Toeplitz Unlabeled Sensing

TL;DR

This paper investigates the problem of recovering vectors from subspaces with Toeplitz structure under unknown permutations, advancing understanding of unlabeled sensing in structured subspaces.

Contribution

It introduces a novel analysis of unlabeled sensing specifically for Toeplitz subspaces, highlighting unique challenges and solutions for this structured class.

Findings

Characterization of conditions for successful recovery

Development of algorithms tailored for Toeplitz subspace sensing

Theoretical bounds on permutation recovery accuracy

Abstract

Unlabeled sensing is the problem of recovering an element of a vector subspace of R^n, from its image under an unknown permutation of the coordinates and knowledge of the subspace. Here we study this problem for the special class of subspaces that admit a Toeplitz basis.