A hearing device, e.g. a hearing aid, is configured to be worn by a user at or in an ear or to be fully or partially implanted in the head at an ear of the user. The hearing device comprises a) an input unit for providing at least one electric input signal in a time frequency representation k, m, where k and m are frequency and time indices, respectively, and k represents a frequency channel, the at least one electric input signal being representative of sound and comprising target signal components and noise components; and b) a signal processor comprising b1) a target signal estimator for providing an estimate of the target signal; b2) a noise estimator for providing an estimate of the noise; b3) a gain estimator for providing respective gain values in said time frequency representation in dependence of said target signal estimate and said noise estimate, wherein said gain estimator comprises a neural network, wherein the weights of the neural network have been trained with a plurality of training signals, and wherein the outputs of the neural network comprise real or complex valued gains, or separate real valued gains and real valued phases. The invention may e.g. be used in audio devices, such as hearing aids, headsets, mobile telephones, etc., operating in noisy acoustic environments.