1. A method of de-noising a noisy acoustic signal for a multi-microphone audio device operating in noisy surroundings, in particular a “hands-free” telephone device, the noisy acoustic signal comprising a useful component coming from a speech source and an interfering noise component, said device comprising an array of sensors forming a plurality of microphone sensors arranged in a predetermined configuration and suitable for picking up the noisy signal, wherein the method comprises the following processing steps in the frequency domain for a plurality of frequency bands defined for successive time frames of the signal: a) estimating a probability that speech is present in the noisy signal as picked up; b) estimating a spectral covariance matrix of the noise picked up by the sensors, this estimate being modulated by the probability that speech is present; c) estimating the transfer functions of the acoustic channels between the speech source and at least some of the sensors, this estimation being performed relative to a reference useful signal constituted by the signal picked up by one of the sensors, and also being modulated by the probability that speech is present; d) calculating an optimal linear projector giving a single de-noised combined signal derived from the signals picked up by at least some of the sensors, from the spectral covariance matrix estimated in step b), and from the transfer functions estimated in step c); and e) on the basis of the probability of speech being present and of the combined signal given by the projector calculated in step d), selectively reducing the noise by applying variable gain specific to each frequency band and to each time frame.