Provided are methods and systems for enhancing speech when corrupted by transient noise (e.g., keyboard typing noise). The methods and systems utilize a reference microphone input signal for the transient noise in a signal restoration process used for the voice part of the signal. A robust Bayesian statistical model is used to regress the voice microphone on the reference microphone, which allows for direct inference about the desired voice signal while marginalizing the unwanted power spectral values of the voice and transient noise. Also provided is a straightforward and efficient Expectation-maximization (EM) procedure for fast enhancement of the corrupted signal. The methods and systems are designed to operate easily in real-time on standard hardware, and have very low latency so that there is no irritating delay in speaker response.