13 February 2007 Perspectives in Fourier-based image reconstruction in photoacoustic tomography
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Photoacoustic tomography (PAT) is an emerging imaging technique with great potential for a wide range of biomedical imaging applications. The reconstruction problem of PAT is an inverse source problem, in which the photoacoustic source of interest is induced by a probing optical wavefield. In this work, we revisit the PAT reconstruction problem from a Fourier perspective. By use of standard analytic techniques from inverse source theory, we derive a mathematical relationship between the pressure wavefield data function and its normal derivative measured on an arbitrary aperture that encloses the object and the three-dimensional Fourier transform of the optical absorption distribution evaluated on concentric spheres. We refer to this relationship as a "Fourier-shell identity", which is analogous to the well-known Fourier-slice theorem of X-ray tomography. Potential applications of the Fourier-shell identity are identified and discussed.
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Mark A. Anastasio, Mark A. Anastasio, Jin Zhang, Jin Zhang, Daxin Shi, Daxin Shi, Xiaochuan Pan, Xiaochuan Pan, } "Perspectives in Fourier-based image reconstruction in photoacoustic tomography", Proc. SPIE 6437, Photons Plus Ultrasound: Imaging and Sensing 2007: The Eighth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics, 64371D (13 February 2007); doi: 10.1117/12.701260; https://doi.org/10.1117/12.701260

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