1. A method comprising: estimating noise basis vectors with respect to a noise signal that is received from a first sensor of a communication device that is configured to be distal a mouth of a user during operation of the communication device to provide a noise model that represents noise provided by audio sources other than the user; estimating speech basis vectors, speech weights that correspond to the speech basis vectors, and noise weights that correspond to the noise basis vectors based on a noisy speech signal that is received from a second sensor of the communication device that is configured to be proximate the mouth of the user during the operation of the communication device and further based on the noise basis vectors using a non-negative matrix factorization technique, the noisy speech signal representing a combination of speech and the noise; and estimating a clean speech signal based on the speech basis vectors and the speech weights, the clean speech signal representing the speech without the noise.