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The removal of noise and interference from an array of received signals is a most fundamental problem in signal processing research. To date, many well-known solutions based on second-order statistics (SOS) have been proposed. This paper views the signal enhancement problem as one of maximizing the mutual information between the source signal and array output. It is shown that if the signal and noise are Gaussian, the maximum mutual information estimation (MMIE) solution is not unique but consists of an infinite set of solutions which encompass the SOS-based optimal filters. The application of the MMIE principle to Laplacian signals is then examined by considering the important problem of estimating a speech signal from a set of noisy observations. It is revealed that while speech (well modeled by a Laplacian distribution) possesses higher order statistics (HOS), the well-known SOS-based optimal filters maximize the Laplacian mutual information as well; that is, the Laplacian mutual information differs from the Gaussian mutual information by a single term whose dependence on the beamforming weights is negligible. Simulation results verify these findings.