Sparse image super-resolution via superset selection and pruning

Abstract

This note extends the superset method for sparse signal recovery from bandlimited measurements to the two-dimensional case. The algorithm leverages translation-invariance of the Fourier basis functions by constructing a Hankel tensor, and identifying the signal subspace from its range space. In the noisy case, this method determines a superset which then needs to undergo pruning. The method displays reasonable robustness to noise, and unlike ℓ [subscript 1] minimization, always succeeds in the noiseless case.