This disclosure is directed to processes and systems that generate enhanced-resolution seismic images by interpolating sparsely recorded seismic data. Structured dictionary learning is employed to train a set of basis vectors, called “atoms,” and corresponding sparse coefficients on patches of the recorded seismic data. The atoms are constrained to represent the geometric structure of reflection events in the recorded seismic data gather. Linear combinations of the atoms are used to compute interpolated patches over a finer receiver-coordinate grid. The interpolated patches replace the original patches in the recorded seismic data to obtain interpolated seismic data that can be used to generate an image of the subterranean formation.