Information-optimal measurement: From fixed sampling protocols to adaptive spectroscopy

TL;DR

This paper introduces a new framework for information-optimal measurement that leverages prior knowledge to surpass traditional sampling limits, demonstrated through adaptive spectroscopy in various scientific and medical applications.

Contribution

It develops a rigorous statistical framework for adaptive measurement, enabling devices to operate as information-optimal agents and improve data collection efficiency.

Findings

Adaptive measurements outperform fixed protocols in information gain.

Performance guarantees match or exceed traditional sampling methods.

Real-time uncertainty quantification enhances measurement reliability.

Abstract

All measurements of continuous signals rely on taking discrete snapshots, with the Nyquist-Shannon theorem dictating sampling paradigms. We present a broader framework of information-optimal measurement, showing that traditional sampling is optimal only when we are entirely ignorant about the system under investigation. This insight unlocks methods that efficiently leverage prior information to overcome long-held fundamental sampling limitations. We demonstrate this for optical spectroscopy - vital to research and medicine - and show how adaptively selected measurements yield higher information in medical blood analysis, optical metrology, and hyperspectral imaging. Through our rigorous statistical framework, performance never falls below conventional sampling while providing complete uncertainty quantification in real time. This establishes a new paradigm where measurement devices operate as information-optimal agents, fundamentally changing how scientific instruments collect and process data.