Performance of maximum-likelihood deconvolution for Bernoulli-Gaussian processes

A performance analysis is proposed for Bernoulli-Gaussian processes distorted by a linear time invariant system with regard to false alarms, correct detections, and the resolution for the well-known maximum-likelihood deconvolution (MLD). The analysis led to six main conclusions with regard to the dependence of the performance of the single-most-likely-replacement algorithm upon both SNR and the mainlobe width of the normalized autocorrelation function γ(k) of ν(k): the performance is better for larger SNR and γ( k) with a narrower mainlobe; the performance is not dependent upon the wavelet length; the performance can be infinitely improved by increasing SNR no matter whether the mainlobe of γ(k) is broad or narrow; although false alarms for γ(k) with a broad mainlobe cannot be removed by increasing SNR, their amplitudes tend to be smaller for larger SNR; for the same performance, a higher SNR is required for γ(k) with a broad mainlobe than for γ(k) with a narrow mainlobe; and the resolution is better for γ(k) with a narrower mainlobe. It is believed that these conclusions should apply to other comparable suboptimal ML algorithms and that this analysis can help users explain the deconvolved data from the viewpoints of both SNR and γ(k). Simulation results using synthetic data which support the proposed analysis are presented