Revisiting Atomic Norm Minimization: A Sequential Approach for Atom Identification and Refinement

TL;DR

This paper introduces a novel limit-based formulation of atomic norm minimization that avoids semidefinite programming, enabling a low-complexity, accurate, and versatile approach for line spectral estimation.

Contribution

The paper presents a new limit-based formulation of ANM, extending its applicability and connecting it with Bayesian methods, along with a low-complexity algorithm called SAIR.

Findings

SAIR outperforms existing methods in accuracy

SAIR offers reduced computational complexity

The formulation extends to general atomic sets

Abstract

Atomic norm minimization (ANM) is a key approach for line spectral estimation (LSE). Most related algorithms formulate ANM as a semidefinite programming (SDP), which incurs high computational cost. In this letter, we revisit the ANM problem and present a novel limit-based formulation, which dissects the essential components of the semidefinite characterization of ANM. Our new formulation does not depend on SDP and can be extended to handle more general atomic sets beyond mixture of complex sinusoids. Furthermore, we reveal the connection between ANM and Bayesian LSE approaches, bridging the gap between these two methodologies. Based on this new formulation, we propose a low-complexity algorithm called Sequential Atom Identification and Refinement (SAIR) for ANM. Simulation results demonstrate that SAIR achieves superior estimation accuracy and computational efficiency compared to other state-of-the-art methods.