Time-domain reconstruction algorithms and numerical simulations for thermoacoustic tomography in various geometries

In this paper, we present time-domain reconstruction algorithms for the thermoacoustic imaging of biological tissues. The algorithm for a spherical measurement configuration has recently been reported in another paper. Here, we extend the reconstruction algorithms to planar and cylindrical measurement configurations. First, we generalize the rigorous reconstruction formulas by employing Green's function technique. Then, in order to detect small (compared with the measurement geometry) but deeply buried objects, we can simplify the formulas when two practical conditions exist: 1) that the high-frequency components of the thermoacoustic signals contribute more to the spatial resolution than the low-frequency ones, and 2) that the detecting distances between the thermoacoustic sources and the detecting transducers are much greater than the wavelengths of the high-frequency thermoacoustic signals (i.e., those that are useful for imaging). The simplified formulas are computed with temporal back projections and coherent summations over spherical surfaces using certain spatial weighting factors. We refer to these reconstruction formulas as modified back projections. Numerical results are given to illustrate the validity of these algorithms.