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The noise reduction problem is traditionally approached in the time, frequency, or transform domain. Having a signal dependent transform has shown some advantages over the traditional signal independent transform. Recently, the single-channel noise reduction problem in the Karhunen-Loève expansion (KLE) domain has received special attention. In this paper, the noise reduction problem in the KLE domain is studied from a multichannel perspective. We present a new formulation of the problem, in which inter-channel and inter-mode correlations are optimally exploited. We derive different optimal noise reduction filters and present a set of useful performance measures within this framework. The performance of the different filters is then evaluated through experiments in which not only noise but also competing speech sources are present. It is shown that the proposed multichannel formulation is more robust to competing speech sources than the single-channel approach and that a better compromise between noise reduction and speech distortion can be obtained.