Born approximated inverse scattering using beam basis functions

We present a novel beam-based inverse scattering algorithm within the Born approximation, utilizing data measured by arrays of point sources and receivers (transducers). In this approach, the measured point-source/receiver data is first converted into a beam-domain data where the source and the receiver arrays are described by phase-space sets of beam waves. The beam-domain data describes the scattering amplitudes 'measured' by the receiver beams due to each source beam. In the new inversion approach presented here, the unknown medium is spanned using a basis of beam-waves, and the expansion coefficients are determined by multiplying the beam-domain data with pseudo inverse of the correlation matrix of the beam basis function. The scheme benefits from the sparseness of the beam-domain data and from the spatial localization of the beam spanning functions.