Time-Domain Extraction of Broad-Band Sources by Tikhonov-Phillips Regularization of Triangular Toeplitz Kernels*

Single receiver source deconvolution in a shallow waterenvironment is an ill-posed problem whose difficulty is compounded by the
multipath nature of the propagation operator. If only sources that are
quiescent prior to some initial time to are considered, the result of
discretizatizing the problem in the time domain is an ill-conditioned
triangular Toeplitz system. In this paper we show how an algorithm of
Elden can be used to implement Tikhonov-Phillips regularization for this
system. Unlike the multichannel deconvolution techniques used in
underwater acoustics, this method can extract source signatures using the
outputs of a single sensor. In addition, when the propagation is multipath
and source signature extraction is performed as part of an optimization
procedure for environmental inversion, we can work with shorter time
windows so that the process becomes computationally more efficient than
frequency domain deconvolution. A number of examples of the use of the
Tikhonov-Philips regularization method for source series extraction are
provided.
(Also cross-referenced as UMIACS-TR-95-87)