Comparison of the l 1 and l 2 norms applied to one-at-a-time spike extraction from seismic traces

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 l1 (least‐absolute‐values) and l2 (least‐squares) norms, while the third is a faster and more compact version of the l1, algorithm. The l1 procedures are shown to exhibit different characteristics which are often desirable, and the results are generally superior to those of the l2 procedure for one‐at‐a‐time spike extraction. The use of the fast l1 algorithm is advocated in practice for efficient and effective deconvolution.