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The super-resolution theory developed recently by Cand\`{e}s andFernandes-Granda aims to recover fine details of a sparse frequency spectrumfrom coarse scale information only. The theory was then extended to the caseswith compressive samples and/or multiple measurement vectors. However, theexisting atomic norm (or total variation norm) techniques succeed only if thefrequencies are sufficiently separated, prohibiting commonly known highresolution. In this paper, a reweighted atomic-norm minimization (RAM) approachis proposed which iteratively carries out atomic norm minimization (ANM) with asound reweighting strategy that enhances sparsity and resolution. It isdemonstrated analytically and via numerical simulations that the proposedmethod achieves high resolution with application to DOA estimation.

Achieving High Resolution for Super-resolution via Reweighted Atomic Norm Minimization