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Practical applications of thermoacoustic tomography require numericalinversion of the spherical mean Radon transform with the centers of integrationspheres occupying an open surface. Solution of this problem is needed (both in2-D and 3-D) because frequently the region of interest cannot be completelysurrounded by the detectors, as it happens, for example, in breast imaging. Wepresent an efficient numerical algorithm for solving this problem in 2-D(similar methods are applicable in the 3-D case). Our method is based on thenumerical approximation of plane waves by certain single layer potentialsrelated to the acquisition geometry. After the densities of these potentialshave been precomputed, each subsequent image reconstruction has the complexityof the regular filtration backprojection algorithm for the classical Radontransform. The peformance of the method is demonstrated in several numericalexamples: one can see that the algorithm produces very accurate reconstructionsif the data are accurate and sufficiently well sampled, on the other hand, itis sufficiently stable with respect to noise in the data.

Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm