Sparse signal representation and approximation has received a lot of attention during the last few years. This is due to its applicability and high performance in many applications of signal processing. In this paper, we propose a new detection method based on sparse decomposition in a union of subspaces (UoS) model. In addition to robustness against stationary noise, our proposed method has robustness against outlier interference and non-stationary noise. Our proposed detector uses a dictionary that can be interpreted as a bank of matched subspaces. This improves the performance of signal detection regarding generalization of the detector. We demonstrate the high efficiency of our method in two cases including radar signal detection and voice activity detection in speech processing.
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