In recent years, the Ground Penetrating Radar (GPR) has successfully been applied to the problem of buried threat detection (BTD). A large body of research has focused on using computerized algorithms to automatically discriminate between buried threats and subsurface clutter in GPR data. For this purpose, the GPR data is frequently treated as an image of the subsurface, within which the reflections associated with targets often appear with a characteristic shape. In recent years, shape descriptors from the natural image processing literature have been applied to buried threat detection, and the histogram of oriented gradient (HOG) feature has achieved state-of-the-art performance. HOG consists of computing histograms of the image gradients in disjoint square regions, which we call pooling regions, across the GPR images. In this work we create a large body of potential pooling regions and use the group LASSO (GLASSO) to choose a subset of the pooling regions that are most appropriate for BTD on GPR data. We examined this approach on a large collection of GPR data using lane-based cross-validation, and the results indicate that GLASSO can select a subset of pooling regions that lead to superior performance to the original HOG feature, while simultaneously also reducing the total number of features needed. The selected pooling regions also provide insight about the regions in GPR images that are most important for discriminating threat and nonthreat data.