The application relates to an audio processing device comprising a) at least one input unit for providing time-frequency representation Y(k,n) of an electric input signal representing a time variant sound signal consisting of target speech signal components S(k,n) from a target sound source TS and noise signal components N(k,n) from other sources than the target sound source, where k and n are frequency band and time frame indices, respectively, b) a noise detection and/or reduction system configured to b1) determine an a posteriori signal to noise ratio estimate γ(k,n) of said electric input signal, and to b2) determine an a priori target signal to noise signal ratio estimate ζ(k,n) of said electric input signal from said a posteriori signal to noise ratio estimate γ(k,n) based on a recursive decision directed algorithm. The a priori target signal to noise signal ratio estimate ζ(k,n) for the n th timeframe is determined from the a priori target signal to noise signal ratio estimate ζ(k,n-1) for the (n-1) th timeframe and the a posteriori signal to noise ratio estimate γ(k,n) for the n th timeframe. The application further relates to a method of of estimating an a priori signal to noise ratio. Thereby improved noise reduction may be provided. The invention may e.g. be used for the hearing aids, headsets, ear phones, active ear protection systems, handsfree telephone systems, mobile telephones, etc.