This method comprises the following steps in the frequency domain: a) estimating a probability that speech is present; b) estimating a spectral covariance matrix of the noise picked up by the sensors, this estimation being modulated by the probability that speech is present; c) estimating the transfer functions of the acoustic channels between the source of speech and at least some of the sensors relative to a reference constituted by the signal picked up by one of the sensors, this estimation being modulated by the probability that speech is present; d) calculating an optimal linear projector giving a single combined signal from the signals picked up by at least some of the sensors, from the spectral covariance matrix, and from the estimated transfer functions; and e) on the basis of the probability that speech is present and of the combined signal output from the projector, selectively reducing the noise by applying variable gain.