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In this paper we consider the tracking problem of a moving target competing against noise and clutter in a surveillance radar scenario. For a single array-antenna multiple-target tracking system and according to the Track-Before-Detect paradigm, we present a novel approach based on a three-stage processing chain that involves the Sparse Learning via Iterative Minimization algorithm, the <i>k-means</i> clustering method and the ad hoc detector by exploiting the sparse nature of the operating scenario. Under the latter assumption, the detection strategy declares the presence of targets subsequently to the retrieval of their corresponding tracks performed by jointly processing the received echoes of multiple consecutive radar scans. Simulation results show that the proposed approach is able to provide good tracking and detection capabilities for different multiple target trajectories with low Signal-to-Interference-plus-Noise ratio and results in providing advantages when compared to a number of other reference Track-Before-Detect strategies based on sparse data processing techniques.