One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models

Chang, J. H. Rick; Li, Chun-Liang; Póczos, Barnabás; Kumar, B. V. K. Vijaya

doi:10.1109/iccv.2017.627

Cited by 272 publications

(238 citation statements)

References 48 publications

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“…Some recent papers have approached learning the primal proximal operator [10,39] in the scope of ADMM, but these do not consider learning the dual. It is likely that learning the dual proximal offers an advantage since this allows the inclusion of various operators into the learning.…”

Section: Discussionmentioning

confidence: 99%

“…An example of such an extension to solving inverse problems is [39], which learns an ADMM-like scheme for MRI reconstruction. Another is [10], which learns a "proximal" in an ADMM-like scheme for various image restoration problems. Finally, [30] considers solving finite dimensional linear inverse problems typically arising in image restoration.…”

Section: Survey Of the Fieldmentioning

confidence: 99%

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Solving ill-posed inverse problems using iterative deep neural networks

2017

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We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration.We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

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Section: Discussionmentioning

confidence: 99%

Section: Survey Of the Fieldmentioning

confidence: 99%

Solving ill-posed inverse problems using iterative deep neural networks

2017

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“…random vector, typically with a Gaussian distribution. Consequently, to recover x 0 from a linear-AWGN measurement of the form y = Ax 0 + ξ, the compressed-sensing approach in (3) can be extended to a regularized least-squares problem [18] of the form x = G( z 0 ) for z 0 := arg min z 0…”

Section: A Inference With Deep Generative Priorsmentioning

confidence: 99%

Inference With Deep Generative Priors in High Dimensions

Pandit

Sahraee-Ardakan

Rangan

et al. 2020

IEEE J. Sel. Areas Inf. Theory

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Deep generative priors offer powerful models for complex-structured data, such as images, audio, and text. Using these priors in inverse problems typically requires estimating the input and/or hidden signals in a multi-layer deep neural network from observation of its output. While these approaches have been successful in practice, rigorous performance analysis is complicated by the non-convex nature of the underlying optimization problems. This paper presents a novel algorithm, Multi-Layer Vector Approximate Message Passing (ML-VAMP), for inference in multi-layer stochastic neural networks. ML-VAMP can be configured to compute maximum a priori (MAP) or approximate minimum mean-squared error (MMSE) estimates for these networks. We show that the performance of ML-VAMP can be exactly predicted in a certain high-dimensional random limit. Furthermore, under certain conditions, ML-VAMP yields estimates that achieve the minimum (i.e., Bayes-optimal) MSE as predicted by the replica method. In this way, ML-VAMP provides a computationally efficient method for multi-layer inference with an exact performance characterization and testable conditions for optimality in the large-system limit.

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“…This second step is often thought of as a denoising step. One approach to learning to solve inverse problems is to implicitly learn r(·) by explicitly learning a proximal operator in the form of a denoising autoencoder [18,27,28].…”

Section: Decoupledmentioning

confidence: 99%

Neumann Networks for Linear Inverse Problems in Imaging

Gilton

Ongie

Willett

2020

IEEE Trans. Comput. Imaging

162

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Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers minimize a cost function consisting of a data-fit term, which measures how well an image matches the observations, and a regularizer, which reflects prior knowledge and promotes images with desirable properties like smoothness. Recent advances in machine learning and image processing have illustrated that it is often possible to learn a regularizer from training data that can outperform more traditional regularizers. We present an end-to-end, data-driven method of solving inverse problems inspired by the Neumann series, which we call a Neumann network. Rather than unroll an iterative optimization algorithm, we truncate a Neumann series which directly solves the linear inverse problem with a data-driven nonlinear regularizer. The Neumann network architecture outperforms traditional inverse problem solution methods, model-free deep learning approaches, and state-of-the-art unrolled iterative methods on standard datasets. Finally, when the images belong to a union of subspaces and under appropriate assumptions on the forward model, we prove there exists a Neumann network configuration that well-approximates the optimal oracle estimator for the inverse problem and demonstrate empirically that the trained Neumann network has the form predicted by theory. Learning to RegularizeIn this paper we consider solving linear inverse problems in imaging in which a p-pixel image, β ∈ R p (in vectorized form), is observed via m noisy linear projections as y = Xβ + , where y, ∈ R m and X ∈ R m×p . This general model is used throughout computational imaging, from basic image restoration tasks like deblurring, super-resolution, and image inpainting [1], to a wide variety of tomographic imaging applications, including common types of magnetic resonance imaging [2], X-ray computed tomography [3], radar imaging [4], among others [5]. The task of estimating * D. Gilton is with the

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One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models

Cited by 272 publications

References 48 publications

Solving ill-posed inverse problems using iterative deep neural networks

Solving ill-posed inverse problems using iterative deep neural networks

Inference With Deep Generative Priors in High Dimensions

Neumann Networks for Linear Inverse Problems in Imaging

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