Time-domain reconstruction for thermoacoustic tomography in a spherical geometry

By Minghua Xu, Lihong V. Wang. IEEE Transactions on Medical Imaging, 2002

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Mathematics of thermoacoustic tomography (2007, background): “Then, modulo some constant coefficients that we will assume all to be equal to 1, the pressure wave p(x, t) satisfies the following problem for the standard wave equation [32, 36, 119, 129]: ⎧⎪⎨⎪⎪⎩ ptt = c (2)(x)∆xp, t 0, x ∈ 3”
Exact frequency-domain reconstruction for thermoacoustic tomography. I. Planar geometry (2002, methodology): “Exact reconstructions have been implemented for TAT in spherical and cylindrical configurations in the companion papers [18], [19].”
Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain (2003, methodology): “Finally, a computer collected the digitized photoacoustic signals to reconstruct the distribution of optical absorption within the sampl”
Determining a Function from Its Mean Values Over a Family of Spheres (2004, methodology): “The recent articles [32], [33], [34] use the work of Norton and Linzer [27] for reconstruction in TCT.”
Thermoacoustic computed tomography with large planar receivers (2004, methodology): “[6, 12, 9, 15]) that the generated thermoacoustic pressure field p(x, t) satisfies the inhomogeneous wave equation”
The Application of Compressed Sensing for Photo-Acoustic Tomography (2009, methodology): “By considering a far-field approximation, the final solution proposed in [13] takes the form”