Abstract

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

Full Article  |  PDF Article

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (1)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (83)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription