L1deconvolution and its application to seismic signal processing

This correspondence reviews fast iterative reweighted least squares (IRLS) and residual steepest descent (RSD) algorithms for L
p
,
1 \leq p \leq 2
, deconvolution. The timing aspects and the implementation of the IRLS algorithm on an array processor are discussed. The effectiveness of L
1
deconvolution and its insensitivity to noise bursts are illustrated using simple synthetic as well as complex seismic data. Finally, it is shown that the L
p
prediction filters in general need not be stable, and that L
1
solutions predict the possibility of nonminimum phase aspects of a given set of data.