Phaseless super-resolution in the continuous domain

TL;DR

This paper introduces a novel SDP-based method for phaseless super-resolution of continuous-domain sparse signals, extending previous grid-based approaches to signals with arbitrary continuous locations.

Contribution

It proposes a new approach for continuous-domain phaseless super-resolution using semidefinite programming, broadening the scope beyond discrete grid signals.

Findings

Successfully recovers sparse Dirac delta functions in continuous domain

Extends prior grid-based super-resolution methods to continuous signals

Demonstrates effectiveness through theoretical analysis and experiments

Abstract

Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac delta functions which can be located anywhere in the continuous time-domain. For such signals in the continuous domain, we propose a novel Semidefinite Programming (SDP) based signal recovery method to achieve the phaseless superresolution. This work extends the recent work of Jaganathan et al. [1], which considered phaseless super-resolution for discrete signals on the grid.