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Noise reduction is an important preprocessing step to analyze the information in the hyperspectral image (HSI). Because the common filtering methods for HSIs are based on the data vectorization or matricization while ignoring the related information between image planes, there are new approaches considering multidimensional data as whole entities, for example, multidimensional Wiener filtering (MWF) based on Tucker3 tensor decomposition. However, if HSIs are not disturbed by white noise, MWF cannot effectively remove the nonwhite noise and obtain the expected signal. To reduce nonwhite noise from HSIs, a new method is proposed in this letter. The first step of this method is to whiten the noise in HSIs through a prewhitening procedure. Then, MWF can help to denoise the prewhitened data. At last, an inverse prewhitening process can rebuild the estimated signal. Comparative studies with existing denoising methods show that the proposed approach has promising prospects in this field.