This paper presents multichannel Wiener filtering-based algorithms for noise reduction in cochlear implants. In a single speech scenario, the autocorrelation matrix of the speech signal can be approximated by a rank-1 matrix. It is then possible to derive noise reduction filters that deliver improved signal-to-noise ratio performance. The link between these different filters is investigated here and an eigenvalue decomposition based algorithm is demonstrated to be more stable at low input signal-to-noise ratio compared to previous algorithms.