Recovery of Missing Samples with Sparse Approximations

In most missing samples problems, the signals are assumed to be bandlimited. That is, the signals are assumed to be sparsely approximated by a known subset of the discrete Fourier transform basis vectors. We discuss the recovery of missing samples when the signals can be sparsely approximated by an unknown subset of certain unitary basis vectors. We propose the use of the orthogonal matching pursuit to recover missing samples by sparse approximations.