Regularizing Ill-Posed Inverse Problems: Deblurring Barcodes
Numerical Analysis
2025-05-23 v1 Numerical Analysis
Abstract
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a calculus problem into a linear algebra problem by discretization. Inverting the blurring process should sharpen up an image; this requires the solution of a system of linear algebraic equations. Solving this linear system of equations turns out to be delicate, as deblurring is an example of an ill-posed inverse problem. To address this challenge, recast the system as a regularized least squares problem (also known as ridge regression).
Cite
@article{arxiv.2505.16045,
title = {Regularizing Ill-Posed Inverse Problems: Deblurring Barcodes},
author = {Mark Embree},
journal= {arXiv preprint arXiv:2505.16045},
year = {2025}
}