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: 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 component from one sensor to the other, between sensors of the first sub-array, by means of a first adaptive algorithm estimator ( 14 ) including calculation of an optimal linear projector, and b2) for the low frequency part, a denoising by prediction of the spurious noise component from one sensor to the other, between sensors of the second sub-array, by means of a second adaptive algorithm estimator ( 18 ) including a linear prediction adaptive filter.