Neural Proximal Gradient Descent for Compressive Imaging

Mardani, Morteza; Sun, Qiao; Vasawanala, Shreyas; Papyan, Vardan; Monajemi, Hatef; Pauly, John M.; Donoho, David L.

doi:10.48550/arxiv.1806.03963

Cited by 10 publications

(12 citation statements)

References 26 publications

(46 reference statements)

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“…( 1)- (3), where the likelihood p(u|x) is a multivariate Gaussian distribution, i.e. p(u|x) ∝ e − 1 2 Σ −1/2 (u−x) 2 2 . Including the prior and taking the negative logarithm gives the expression of the denoiser:…”

Section: General Gaussian Denoisermentioning

confidence: 99%

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Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration

Pendu¹,

Guillemot²

2021

Preprint

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Plug-and-Play optimization recently emerged as a powerful technique for solving inverse problems by plugging a denoiser into a classical optimization algorithm. The denoiser accounts for the regularization and therefore implicitly determines the prior knowledge on the data, hence replacing typical handcrafted priors. In this paper, we extend the concept of plug-and-play optimization to use denoisers that can be parameterized for non-constant noise variance. In that aim, we introduce a preconditioning of the ADMM algorithm, which mathematically justifies the use of such an adjustable denoiser. We additionally propose a procedure for training a convolutional neural network for high quality non-blind image denoising that also allows for pixel-wise control of the noise standard deviation. We show that our pixel-wise adjustable denoiser, along with a suitable preconditioning strategy, can further improve the plug-and-play ADMM approach for several applications, including image completion, interpolation, demosaicing and Poisson denoising.

show abstract

Section: General Gaussian Denoisermentioning

confidence: 99%

“…In order to increase the interpretability and genericity of deep neural networks, the field is evolving towards methods that combine them with traditional optimization algorithms. A popular approach, seen for example in [1], [2], [3], [4], [5], [6], [7], consists in defining so-called "unrolled" neural…”

Section: Introductionmentioning

confidence: 99%

Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration

Pendu¹,

Guillemot²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Because we differentiate through a cone program by implicitly differentiating its solution map, our method can be paired with any algorithm for solving convex cone programs. In contrast, methods that differentiate through every step of an optimization procedure must be customized for each algorithm (e.g., [33,30,56]). Moreover, such methods only approximate the derivative, whereas we compute it analytically (when it exists).…”

Section: Related Workmentioning

confidence: 99%

Differentiable Convex Optimization Layers

Agrawal,

Amos,

Barratt

et al. 2019

Preprint

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Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.

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“…Currently, deep learning(DL) techniques have been widely adopted in CT and demonstrate promising reconstruction performance [2,8,24,28,32,33]. By further combining the iterative algorithms with DL, a series of iterative frameworks with the accordingly designed neural-network-based modules are proposed [1,3,5,7,13,19,29]. ADMMNet [25] introduces a neural-network-based module in reconstruction problem and achieves remarkable performance.…”

Section: Introductionmentioning

confidence: 99%

Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation

Wang¹,

Zhang²,

Li³

et al. 2021

Preprint

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Computed tomography (CT) reconstruction from X-ray projections acquired within a limited angle range is challenging, especially when the angle range is extremely small. Both analytical and iterative models need more projections for effective modeling. Deep learning methods have gained prevalence due to their excellent reconstruction performances, but such success is mainly limited within the same dataset and does not generalize across datasets with different distributions. Hereby we propose ExtraPolationNetwork for limited-angle CT reconstruction via the introduction of a sinogram extrapolation module, which is theoretically justified. The module complements extra sinogram information and boots model generalizability. Extensive experimental results show that our reconstruction model achieves state-of-the-art performance on NIH-AAPM dataset, similar to existing approaches. More importantly, we show that using such a sinogram extrapolation module significantly improves the generalization capability of the model on unseen datasets (e.g., COVID-19 and LIDC datasets) when compared to existing approaches.

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Neural Proximal Gradient Descent for Compressive Imaging

Cited by 10 publications

References 26 publications

Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration

Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration

Differentiable Convex Optimization Layers

Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation

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