The destriping technique is a viable tool for removing different kinds of systematic effects in CMB related experiments. It has already been proven to work for gain instabilities that produce the so-called 1/f noise and periodic fluctuations due to e.g. thermal instability. Both effects when coupled with the observing strategy result in stripes on the observed sky region. Here we present a maximum-likelihood approach to this type of technique and provide also a useful generalization. As a working case we consider a data set similar to what the Planck satellite will produce in its Low Frequency Instrument (LFI). We compare our method to those presented in the literature and find some improvement in performance. Our approach is also more general and allows for different base functions to be used when fitting the systematic effect under consideration. We study the effect of increasing the number of these base functions on the quality of signal cleaning and reconstruction. This study is related to Planck LFI activities.
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