Identifiability through special linear measurements

TL;DR

This paper proves that a point on an algebraic variety can be uniquely identified using a minimal number of generic linear measurements, which is one more than the variety's dimension, highlighting the sharpness of this bound.

Contribution

The authors establish a minimal measurement threshold for unique identifiability on algebraic varieties, improving understanding of measurement sufficiency in algebraic geometry.

Findings

Unique identification with im X + 1 measurements

im X measurements are generally insufficient

The result is sharp, as demonstrated by examples

Abstract

We show that one can always identify a point on an algebraic variety $X$ uniquely with $\dim X +1$ generic linear measurements taken themselves from a variety under minimal assumptions. As illustrated by several examples the result is sharp, that is, $\dim X$ measurements are in general not enough for unique identifiability.