In this chapter, we review biomedical applications and breakthroughs via leveraging algorithm unrolling, an important technique that bridges between traditional iterative algorithms and modern deep learning techniques. To provide context, we start by tracing the origin of algorithm unrolling and providing a comprehensive tutorial on how to unroll iterative algorithms into deep networks. We then extensively cover algorithm unrolling in a wide variety of biomedical imaging modalities and delve into several representative recent works in detail. Indeed, there is a rich history of iterative algorithms for biomedical image synthesis, which makes the field ripe for unrolling techniques. In addition, we put algorithm unrolling into a broad perspective, in order to understand why it is particularly effective, and discuss recent trends. Finally, we conclude the chapter by discussing open challenges and suggesting future research directions.

From unconditional synthesis to conditional synthesis, GANs have shown that they are a perfect fit for such problems thanks to their ability to learn probability distributions. For unconditional synthesis, the objective is to stochastically generate MR images of target contrast. Conditional synthesis refers to the case where the model learns nonlinear mapping to the different MR tissue contrasts without altering the physiological information. Furthermore, by merging collaborative information of multiple contrast images, missing data imputation among many different domains is also effectively solved with GANs. Although promising results are seen, development in the area is still at its early stage. Interesting research directions are proposed from prior work, including the application of more advanced methods and rigorous validation in clinical settings. In effect, MRI image synthesis techniques should be able to reduce the burden of costly MR scans, benefiting both patients and hospitals.

The development of deep learning reconstruction methods for accelerated MR acquisitions has been an ongoing area of research for the last several years. It has been repeatedly demonstrated that deep learning methods can outperform classic reconstruction approaches in terms of both quantitative image metrics like MSE to ground truth as well as qualitative reader studies where radiologists have been questioned in a subjective way. We present the basics and well-known approaches for MR image reconstruction via deep learning.

In this chapter, we review largely targeted tasks in the computed tomography (CT) literature, including low-dose CT, sparse-view CT, limited angle CT, interior CT, etc. We present deep-learning-based methods which operate as image post-processing techniques or raw-to-image mapping techniques.

This chapter provides a summary of some popular model-based deep learning methods and their extensions. Section 8.1 briefly describes classical model-based methods and their benefit as well as limitations. Section 8.2 describes how deep learning can help in overcoming some limitations of classical model-based methods. Section 8.3 discusses how to incorporate a pre-trained deep network as a regularizer using the plug-and-play approach. Section 8.4 describes end-to-end training using a model-based deep learning framework. This section also discusses some benefits and limitations of end-to-end training. Section 8.5 and 8.6 describe unsupervised model-based deep learning approaches when a clean training dataset is not available. Section 8.6 considers model mismatch issues as well as the joint design of acquisition and reconstruction frameworks.

With the present demand for high-quality image reconstruction and signal extraction from less (e.g., unfocused or parallel) transmissions that facilitate fast imaging, and the push towards compact probes, modern ultrasound imaging leans heavily on innovations in powerful digital receive channel processing. Beamforming, the process of mapping received ultrasound echoes to the spatial image domain, naturally lies at the heart of the ultrasound image formation chain. In this chapter, we discuss why and when deep learning methods can play a compelling role in the digital beamforming pipeline, and then show how these data-driven systems can be leveraged for improved ultrasound image reconstruction.

This chapter focuses on biomedical image reconstruction methods at the intersection of MBIR and machine learning. After briefly reviewing classical MBIR methods for image reconstruction, we discuss the combination of MBIR with unsupervised learning, supervised learning, or both. Such combinations offer potential advantages for learning even with limited data.

In this chapter, we show that image-domain deep-learning-only reconstruction methods have intrinsic limitations in reconstruction accuracy and generalizability to individual patients owing to the regressive nature of the method. The combination of deep learning methods with analytic reconstruction methods or statistical IR methods offers a promising opportunity to achieve personalized reconstruction with improved reconstruction accuracy and enhanced generalizability.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks.

The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks.

The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks.

The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks.

The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.