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In this correspondence, we propose a fast maximum likelihood detection and estimation algorithm, called a multiple-mostlikely-replacement (MMLR) detector, for Bernoulli-Gaussian processes which are distorted by a linear time-invariant system and contaminated by a white Gaussian noise. This new detector works as well as the well-known single-most-likely-replacement (SMLR) detector. However, the former is computationally faster than the latter. We discuss two examples which demonstrate the computational advantage of the proposed algorithm using synthetic data.