Upcoming phased-array 2-D sensors will soon enable fast high-definition 3-D ultrasound imaging. Currently, the communication of raw radio-frequency (RF) channel data from the probe to the computer for digital beamforming is a bottleneck. For reducing the amount of transferred data samples, this paper investigates the design of an adapted sparse sampling technique for image reconstruction inspired by the compressed sensing framework. Echo responses from isolated points are generated using a physically based simulation of ultrasound wave propagation through tissues. These point spread functions form a dictionary of shift-variant bent waves, which depend on the specific sound excitation and acquisition protocols. Speckled ultrasound images can be approximately decomposed in this dictionary where sparsity is enforced at the system matrix design. The Moore-Penrose pseudoinverse is precomputed and used at the reconstruction stage for fast minimum-norm recovery from nonuniform pseudorandom sampled raw RF data. Results on simulated and acquired phantoms demonstrate the benefits of an optimized basis function design for high-quality B-mode image recovery from few RF channel data samples.