1. A method for denoising a noisy acoustic signal for a multi-microphone audio device operating in a noisy environment, the noisy acoustic signal comprising a useful component coming from a source of speech and a spurious noise component, said device comprising an array of sensors formed of a plurality of microphone sensors (M 1. .. M 4 ) arranged according to a predetermined configuration and adapted to collect the noisy signal, the sensors being grouped into two sub-arrays, with a first sub-array (R 1 ) of sensors adapted to collect a high frequency part of the spectrum, and a second sub-array (R 2 ) adapted to collect a low frequency part of the spectrum, distinct of said high frequency part, said method comprising the following steps: a) partitioning the spectrum of the noisy signal into said high frequency part (HF) and said low frequency part (LF), by filtering ( 10 , 16 ) above and below a predetermined pivot frequency, respectively, b) denoising each of the two parts of the spectrum with implementation of an adaptive algorithm estimator; and c) reconstructing the spectrum by combining ( 22 ) together the signals delivered after denoising of the two parts of the spectrum at steps b1) and b2), the method being characterized in that the step b) of denoising is operated by distinct processes for each of the two parts of the spectrum, with: b1) for the high frequency part, a denoising exploiting the predictable character of the useful signal from one sensor to the other, between sensors of the first sub-array, by means of a first adaptive algorithm estimator ( 14 ), and b2) for the low frequency part, a denoising by prediction of the noise from one sensor to the other, between sensors of the second sub-array, by means of a second adaptive algorithm estimator ( 18 ).