# Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks

## TL;DR

This tutorial reviews the evolution of biomedical image reconstruction methods from traditional techniques to modern deep learning approaches, highlighting common principles and the integration of different generations.

## Contribution

It unifies diverse research on biomedical image reconstruction, clarifies connections between classical, sparsity-based, and learning-based methods, and provides a comprehensive framework for understanding their development.

## Key findings

- Classical methods serve as modules in modern algorithms
- Deep learning approaches outperform traditional techniques
- Unified framework aids in designing advanced reconstruction algorithms

## Abstract

This tutorial covers biomedical image reconstruction, from the foundational concepts of system modeling and direct reconstruction to modern sparsity and learning-based approaches. Imaging is a critical tool in biological research and medicine, and most imaging systems necessarily use an image-reconstruction algorithm to create an image; the design of these algorithms has been a topic of research since at least the 1960's. In the last few years, machine learning-based approaches have shown impressive performance on image reconstruction problems, triggering a wave of enthusiasm and creativity around the paradigm of learning. Our goal is to unify this body of research, identifying common principles and reusable building blocks across decades and among diverse imaging modalities. We first describe system modeling, emphasizing how a few building blocks can be used to describe a broad range of imaging modalities. We then discuss reconstruction algorithms, grouping them into three broad generations. The first are the classical direct methods, including Tikhonov regularization; the second are the variational methods based on sparsity and the theory of compressive sensing; and the third are the learning-based (also called data-driven) methods, especially those using deep convolutional neural networks. There are strong links between these generations: classical (first-generation) methods appear as modules inside the latter two, and the former two are used to inspire new designs for learning-based (third-generation) methods. As a result, a solid understanding of all of three generations is necessary for the design of state-of-the-art algorithms.