A Note on Shift Retrieval Problems

TL;DR

This paper explores classical and compressed shift retrieval problems, demonstrating how circulant matrices can be used to recover shifts from a single measurement, thus connecting different approaches in the field.

Contribution

It establishes a link between classical and compressed shift retrieval problems using circulant matrices and shows how shifts can be recovered efficiently from minimal measurements.

Findings

Shift retrieval problems can be connected via circulant matrices.

Shifts can be recovered from a single measurement using properties of circulant matrices.

The paper provides theoretical insights into the properties of circulant matrices for shift recovery.

Abstract

In this note, we discuss the shift retrieval problems, both classical and compressed, and provide connections between them using circulant matrices. We review the properties of circulant matrices necessary for our calculations and then show how shifts can be recovered from a single measurement.