Fast and Accurate Linear Fitting for Incompletely Sampled Gaussian Function With a Long Tail

TL;DR

This paper introduces a fast and precise method for fitting Gaussian functions to data, especially when the data is incomplete and has a long tail, improving accuracy and efficiency in various scientific applications.

Contribution

The paper presents a novel linear fitting technique tailored for incomplete Gaussian data with long tails, enhancing speed and accuracy over existing methods.

Findings

Achieves faster fitting with comparable or better accuracy.

Effectively handles incomplete data with long tails.

Applicable across multiple scientific disciplines.

Abstract

Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data fitting into estimating the unknown parameters of a function. Among analytical functions for data fitting, Gaussian function is the most widely used one due to its extensive applications in numerous science and engineering fields. To name just a few, Gaussian function is highly popular in statistical signal processing and analysis, thanks to the central limit theorem [1]; Gaussian function frequently appears in the quantum harmonic oscillator, quantum field theory, optics, lasers, and many other theories and models in Physics [2]; moreover, Gaussian function is widely applied in chemistry for depicting molecular orbitals, in computer science for imaging processing and in artificial intelligence for defining neural networks.