Abstract
Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the measured data are more accurately described as a linear combination of the acoustic pressure and its normal derivative on the detection surface. In this paper, we consider the inverse source problem for data that are a combination of the acoustic pressure and its normal derivative. For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas. We present numerical results showing the robustness and validity of the derived formulas. Moreover, we compare several different combinations of the pressure and its normal derivative showing that used measurement model significantly affects the recovered initial pressure.
Highlights
Photoacoustic Tomography (PAT) is a hybrid imaging technique that combines high optical contrast with good ultrasonic resolution
We consider the inverse source problem for data that are a combination of an acoustic pressure of the wave equation and its normal derivative For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas
We investigated PAT with the direction dependent data model (2.1), which uses linear a C combinations Mc1;c2f c1M1;0f c2M0;1f of the acoustic pressure and its normal derivative
Summary
Photoacoustic Tomography (PAT) is a hybrid imaging technique that combines high optical contrast with good ultrasonic resolution. The case where measurements are modeled by the normal derivative of the pressure a H Ta H (c1 and c2 in (1.2)) is studied much less It has been considered in [6, 9], where an explicit inversion formula of the backprojection type is derived for the case that the detection surface is a sphere in three spatial dimensions. P dependent data model (1.2) allowing arbitrary values of c1; c2 R, for the case that the measurement surface is a sphere. Our approach is based on expansions in spherical harmonics and an explicit formula relating the spherical harmonics coefficients of the direction dependent data, as a function of time, and the Fourier coefficients of the initial pressure distribution f , as a function of distance to the origin (see Section 2).
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