Abstract
We study reflection imaging as an incomplete data problem in frequency domain. It turns out that this amounts to inverting the Fourier transform using only frequencies outside some set. By numerical simulations we show the effect of this incompleteness on concrete reconstruction problems. We try to complete the data by analytic continuation. An explicit formula is obtained by an inversion formula for the exponential Radon transform. We discuss the application to medical ultrasound tomography and to seismic imaging. We describe an alternative method based on the presence of reflectors.
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