Deep Convolutional Neural Network for Inverse Problems in Imaging

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...

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Bibliographic Details
Published in:	IEEE transactions on image processing Vol. 26; no. 9; pp. 4509 - 4522
Main Authors:	Jin, Kyong Hwan, McCann, Michael T., Froustey, Emmanuel, Unser, Michael
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.09.2017
Subjects:	biomedical imaging biomedical signal processing Computed tomography Convolution Image reconstruction Image restoration Inverse problems Iterative methods magnetic resonance imaging Neural networks reconstruction algorithms tomography
ISSN:	1057-7149, 1941-0042, 1941-0042
Online Access:	Get full text
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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 practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (HH, where H is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU.
AbstractList	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 practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (HH, where H is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU. 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 practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (HH, where H is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU.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 practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (HH, where H is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU.
Author	Jin, Kyong Hwan Froustey, Emmanuel Unser, Michael McCann, Michael T.
Author_xml	– sequence: 1 givenname: Kyong Hwan orcidid: 0000-0001-7885-4792 surname: Jin fullname: Jin, Kyong Hwan email: kyonghwan.jin@gmail.com organization: Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland – sequence: 2 givenname: Michael T. orcidid: 0000-0001-7645-252X surname: McCann fullname: McCann, Michael T. email: michael.mccann@epfl.ch organization: Center for Biomedical Imaging, Signal Processing Core and the Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland – sequence: 3 givenname: Emmanuel surname: Froustey fullname: Froustey, Emmanuel organization: Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland – sequence: 4 givenname: Michael surname: Unser fullname: Unser, Michael email: michael.unser@epfl.ch organization: Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/28641250$$D View this record in MEDLINE/PubMed
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Snippet	In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative...
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SubjectTerms	biomedical imaging biomedical signal processing Computed tomography Convolution Image reconstruction Image restoration Inverse problems Iterative methods magnetic resonance imaging Neural networks reconstruction algorithms tomography
Title	Deep Convolutional Neural Network for Inverse Problems in Imaging
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