Abstract
We derive and implement in this paper a maximumlikelihood deconvolution (MLD) algorithm, based on the same channel and statistical models used by Kormylo and Mendel, that leads to much fewer computations than theirs. Both algorithms can simultaneously estimate a nonminimum-phase wavelet and statistical parameters, detect spike locations, and deconvolve the data. Our MLD algorithm is implemented by a two-phase block component method (BCM). The phase-l block functions like a coarse adjustment of unknown quantities and provides a set of good initial conditions for the phase-2 block, which functions like a fine adjustment of unknown quantities. Four stages are included in our BCM: detection of spike locations, update of spike density, estimation of spike amplitudes, and estimation of wavelet and noise variance parameters. The major difference between our BCM and Kormylo and Mendel's is that we estimate wavelet parameters using an estimated input (reflectivity). This leads to a pure system identification problem. Kormylo and Mendel, on the other hand, estimate wavelet parameters using only estimated spike locations. Two examples are given which illustrate our MLD algorithm. We demonstrate good performance of our algorithm for both synthetic and real data.