Compressive Shift Retrieval

TL;DR

This paper introduces a compressive sensing approach to shift retrieval, enabling accurate shift estimation from fewer samples, especially from Fourier coefficients, with potential computational advantages over classical methods.

Contribution

It demonstrates that shift can be recovered directly from compressed signals, often with just one Fourier coefficient, under mild conditions, improving efficiency.

Findings

Shift can be estimated from fewer samples using compressive sensing.

Only one Fourier coefficient may suffice for accurate shift recovery.

The method reduces computational complexity compared to classical approaches.

Abstract

The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift.