  We propose three fast algorithms for solving the inverse problem of the
thermoacoustic tomography corresponding to certain acquisition geometries. Two
of these methods are designed to process the measurements done with point-like
detectors placed on a circle (in 2D) or a sphere (in 3D) surrounding the object
of interest. The third inversion algorithm works with the data measured by the
integrating line detectors arranged in a cylindrical assembly rotating around
the object. The number of operations required by these techniques is equal to
O(n^3 log n) and O(n^3 log^2 n) for the 3D techniques (assuming the
reconstruction grid with n^3 nodes) and to O(n^2 log n) for the 2D problem with
n-by-n discretizetion grid. Numerical simulations show that our methods are at
least two orders of magnitude faster than the existing algorithms, without any
sacrifice in accuracy or stability. The results of reconstructions from real
measurements done by the integrating line detectors are also presented, to
demonstrate the practicality of our methods.
