Improved maximum-likelihood detection and estimation of Bernoulli-Gaussian processes

When a wavelet to be estimated is not spiky, then a single most likely replacement (SMLR) detector, which is used to detect randomly located impulsive events that have Gaussian-distributed amplitudes, may split a large spike into two smaller ones and may also detect some spikes at wrong locations, although these locations are very close to their true ones. Presented here are two new detection algorithms, namely a single-spike-shift (SSS) detector and an SSS-SMLR detector both of which help correct the SMLR detector’s spike-splitting and shifting problem.