Linearized inverse problem of scattering in monochromatic and pulse modes

A procedure for the reconstruction of weak multidimensional inhomogeneities was investigated. The monochromatic-mode recover algorithm has a number of advantages over recently reported methods both with and without the use of interpolation. The algorithm was generalized for the case of flat probing pulses with an arbitrary duration and shape. In the pulse mode, the recovery of a scatter in each cell of its spatial quantization is reduced to the weighted summation of the scattered signals sampled for all directions of incidence and observation at the appropriate instants. This procedure does not appreciably increase the number of computational operations, as compared with monochromatic sounding. The probing of weak scatterers with pulses from point sources (for point-type receivers) was handled with correction factors. The reconstruction algorithms that have been developed allow for the elaboration of software used for acoustic ultrasound tomographs.