ABSTRACT
Recent years have brought about exciting new developments in computerized tomography. In particular, a novel, very promising approach to the creation of diagnostic techniques consists in combining different imaging modalities, in order to take advantage of their individual strengths. Perhaps the most successful example of such a combination is the thermoacoustic tomography (TAT). Major progress has been made recently in developing the mathematical foundations of TAT, including proving uniqueness of reconstruction, obtaining range descriptions for the relevant operators, deriving inversion formulas and algorithms, understanding solutions of incomplete data problems and stability of solutions. The standard way of inverting Radon transform in tomographic applications is by using filtered backprojection-type formulas. When all the plane integrals are computed, the function is reconstructed by applying inversion formulas for the regular Radon transform. For more general transforms of Radon type it is often easier to find analogs of the moment conditions, while counterparts of the evenness conditions could be elusive.
