Achieving High Resolution for Super-resolution via Reweighted Atomic Norm Minimization
arXiv:1410.4319
Abstract
The super-resolution theory developed recently by Candès and Fernandes-Granda aims to recover fine details of a sparse frequency spectrum from coarse scale information only. The theory was then extended to the cases with compressive samples and/or multiple measurement vectors. However, the existing atomic norm (or total variation norm) techniques succeed only if the frequencies are sufficiently separated, prohibiting commonly known high resolution. In this paper, a reweighted atomic-norm minimization (RAM) approach is proposed which iteratively carries out atomic norm minimization (ANM) with a sound reweighting strategy that enhances sparsity and resolution. It is demonstrated analytically and via numerical simulations that the proposed method achieves high resolution with application to DOA estimation.
arXiv comment5 pages, 3 figures, submitted to ICASSP 2015, Brisbane, Australia, April 2015