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This article proposes model-based homogeneity (MBH) to extend compressed sensing (CS) for landmine-detection ground penetrating radar (GPR). Conventional CS methods have difficulty in distinguishing landmines from clutter, since it principally pays attention to signal magnitude. In contrast, our method visualizes landmines based on homogeneity of high-dimensional scattering features in a spatial model. It realizes both the exclusion of clutter and the reduction of measurement points. Experiments demonstrate that the total measurement and processing time are reduced to one-twentieth of a conventional dense measurement case. We also investigate the influence of model size and number of landmines on the performance. The proposed method is capable of visualizing any objects having respective shapes by configuring corresponding models. [ABSTRACT FROM AUTHOR]