Achieving Super-Resolution in Multi-Rate Sampling Systems via Efficient Semidefinite Programming

TL;DR

This paper demonstrates that super-resolution techniques can precisely recover spectral components in multi-rate sampling systems using a semidefinite programming approach, under certain conditions like a common grid and minimal separation.

Contribution

It introduces a novel SDP-based method for joint spectral recovery in multi-rate systems, extending Gram parametrization for minimal complexity.

Findings

Exact joint frequency recovery under minimal separation

Development of an equivalent low-dimensional SDP

Analysis of algorithmic complexity for practical implementation

Abstract

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in multi-rate sampling systems. It shows that, under the existence of a common supporting grid, and under a minimal separation constraint, the frequencies of a spectrally sparse signal can be exactly jointly recovered from the output of a semidefinite program (SDP). The algorithmic complexity of this approach is discussed, and an equivalent SDP of minimal dimension is derived by extending the Gram parametrization properties of sparse trigonometric polynomials.