Speech is a fundamental means of human communication. In the last several decades, much effort has been devoted to the efficient transmission and storage of speech signals. With advances in technology making mobile communication ubiquitous, communications anywhere has become a reality. The freedom and flexibility offered by mobile technology brings with it new challenges, one of which is robustness to acoustic background noise. Speech enhancement systems form a vital front-end for mobile telephony in noisy environments such as in cars, cafeterias, subway stations, etc., in hearing aids, and to improve the performance of speech recognition systems. In this thesis, which consists of four research articles, we discuss both single and multi-microphone approaches to speech enhancement. The main contribution of this thesis is a framework to exploit available prior knowledge about both speech and noise. The physiology of speech production places a constraint on the possible shapes of the speech spectral envelope, and this information s captured using codebooks of speech linear predictive (LP) coefficients obtained from a large training database. Similarly, information about commonly occurring noise types is captured using a set of noise codebooks, which can be combined with sound environment classi¯cation to treat different environments differently. In paper A, we introduce maximum-likelihood estimation of the speech and noise LP parameters using the codebooks. The codebooks capture only the spectral shape. The speech and noise gain factors are obtained through a frame-by-frame optimization, providing good performance in practical nonstationary noise environments. The estimated parameters are subsequently used in a Wiener filter. Paper B describes Bayesian minimum mean squared error estimation of the speech and noise LP parameters and functions there-of, while retaining the in- stantaneous gain computation. Both memoryless and memory-based estimators are derived. While papers A and B describe single-channel techniques, paper C describes a multi-channel Bayesian speech enhancement approach, where, in addition to temporal processing, the spatial diversity provided by multiple microphones s also exploited. In paper D, we introduce a multi-channel noise reduction technique motivated by blind source separation (BSS) concepts. In contrast to standard BSS approaches, we use the knowledge that one of the signals is speech and that the other is noise, and exploit their different characteristics. / QC 20100929