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# Deep Convolutional Neural Network for Inverse Problems in Imaging.

IEEE Transactions on Image Processing, no. 9 (2017): 4509-4522

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Abstract

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practic...More

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Introduction

- Manuscript received November 4, 2016; revised April 10, 2017 and May 24, 2017; accepted May 24, 2017.
- The associate editor coordinating the review of this manuscript and approving it for publication was Prof.
- E. Froustey was with the Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
- Froustey was with the Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- He is with Dassault Aviation, 92210 Saint-Cloud, France

Highlights

- O VER the past decades, iterative reconstruction methods have become the dominant approach to solving inverse

Manuscript received November 4, 2016; revised April 10, 2017 and May 24, 2017; accepted May 24, 2017 - Though the FBPConvNet algorithm is general, we focus here on sparse-view X-ray computed tomography reconstruction
- We compare the results of applying the TV and filtered back projection methods to the subsampled sinogram with the results of applying the FBPConvNet to the same. This type of sparse-view reconstruction is of particular interest for human imaging because, e.g., a twenty times reduction in the number of views corresponds to a twenty times reduction in the radiation dose received by the patient
- We proposed a deep convolutional network for inverse problems with a focus on biomedical imaging
- The structure of the convolutional neural network is based on U-net, with the addition of residual learning
- This approach was motivated by the convolutional structure of several biomedical inverse problems, including computed tomography, magnetic resonance imaging, and diffraction tomography

Methods

- The success of iterative methods consisting of filtering plus pointwise nonlinearities on normal-convolutional inverse problems suggests that CNNs may be a good fit for these problems as well.
- Based on this insight, the authors propose a new approach to these problems, which the authors call the FBPConvNet. B.
- There are several properties of this architecture that recommend it for the purposes

Results

- The authors describe the experimental setup and results. Though the FBPConvNet algorithm is general, the authors focus here on sparse-view X-ray CT reconstruction.
- The authors compare FBPConvNet to FBP alone and a state-of-the-art iterative reconstruction method [14]
- This method solves a version of Eq (1) with the popular TV regularization via ADMM.
- The authors compare the results of applying the TV and FBP methods to the subsampled sinogram with the results of applying the FBPConvNet to the same
- This type of sparse-view reconstruction is of particular interest for human imaging because, e.g., a twenty times reduction in the number of views corresponds to a twenty times reduction in the radiation dose received by the patient.

Conclusion

- The experiments provide strong evidence for the feasibility of the FBPConvNet for sparse-view CT reconstruction.
- The conventional iterative algorithm with TV regularization outperformed the FBPConvNet in the ellipsoidal dataset, while the reverse was true for the biomedical and experimental datasets
- In these more-realistic datasets, the SNR improvement of the FBPConvNet came from its ability to preserve fine details in the images.
- This results suggests that CNNs are well-suited to this subclass of inverse problems

- Table1: COMPARISON OF SNR BETWEEN DIFFERENT RECONSTRUCTION ALGORITHMS FOR NUMERICAL ELLIPSOIDAL DATASET
- Table2: COMPARISON OF SNR BETWEEN DIFFERENT RECONSTRUCTION ALGORITHMS FOR BIOMEDICAL DATASET
- Table3: COMPARISON OF SNR BETWEEN DIFFERENT ARCHITECTURES FOR BIOMEDICAL DATASET
- Table4: COMPARISON OF SNR BETWEEN DIFFERENT RECONSTRUCTION ALGORITHMS FOR EXPERIMENTAL DATASET

Funding

- This work was supported in part by the European Union’s Horizon 2020 Framework Programme for Research and Innovation under Grant 665667 (call 2015), in part by the Center for Biomedical Imaging of the Geneva-Lausanne Universities and EPFL, in part by the European Research Council under Grant 692726 (H2020-ERC Project GlobalBioIm), and in part by the National Institute of Biomedical Imaging and Bioengineering under Grant EB017095 and under Grant EB017185

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- Michael T. McCann (S’10–M’15) received the B.S.E. in biomedical engineering from the University of Michigan in 2010 and the Ph.D. degree in biomedical engineering from Carnegie Mellon University in 2015. He is currently a Scientist with the Laboratoire d’Imagerie biomédicale and centre d’imagerie biomédicale, École Polytechnique Fédérale de Lausanne, where he is involved in X-ray CT reconstruction. His research interest centers on developing signal processing tools to answer biomedical questions.
- Emmanuel Froustey received the Dipl.Eng. degree from CentraleSupélec, Châtenay-Malabry, France, in 2012, and the M.Sc. degree in computational science and engineering from the École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, in 2014. He is currently a Research and Development Engineer with Dassault Aviation. His research interests include variational models and optimization algorithms with applications to biomedical imaging.

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