Regularizing Ill-Posed Inverse Problems: Deblurring Barcodes

Mark Embree

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arXiv · 2505.16045

Regularizing Ill-Posed Inverse Problems: Deblurring Barcodes

Mark Embree

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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).

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Mark Embree. 2025-05-21. Regularizing Ill-Posed Inverse Problems: Deblurring Barcodes. https://arxiv.org/abs/2505.16045

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