A noise attenuation apparatus receives a first signal comprising a desired and a noise signal component. Two codebooks (109, 111) comprise respectively desired signal candidates and noise signal candidates representing possible desired and noise signal components respectively. A noise attenuator (105) generates estimated signal candidates by for each pair of desired and noise signal candidates generating an estimated signal candidate as a combination of the desired signal candidate and the noise signal candidate. A signal candidate is then determined from the estimated signal candidates and the first signal is noise compensated based on this signal candidate. A sensor signal representing a measurement of the desired source or the noise in the environment is used to reduce the number of candidates searched thereby substantially reducing complexity and computational resource usage. The noise attenuation may specifically be audio noise attenuation.