Lecture note on inverse problems and reconstruction methods

TL;DR

This lecture note discusses mathematical methods for solving inverse problems across various disciplines, focusing on challenges like ill-posedness and solution instability in applications such as medical imaging.

Contribution

It provides an overview of inverse problem-solving techniques, emphasizing their interdisciplinary nature and addressing issues like ill-posedness and stability.

Findings

Overview of inverse problem methods

Discussion on ill-posedness and stability

Applications in medical imaging

Abstract

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly observed. Examples include medical imaging techniques such as X-ray CT and optical tomography. Indeed, the mathematics of inverse problems has often originated from challenges posed by other fields. Inverse problems are often ill-posed and solutions are unstable. In this lecture, we will explore methods to solve such inverse problems.