Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

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Solving inverse problems using data-driven models

Over past several years, machine learning, or more generally artificial intelligence, has generated overwhelming research interest and attracted unprecedented public attention. As tomographic imaging researchers, we share the excitement from our imaging perspective [item 1) in the Appendix], and organized this special issue dedicated to the theme of “Machine learning for image reconstruction.” This special issue is a sister issue of the special issue published in May 2016 of this journal with the theme “Deep learning in medical imaging” [item 2) in the Appendix]. While the previous special issue targeted medical image processing/analysis, this special issue focuses on data-driven tomographic reconstruction. These two special issues are highly complementary, since image reconstruction and image analysis are two of the main pillars for medical imaging. Together we cover the whole workflow of medical imaging: from tomographic raw data/features to reconstructed images and then extracted diagnostic features/readings.

Image Reconstruction is a New Frontier of Machine Learning

This paper tries to give a gentle introduction to deep learning in medical image processing, proceeding from theoretical foundations to applications. We first discuss general reasons for the popularity of deep learning, including several major breakthroughs in computer science. Next, we start reviewing the fundamental basics of the perceptron and neural networks, along with some fundamental theory that is often omitted. Doing so allows us to understand the reasons for the rise of deep learning in many application domains. Obviously medical image processing is one of these areas which has been largely affected by this rapid progress, in particular in image detection and recognition, image segmentation, image registration, and computer-aided diagnosis. There are also recent trends in physical simulation, modeling, and reconstruction that have led to astonishing results. Yet, some of these approaches neglect prior knowledge and hence bear the risk of producing implausible results. These apparent weaknesses highlight current limitations of deep ()learning. However, we also briefly discuss promising approaches that might be able to resolve these problems in the future.

A gentle introduction to deep learning in medical image processing

Deep-learning-based tomographic imaging is an important application of artificial intelligence and a new frontier of machine learning. Deep learning has been widely used in computer vision and image analysis, which deal with existing images, improve these images, and produce features from them. Since 2016, deep learning techniques have been actively researched for tomographic imaging, especially in the context of biomedicine, with impressive results and great potential. Tomographic reconstruction produces images of multi-dimensional structures from externally measured ‘encoded’ data in the form of various tomographic transforms (integrals, harmonics, echoes and so on). In this Review, we provide a general background, highlight representative results with an emphasis on medical imaging, and discuss key issues that need to be addressed in this emerging field. In particular, tomographic imaging is an integral part of modern medicine, and will play a key role in personalized, preventive and precision medicine and make it intelligent, inexpensive and indiscriminate. The popularity of deep learning is leading to new areas in biomedical applications. Wang and colleagues summarize in this Review the recent development and future directions of deep neural networks for superior image quality in the tomographic imaging field.

Deep learning for tomographic image reconstruction

This paper tries to give a gentle introduction to deep learning in medical image processing, proceeding from theoretical foundations to applications. We first discuss general reasons for the popularity of deep learning, including several major breakthroughs in computer science. Next, we start reviewing the fundamental basics of the perceptron and neural networks, along with some fundamental theory that is often omitted. Doing so allows us to understand the reasons for the rise of deep learning in many application domains. Obviously medical image processing is one of these areas which has been largely affected by this rapid progress, in particular in image detection and recognition, image segmentation, image registration, and computer-aided diagnosis. There are also recent trends in physical simulation, modelling, and reconstruction that have led to astonishing results. Yet, some of these approaches neglect prior knowledge and hence bear the risk of producing implausible results. These apparent weaknesses highlight current limitations of deep learning. However, we also briefly discuss promising approaches that might be able to resolve these problems in the future.

A Gentle Introduction to Deep Learning in Medical Image Processing

In this paper, we present a new deep learning framework for 3-D tomographic reconstruction. To this end, we map filtered back-projection-type algorithms to neural networks. However, the back-projection cannot be implemented as a fully connected layer due to its memory requirements. To overcome this problem, we propose a new type of cone-beam back-projection layer, efficiently calculating the forward pass. We derive this layer’s backward pass as a projection operation. Unlike most deep learning approaches for reconstruction, our new layer permits joint optimization of correction steps in volume and projection domain. Evaluation is performed numerically on a public data set in a limited angle setting showing a consistent improvement over analytical algorithms while keeping the same computational test-time complexity by design. In the region of interest, the peak signal-to-noise ratio has increased by 23%. In addition, we show that the learned algorithm can be interpreted using known concepts from cone beam reconstruction: the network is able to automatically learn strategies such as compensation weights and apodization windows.

Yixin Huang

Papers

Deep Learning Computed Tomography: Learning Projection-Domain Weights From Image Domain in Limited Angle Problems