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

TL;DR

This paper introduces a reweighted atomic norm minimization method that iteratively enhances sparsity and resolution, enabling super-resolution of sparse frequency spectra even with closely spaced frequencies.

Contribution

The paper proposes a novel reweighted atomic norm minimization approach that overcomes the resolution limitations of existing methods, achieving high resolution in super-resolution tasks.

Findings

The proposed RAM method improves resolution in super-resolution tasks.

Analytical and numerical results confirm high-resolution capabilities.

Application demonstrated in DOA estimation.

Abstract

The super-resolution theory developed recently by Cand\`{e}s 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.