Techniques for processing audio signals include removing noise from the audio signals or otherwise clarifying the audio signals prior to outputting the audio signals. The disclosed techniques may employ minimum mean squared error (MMSE) analyses on audio signals received from a primary microphone and at least one reference microphone, and to techniques in which the MMSE analyses are used to reduce or eliminate noise from audio signals received by the primary microphone. Optionally, confidence intervals may be assigned to different frequency bands of an audio signal, with each confidence interval corresponding to a likelihood that its respective frequency band includes targeted audio, and each confidence interval representing a contribution of its respective frequency band in a reconstructed audio signal from which noise has been removed.