Source reconstruction using windowed Fourier transforms and the filtered backprojection
Roland Griesmaier
Abstract:
The reconstruction of time-harmonic acoustic or electromagnetic sources from measurements of corresponding radiated waves is an ill-posed problem with fascinating applications in science and technology. It has a long tradition and there exists a variety of theoretical results and numerical reconstruction algorithms. We present a new approach to this inverse problem, observing that the windowed Fourier transform of the far field of the radiated wave is related to an exponential Radon transform with purely imaginary exponent of a mollified approximation of the source. Based on this observation we present a filtered backprojection algorithm to recover information on the support of the unknown source. We discuss this algorithm, consider numerical results, and comment on possible extensions of the reconstruction method to inverse scattering problems.