Varslot, TrondMorales, Hector JCheney, Margaret2015-12-100036-1399http://hdl.handle.net/1885/60009In this paper we analyze the problem of optimal waveform design for syntheticapertureradar (SAR) imaging through a dispersive medium. We use a scalar model for wave propagation, together with the single-scattering approximation, and we assume that measurements arepolluted with thermal noise whose statistics are known. For image formation, we use a filtered backprojectionalgorithm in which the filter is determined by knowledge of the power-spectral densities of the scene and noise. In this framework, we derive a waveform which is optimal in the sense of minimizing the mean-square-error of the reconstructed image. We show the results of simulationsfor the example of imaging point scatterers embedded in a certain dispersive background. We showthat for low signal-to-noise ratios, the optimal waveform resembles what is known as a precursor: awave that is generated from propagating ultrawideband waveforms through the medium.Keywords: Dispersive media; Dispersive medium; Dispersive wave propagation; Low signal-to-noise ratio; Pulse echoes; Reconstructed image; Scalar model; Single scattering; Wave forms; Waveform designs; Design; Dispersion (waves); Imaging systems; Optimization; Signa Dispersive wave propagation; Imaging; Pulse-echo imaging; Synthetic aperture radar; Waveform design201110.1137/1008024382016-02-24