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Traditional outlier detection methods such as the minimum volume ellipsoid method and MCD method are all based on normal distance. As is well known, the norm-based distance is only effective in detecting difference with dense signals. However, these existing approaches will encounter detection power loss under the sparse signals settings. In this paper, we try to solve the problem of detecting outliers under the sparsity assumption by adapting the thresholding method. The proposed outlier detection procedure finds the clean set by the minimum diagonal product algorithm, then the maximum thresholding statistic is employed to identify the outlier. The finite sample performance of our method is evaluated through simulations. Compared with the existing outlier detection methods, simulation results show that our proposed outlier detection procedure is very efficient under sparse settings. [ABSTRACT FROM AUTHOR]