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Target detection is a key issue in processing hyperspectral images (HSIs). Spectral-identification-based algorithms are sensitive to spectral variability and noise in acquisition. In most cases, both the target spatial distributions and the spectral signatures are unknown, so each pixel is separately tested and appears as a target when it significantly differs from the background. In this paper, we propose two algorithms to improve the signal-to-noise ratio (SNR) of hyperspectral data, leading to detectors that are robust to noise. These algorithms consist in integrating adaptive spatial/spectral filtering into the adaptive matched filter and adaptive coherence estimator. Considering the HSIs as tensor data, our approach introduces a data representation involving multidimensional processing. It combines the advantages of spatial and spectral information using an alternating least square algorithm. To estimate the signal subspace dimension in each spatial mode, we extend the Akaike information criterion, and we develop an iterative algorithm for spectral-mode rank estimation. We demonstrate the interest of integrating the quadtree decomposition to perform an adaptive 3-D filtering and thereby preserve the local image characteristics. This leads to a significant improvement in terms of denoised tensor SNR and, consequently, in terms of detection probability. The performance of our method is exemplified using simulated and real-world HYperspectral Digital Imagery Collection Experiment images.