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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 6 — Jun. 1, 2000
  • pp: 1077–1085

Frame-theory-based approach for determining the time–frequency distribution characterizing a dense group of reflecting objects

Laura Rebollo-Neira and A. Plastino  »View Author Affiliations

JOSA A, Vol. 17, Issue 6, pp. 1077-1085 (2000)

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An inverse-scattering problem concerning the determination of a time–frequency spreading function is addressed. Such a function characterizes a dense group of reflecting objects at different ranges and moving with different velocities. The problem, arising in radar and other remote-sensing techniques, is a classical inverse problem. The aim is to reconstruct a function of two variables by means of signals (of one variable) reflected from the environment being observed. The proposed approach is developed by recourse to the frame theory in order to provide a reconstruction formula that asymptotically converges to a unique spreading function. The realistic situation with respect to the transmission of a finite number of signals is further considered. In this case the reconstruction formula is shown to yield the orthogonal projection of the spreading function onto a subspace generated by the outgoing signals.

© 2000 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.3190) Image processing : Inverse problems
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(280.5600) Remote sensing and sensors : Radar
(290.3200) Scattering : Inverse scattering

Original Manuscript: July 29, 1999
Revised Manuscript: February 1, 2000
Manuscript Accepted: February 1, 2000
Published: June 1, 2000

Laura Rebollo-Neira and A. Plastino, "Frame-theory-based approach for determining the time–frequency distribution characterizing a dense group of reflecting objects," J. Opt. Soc. Am. A 17, 1077-1085 (2000)

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