Weighted expectation maximization reconstruction algorithms for thermoacoustic tomography

Thermoacoustic tomography (TAT) is an emerging imaging technique with potential for a wide range of biomedical imaging applications. In this correspondence, we propose an infinite family of weighted expectation maximization (EM) algorithms for reconstruction of images from temporally truncated TAT measurement data. The weighted EM algorithms are equivalent mathematically to the conventional EM algorithm, but are shown to propagate data inconsistencies in different ways. Using simulated and experimental TAT measurement data, we demonstrate that suitable choices of weighted EM algorithms can effectively mitigate image artifacts that are attributable to temporal truncation of the TAT data function

Weighted expectation maximization reconstruction algorithms for thermoacoustic tomography

Thermoacoustic tomography (TAT) is an emerging imaging technique with potential for a wide range of biomedical imaging applications. In this correspondence, we propose an infinite family of weighted expectation maximization (EM) algorithms for reconstruction of images from temporally truncated TAT measurement data. The weighted EM algorithms are equivalent mathematically to the conventional EM algorithm, but are shown to propagate data inconsistencies in different ways. Using simulated and experimental TAT measurement data, we demonstrate that suitable choices of weighted EM algorithms can effectively mitigate image artifacts that are attributable to temporal truncation of the TAT data function

Inversion of circular means and the wave equation on convex planar domains

We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary \partial \Om of a smooth convex bounded domain \Om \subset \R^2. As a main result we establish back-projection type inversion formulas that recover any initial data with support in \Om modulo an explicitly computed smoothing integral operator \K_\Om. For circular and elliptical domains the operator \K_\Om is shown to vanish identically and hence we establish exact inversion formulas of the back-projection type in these cases. Similar results are obtained for recovering a function from its mean values over circles with centers on \partial \Om. Both reconstruction problems are, amongst others, essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography.Comment: [14 pages, 2 figures