Benford Analysis: A useful paradigm for spectroscopic analysis

TL;DR

This paper explores the application of Benford's law to spectroscopic data, demonstrating its utility in detecting weak signals, correcting spectra, and processing MRI images, thus offering a novel analytical paradigm.

Contribution

It introduces the novel use of Benford's law in spectroscopic analysis, including NMR signal detection, spectral correction, and MRI image processing.

Findings

Benford analysis effectively detects weak NMR signals.

It aids in spectral correction processes.

Potential application in MRI image processing.

Abstract

Benford's law is a statistical inference to predict the frequency of significant digits in naturally occurring numerical databases. In such databases this law predicts a higher occurrence of the digit 1 in the most significant place and decreasing occurrences to other larger digits. Although counter-intuitive at first sight, Benford's law has seen applications in a wide variety of fields like physics, earth-science, biology, finance etc. In this work, we have explored the use of Benford's law for various spectroscopic applications. Although, we use NMR signals as our databases, the methods described here may also be extended to other spectroscopic techniques. In particular, with the help of Benford analysis, we demonstrate the detection of weak NMR signals and spectral corrections. We also explore a potential application of Benford analysis in the image-processing of MRI data.