BIRS Workshop Lecture Videos
Evanescence, Translation, and Uncertainty Principles in the Inverse Source Problem Sylvester, John
"The inverse source problem for the Helmholtz equation (time harmonic wave equation) seeks to recover information about a radiating source from remote observations of a monochromatic (single frequency) radiated wave measured far from the source (the far field). The two properties of far fields that we use to deduce information about shape and location of sources depend on the physical phenomenon of evanescence, which limits imaging resolution to the size of a wavelength, and the formula for calculating how a far field changes when the source is translated. We will show how adaptations of ""uncertainty principles"", as described by Donoho and Stark  provide a very useful and simple tool for this kind of analysis. This is joint work with Roland Griesmaier.  Donoho and Stark -- Uncertainty Principles and Signal Recovery SJAP 1989"
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