Abstract
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.
Highlights
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high spatial resolution of ultrasound and high contrast of optical tomography [1,2,3,4,5]
The results with the Fourier method show a large reconstruction error and are very similar to the reconstruction result using the steepest descent method assuming constant sound speed. This demonstrates that the artifacts in both cases are due to the wrong wave propagation model, which further supports the importance of taking sound speed variations into account in full field detection photoacoustic tomography (FFD-PAT) image reconstruction
We investigated FFD-PAT, where projection data of acoustic pressure are measured
Summary
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high spatial resolution of ultrasound and high contrast of optical tomography [1,2,3,4,5]. In [30,31] we go one step further and show that projection data from different directions allow for a full 3D reconstruction of the initial pressure by Radon or Fourier transform techniques We refer to this approach as full field detection photoacoustic tomography (FFD-PAT). It is assumed to satisfy the so-called non-trapping condition, which means that the supremum of the lengths of all geodesics connecting any two points inside the volume enclosed by the measurement surface S is finite Under these assumptions, it is known that the initial pressure can be stably reconstructed from pressure data given on S × [0, T ]. As main theoretical results of this paper, we establish uniqueness and stability of the final time wave inversion problem (see Section 3) This implies linear convergence for the proposed iterative reconstruction methods. The presented numerical results clearly highlight the importance of taking sound speed variations into account in FFD-PAT image reconstruction
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