Generalized inverses in signal processing and remote sensing

An important class of remote sensing and time-varying medium characterization problems fall into the conceptual framework of the theory of generalized inverses. Fundamental theory associated with generalized inverses of linear operators establishes the processing structure for these inverse problems. To illustrate general ideas with specific examples, the problem of characterizing time-varying propagation and scattering by delay-Doppler (narrowband) and delay-time-scale (wideband) spreading functions is examined in detail. We show that the adjoint operators for estimation of these spreading functions are in the forms of Gabor and wavelet transforms, respectively. Underlying group structure as exploited to obtain reproducing properties of narrowband (NB) and wideband (WB) ambiguity functions that arise in spreading function identification. These results can provide insight into the design of optimum probing signals