We present an algorithm for deconvolving a seismic trace by extracting spikes one at a time, thereby obtaining a sparsely populated spike train. Three versions of this algorithm are then compared empirically, by applying them to several examples of synthetic and real seismic data. The first two versions correspond to the use of the l 1 (least-absolute-values) and l 2 (least-squares) norms, while the third is a faster and more compact version of the l 1 algorithm.The l 1 procedures are shown to exhibit different characteristics which are often desirable, and the results are generally superior to those of the l 2 procedure for one-at-a-time spike extraction. The use of the fast l 1 algorithm is advocated in practice for efficient and effective deconvolution.
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Barrodale et al. (1984) studied this question.