Abstract--The problem of noise reduction using multiple microphones has long been an active area of research. Over the past few decades, most efforts have been devoted to beamforming techniques, which aim at recovering the desired source signal from the outputs of an array of microphones. In order to work reasonably well in reverberant environments, this approach often requires such knowledge as the direction of arrival (DOA) or even the room impulse responses, which are difficult to acquire reliably in practice. In addition, beamforming has to compromise its noise reduction performance in order to achieve speech dereverberation at the same time. This paper presents a new multichannel algorithm for noise reduction, which formulates the problem as one of estimating the speech component observed at one microphone using the observations from all the available microphones. This new approach explicitly uses the idea of spatial