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

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 with noisy labels: exploring techniques and remedies in medical image analysis

Commercial iterative reconstruction techniques help to reduce CT radiation dose but altered image appearance and artifacts limit their adoptability and potential use. Deep learning has been investigated for low-dose CT (LDCT). Here we design a modularized neural network for LDCT and compared it with commercial iterative reconstruction methods from three leading CT vendors. While popular networks are trained for an end-to-end mapping, our network performs an end-to-process mapping so that intermediate denoised images are obtained with associated noise reduction directions towards a final denoised image. The learned workflow allows radiologists-in-the-loop to optimize the denoising depth in a task-specific fashion. Our network was trained with the Mayo LDCT Dataset, and tested on separate chest and abdominal CT exams from Massachusetts General Hospital. The best deep learning reconstructions were systematically compared to the best iterative reconstructions in a double-blinded reader study. This study confirms that our deep learning approach performed either favorably or comparably in terms of noise suppression and structural fidelity, and is much faster than the commercial iterative reconstruction algorithms.

Competitive performance of a modularized deep neural network compared to commercial algorithms for low-dose CT image reconstruction.

In this paper, we present a semi-supervised deep learning approach to accurately recover high-resolution (HR) CT images from low-resolution (LR) counterparts. Specifically, with the generative adversarial network (GAN) as the building block, we enforce the cycle-consistency in terms of the Wasserstein distance to establish a nonlinear end-to-end mapping from noisy LR input images to denoised and deblurred HR outputs. We also include the joint constraints in the loss function to facilitate structural preservation. In this process, we incorporate deep convolutional neural network (CNN), residual learning, and network in network techniques for feature extraction and restoration. In contrast to the current trend of increasing network depth and complexity to boost the imaging performance, we apply a parallel ${1}\times {1}$ CNN to compress the output of the hidden layer and optimize the number of layers and the number of filters for each convolutional layer. The quantitative and qualitative evaluative results demonstrate that our proposed model is accurate, efficient and robust for super-resolution (SR) image restoration from noisy LR input images. In particular, we validate our composite SR networks on three large-scale CT datasets, and obtain promising results as compared to the other state-of-the-art methods.

CT Super-Resolution GAN Constrained by the Identical, Residual, and Cycle Learning Ensemble (GAN-CIRCLE)

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.

Jong Chu Ye

Papers

Image Reconstruction is a New Frontier of Machine Learning