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Detection and classification are key issues in processing hyperspectral images (HSIs). Spectral-identification-based algorithms are sensitive to spectral variability and noise in acquisition. In this paper, we propose two detection algorithms that are robust to noise. These algorithms consist in integrating spatial/spectral filtering into the adaptive matched filter and adaptive coherence/cosine estimator. Considering the HSI as tensor data, our approach introduces a data representation involving multilinear algebra. It combines the advantages of spatial and spectral information using an alternating least squares algorithm. To estimate the signal subspace dimension in each mode, we extended the Akaike information criterion and the minimum description length criterion. We demonstrate that integrating a multiway restoration leads to significant improvement of the detection probability. The performance of our method is exemplified using simulated and real-world Hyperspectral Digital Imagery Collection Experiment images.