This paper addresses the problem of feature selection for the classification of ground penetrating radar signals. We propose a new classification approach based on time-frequency analysis and sparse kernel feature selection. In the proposed approach, a time-frequency or a time-scale transform is first applied to the one-dimensional radar trace. Sparse kernel feature selection is then employed to extract an optimum set of features for classification. The sparse kernel method is formulated as an underdetermined linear system in a high-dimensional space, and the category labels of the training samples are used as measurements to select the most informative features. The proposed approach is evaluated through an industrial application of assessing railway ballast fouling conditions. Experimental results show that the proposed combination of sparse kernel feature selection and support vector machine classification yields very high classification rates using only a small number of features.