MAXIMUM-LIKELIHOOD BLIND DECONVOLUTION - NONWHITE BERNOULLI-GAUSSIAN CASE

Todoeschuck and Jensen [1], [2] recently reported that some reflectivity sequences mu-(k) calculated from sonic logs are not white and have a power spectral density approximately proportional to frequency, called a Joseph spectrum. The well-known MLD algorithms [7]-[13] can simultaneously provide estimates of mu-(k), source wavelet which need not be minimum-phase, and statistical parameters. Although these MLD algorithms work well, they are based on the white Bernoulli-Gaussian (B-G) model for mu-(k). In this paper, assuming that spectrum measurements of mu-(k) are available, we propose a ML algorithm for blind deconvolution as mu-(k) is nonwhite with a general spectrum meanwhile the spectrum of the obtained maximum-likelihood estimate triple-over-dot mu-ML-(k) is consistent with the measured spectrum.