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A hyperspectral imaging sensor can reveal and uncover targets with very narrow diagnostic wavelengths. However, it comes at a price that it can also extract many unknown signal sources such as background and natural signatures as well as unwanted man-made objects, which cannot be identified visually or a priori. These unknown signal sources can be referred to as interferers, which generally play a more dominant role than noise in hyperspectral image analysis. Separating such interferers from signals and annihilating them subsequently prior to detection may be a more realistic approach. In many applications, the signals of interest can be further divided into desired signals for which we want to extract and undesired signals for which we want to eliminate to enhance signal detectability. This paper presents a signal-decomposed and interference-annihilated (SDIA) approach in applications of hyperspectral target detection. It treats interferers and undesired signals as separate signal sources that can be eliminated prior to target detection. In doing so, a signal-decomposed interference/noise (SDIN) model is suggested in this paper. With the proposed SDIN model, the orthogonal subspace projection-based model and the signal/background/noise model can be included as its special cases. As shown in the experiments, the SDIN model-based SDIA approach generally can improve the performance of the commonly used generalized-likelihood ratio test and constrained energy minimization approach on target detection and classification.