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This study considers censoring outliers in a radar scenario with limited sample support. The problem is formulated as obtaining the regularised maximum likelihood (RML) estimate of the outlier index set. Since the RML estimate involves solving a combinatorial optimisation problem, a reduced complexity but approximate RML (ARML) procedure is also devised. As to the selection of the regularisation parameter, the cross-validation technique is exploited. At the analysis stage, the performance of the RML/ARML procedure is evaluated based both on simulated and challenging knowledge-aided sensor signal processing and expert reasoning data, also in comparison with some other outlier excision methods available in the open literature. The numerical results highlight that the RML/ARML algorithm achieves a satisfactory performance level in the presence of limited as well as sufficient sample supports whereas the other counterparts often experience a certain performance degradation for the insufficient training volume.