In this chapter we cover clustering and regression, looking at two traditional machine learning methods: k-means and linear regression. We briefly discuss how to implement these methods in a non-distributed manner first, to then carefully analyze the bottlenecks of these methods when manipulating big data. This enables us to design global-based solutions based on the DataFrame API of Spark. The key focus is on the principles for designing solutions effectively. Nevertheless, some of the challenges in this chapter are to investigate tools from Spark to speed up the processing even further. k-means is an example of an iterative algorithm, and how to exploit caching in Spark, and we analyze its implementation with both RDD and DataFrame APIs. For linear regression, we first implement the closed form, which involves numerous matrix multiplications and outer products, to simplify the processing in big data. Then, we look at gradient descent. These examples give us the opportunity to expand on the principles of designing a global solution, and also allow us to show how knowing the underlying platform, Spark in this case, well is essential to really maximize the performance.

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.

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.