In this paper, we consider the problem of hyperspectral image denoising. Current denoising is based on multichannel restoration filters assuming the separability of the signal covariance, which describes the between-channel and within-channel relationships. We propose a new algorithm for a spectral band restoration scheme, the adaptive multidimensional Wiener filter, based on a local signal model, without assuming spectral and spatial separability. The proposed filter can be applied as a preprocessing step for detection in hyperspectral imagery. We highlight the target detection improvement when the developed method is used before existing methods the well-known hyperspectral imagery detectors as: AMF (Adaptive Matched Filter), ACE (Adaptive coherence/cosine Estimator) and RX (Reed and Xiaoli algotithm). We demonstrate that integrating a multidimensional restoration leads to significant improvement of the detection probability. The performance of our method is exemplified using real-world HYDICE images.