Diffuse arrays that autocorrelate and project as delta-like points

TL;DR

This paper introduces diffuse 2D arrays with delta-like autocorrelation and projections, enabling precise localization through simple intersection of projected rays, complementing traditional autocorrelation methods.

Contribution

The work presents a novel class of arrays with delta-like autocorrelation and projections, facilitating efficient and accurate array localization.

Findings

Arrays exhibit delta-like autocorrelation and projections

Localization achieved via intersection of projected rays

Method complements autocorrelation-based localization

Abstract

Diffuse two-dimensional integer-valued arrays are demonstrated that have delta-like aperiodic autocorrelation and, simultaneously, the array sums form delta-like projections along several directions. The delta-projected views show a single sharp spike at the central ray. When such arrays are embedded in larger blocks of two-dimensional data, their location can be fixed precisely via the fast and simple intersection of the back-projected central rays along two or more directions. This mechanism complements localization of the same array from its delta-like autocorrelation, which, although more robust, is slower and more complex to compute.