New aspects of the inverse source problem with far-field data

The time-dependent inverse source problem with far-field data is investigated within a limited-view Radon inversion framework, analogous to that of a limited-view computed tomography reconstruction problem. We investigate the domains in the Radon and Fourier spaces within which data are available for the reconstruction of the space–time structure of the source. Using a linear inversion formalism we derive a filtered backprojectionlike procedure to reconstruct the minimum-energy source consistent with prescribed far-field data. The source inversion technique developed in the paper is illustrated with a numerical example. The paper also contains a new description of nonradiating sources in the time domain.