When dense clutter appears in certain surveillance areas and once a target enters into the regions, like most tracking algorithm, the random finite set based multi-target tracking (RFS-MTT) filters tend to fail for the tracking task due to larger false alarms and this further results in the loss of all targets. Moreover, the computational cost are greatly increased and this slows down the whole computational speed. To tackle these problems, we propose a sparse algorithm for the clutter measurements under certain threshold of probability of detection. The proposed sparse algorithm is based on the hypothesis testing theory and Chebyshev inequalities for random vector. The final experiment shows that the proposed algorithm could effectively deal with the dense clutter issues for the RFS-MTT filters.