Regulariza\c{c}\~ao, aprendizagem profunda e interdisciplinaridade em problemas inversos mal-postos

TL;DR

This book explores the concept of ill-posed problems and the role of regularization across various fields like inverse problems, statistics, and deep learning, emphasizing interdisciplinary approaches and future perspectives.

Contribution

It provides a comprehensive discussion on regularization methods, their origins, and applications across multiple disciplines, highlighting interdisciplinary connections.

Findings

Regularization is essential for solving ill-posed problems.

Connections between inverse problems, statistics, and deep learning are emphasized.

Future directions include integrating deep learning with traditional regularization techniques.

Abstract

In this book, written in Portuguese, we discuss what ill-posed problems are and how the regularization method is used to solve them. In the form of questions and answers, we reflect on the origins and future of regularization, relating the similarities and differences of its meaning in different areas, including inverse problems, statistics, machine learning, and deep learning.