Sparse recovery over continuous dictionaries-just discretize

In many applications of sparse recovery, the signal has a sparse representation only with respect to a continuously parameterized dictionary. Although atomic norm minimization provides a general framework to handle sparse recovery over continuous dictionaries, the computational aspects largely remain unclear. By establishing various convergence results as the discretization gets finer, we promote discretization as a universal and effective way to approximately solve the atomic norm minimization problem, especially when the dimension of the parameter space is low.