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Deep Learning Techniques for Inverse Problems in Imaging (2005.06001v1)

Published 12 May 2020 in eess.IV, cs.LG, and stat.ML

Abstract: Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy that can be used to categorize different problems and reconstruction methods. Our taxonomy is organized along two central axes: (1) whether or not a forward model is known and to what extent it is used in training and testing, and (2) whether or not the learning is supervised or unsupervised, i.e., whether or not the training relies on access to matched ground truth image and measurement pairs. We also discuss the trade-offs associated with these different reconstruction approaches, caveats and common failure modes, plus open problems and avenues for future work.

Citations (496)

Summary

  • The paper demonstrates how deep learning methods provide effective solutions to inverse imaging problems using both known and partially known forward models.
  • It details the use of supervised, generative, and unsupervised approaches, including methods like CycleGAN and Noise2Noise, to optimize image reconstruction.
  • The research highlights future directions in design optimization, transfer learning, and uncertainty quantification to improve imaging applications.

Overview of Deep Learning Techniques for Inverse Problems in Imaging

This paper addresses the use of deep learning methods to tackle inverse problems in computational imaging, focusing on reconstructing signals from non-invertible observations. The core thesis is that deep neural networks provide viable solutions to various inverse problems, where traditional methods have long relied on optimizing a regularized cost function dependent on known or assumed priors.

Central Themes and Taxonomy

The authors introduce a taxonomy based on two primary axes:

  1. Knowledge of the Forward Model: The approach distinguishes between scenarios where the forward model is fully known, partially known, or unknown. Incorporating a forward model effectively can reduce the number of training samples required.
  2. Learning Paradigm: The taxonomy categorizes solutions as supervised, using paired ground truths and measurements, or unsupervised, reliant on only unpaired data elements or even some cases solely measurements.

Technical Contributions

The exploration into various methods is substantial, including:

  • Supervised Learning: Where both data and model are known, networks like unrolled optimization structures embed the physics model to reduce computational costs and iterations needed for convergence.
  • Generative Models: Techniques such as Compressed Sensing using Generative Models (CSGM) use neural networks to represent the prior distribution of the image space, improving the efficiency of reconstructions across a range of forward models.
  • Unsupervised Approaches: The paper also examines unsupervised learning opportunities, leveraging methods like CycleGAN for tasks with unpaired data, or techniques such as Noise2Noise when only noisy measurements are available.

Implications and Future Directions

The implications of this research circle back to broadening the efficiency and applicability of deep learning in fields like medical imaging (CT, MRI), microscopy, photography, and geophysics. It suggests that well-tailored deep learning approaches can offer substantial improvements in reconstruction quality and speed over traditional methods.

In terms of future directions, the authors highlight several promising areas for further inquiry:

  • Design Optimization: Using deep learning to optimize system design and forward model selection, such as automated sampling pattern optimization in MRIs.
  • Transfer Learning: Explore how to leverage pre-trained models across different domains, allowing adaptation to new problem settings with minimal retraining.
  • Uncertainty Quantification: Embed uncertainty estimates into reconstructions, ensuring solutions offer insights into confidence and potential ambiguities in the inversions.

Conclusion

The paper presents a structured exploration of deep learning's role in inverse problem-solving within imaging. It provides a comprehensive framework for categorizing approaches and facilitates a deeper understanding of potential trade-offs between learning efficiency and reconstruction fidelity, setting a foundation for ongoing innovation.