20,18,9,10]. Little is known, how and when it is (at least) theoretically possible, to recover in addition to the photoacoustic imaging parameter, the absorption density, also sound speed and elastic parameters.…”

Multiwave tomography with reflectors: Landweber's iteration

“…This problems is well studied under the assumption that the waves travel freely away from the body, see, e.g., [13,21,22,23,38,30,31,26,32,7,8,5] and the references there. In some experimental setup, see [10], reflectors are placed around the body and the measurements are made on a part of it.…”

“…In some experimental setup, see [10], reflectors are placed around the body and the measurements are made on a part of it. The mathematical model of this is presented below in (2.1), first studied in [24,17,7,8]. In [33] and [25], see also [1], two different stable ways to solve the problem were proposed, both based on exponentially convergent Neumann series, expanding some ideas introduced first in [30].…”

“…Landweber iterations for the whole space problem were done recently in [7,8] and compared to the sharp time reversal method in [30] implemented numerically in [26]. Another recent work is [5], where several different optimizations are compared, based on different regularization terms.…”