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.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

Thermoacoustic computed tomography provides a novel and promising technology in medical imaging. It is based on the generation of acoustic waves inside tissues by stimulation with electromagnetic waves. Acoustic waves are measured outside the stimulated sample and converted into a three-dimensional (3D) image with high contrast and high resolution. Since optical fibres can be used to guide a laser beam on an arbitrary curve, it is possible to realize an experimental buildup in such a way that the acoustic pressure is measured over circles. The aim of this article is to present the mathematical theory when the acoustic pressure is measured over a stack of circles.

To accelerate photoacoustic data acquisition, in [R. Nuster, G. Zangerl, M. Haltmeier, G. Paltauf (2010). Full field detection in photoacoustic tomography. Optics express, 18(6), 6288–6299] a novel measurement and reconstruction approach has been proposed, where the measured data consist of projections of the full 3D acoustic pressure distribution at a certain time instant T. Existing reconstruction algorithms for this kind of setup assume a constant speed of sound. This assumption is not always met in practice and thus can lead to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, a final time wave inversion problem is solved where the initial pressure distribution is recovered from the known pressure distribution at time T. We derive an iterative solution approach for the final time wave inversion problem and compute the required adjoint operator. Moreover, as the main result of this paper, we derive its uniqueness and stability. Our numerical results demonstrate that the proposed reconstruction scheme is fast and stable, and that ignoring sound speed variations significantly degrades the reconstruction.

Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements is time-consumin...