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The inverse scattering problem concerning the determination of the joint time-delay
Doppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,
involving the echoes of a frame of outgoing signals and its corresponding reciprocal
frame, is developed. A ‘‘realistic’’ situation with respect to the transmission of
a finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.
CitationRebollo Neira, J.; Plastino, A. L.; Fernandez Rubio, J. A. Reconstruction of the join time-delay Doppler-scale reflectivity density in a wide-band regime. A frame theory based approach. Journal of Mathematical Physics, 2000, vol. 41, núm. 8, p. 5325-5341.
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