This paper presents low-rank approximation based multichannel Wiener filter algorithms for noise reduction in speech plus noise scenarios, with application in cochlear implants. In a single speech source scenario, the frequency-domain autocorrelation matrix of the speech signal is often assumed to be a rank-1 matrix, which then allows to derive different rank-1 approximation based noise reduction filters. In practice, however, the rank of the autocorrelation matrix of the speech signal is usually greater than one. Firstly, the link between the different rank-1 approximation based noise reduction filters and the original speech distortion weighted multichannel Wiener filter is investigated when the rank of the autocorrelation matrix of the speech signal is indeed greater than one. DRAFT 2 Secondly, in low input signal-to-noise-ratio scenarios, due to noise non-stationarity, the estimation of the autocorrelation matrix of the speech signal can be problematic and the noise reduction filters can deliver unpredictable noise reduction performance. An eigenvalue decomposition based filter and a generalized eigenvalue decomposition based filter are introduced that include a more robust rank-1, or more generally rank-R, approximation of the autocorrelation matrix of the speech signal. These noise reduction filters are demonstrated to deliver a better noise reduction performance especially in low input signal-to-noise-ratio scenarios. The filters are especially usefull in cochlear implants, where more speech distortion and hence a more agressive noise reduction can be tolerated.