Targets of interest in urban applications often include relatively small objects such as chairs, tables, doors, and potential contraband such as handheld weapons. Therefore, radar imaging and classification of these objects can impose extremely high bandwidth and aperture requirements. Regarding the radar bandwidth, the typical manner of obtaining wideband waveforms is to implement swept or stepped waveforms that are instantaneously narrowband, but cover a wide bandwidth over time. On the other hand, some operational scenarios require relatively fast data collection and instantaneously wideband waveforms, which necessitate either expensive high-speed analog-to-digital converters or compressive, sub-Nyquist sampling. In this chapter, we investigate sub-Nyquist sampling of instantaneously wideband waveforms. Our objective is to optimize analog compression kernels for the underlying goals of imaging and/or recognition of small objects of interest in urban scenarios. We use Gaussian mixture models to represent prior information about a wide variety of target objects while also admitting (1) gradient-based optimization of the compression kernels and (2) injection of prior knowledge of the urban scenario. The models are trained using finite-difference time-domain (FDTD)-generated target signatures. Moreover, interfering objects such as walls between the radar and target are also incorporated into the optimization. Simulated performance of optimized kernels is compared with the performance of random-based compression and with Nyquist sampling of reduced-bandwidth waveforms.