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We present a Wiener filtering based algorithm for the elimination of motion artifacts present in Near Infrared (NIR) spectroscopy measurements. Until now, adaptive filtering was the only technique used in the noise cancellation in NIR studies. The results in this preliminary study revealed that the proposed method gives better estimates than the classical adaptive filtering approach without the need for additional sensor measurements. Moreover, this novel technique has the potential to filter out motion artifacts in functional near infrared (fNIR) signals, too.