Deep Equilibrium Architectures for Inverse Problems in Imaging

Gilton, Davis; Ongie, Greg; Willett, Rebecca

doi:10.1109/tci.2021.3118944

Cited by 91 publications

(101 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For imaging, various different optimization algorithms have been unrolled. These include ISTA [41,42], ADMM [43][44][45], the primal-dual iteration [29,46,47], block coordinate descent [48], POCS [49], as well as approximate message passing algorithms [50], Neumann series [51], field of experts models [52] and various others, including [53]. While successful, we remark that simply unrolling an optimization solver does not ensure stability and robustness of a deep learning procedure [14].…”

Section: Contributions and Related Workmentioning

confidence: 99%

NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems

Neyra-Nesterenko¹,

Adcock²

2022

Preprint

View full text Add to dashboard Cite

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-theart, model-based methods for solving inverse problems. However, it is known that current data-driven approaches face several key issues, notably instabilities and hallucinations, with potential impact in critical tasks such as medical imaging. This raises the key question of whether or not one can construct stable and accurate deep neural networks for inverse problems. In this work, we present a novel construction of an accurate, stable and efficient neural network for inverse problems with general analysis-sparse models. To construct the network, we unroll NESTA, an accelerated first-order method for convex optimization. Combined with a compressed sensing analysis, we prove accuracy and stability. Finally, a restart scheme is employed to enable exponential decay of the required network depth, yielding a shallower, and consequently more efficient, network. We showcase this approach in the case of Fourier imaging, and verify its stability and performance via a series of numerical experiments. The key impact of this work is to provide theoretical guarantees for computing and developing stable neural networks in practice.

show abstract

Section: Contributions and Related Workmentioning

confidence: 99%

NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems

Neyra-Nesterenko¹,

Adcock²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…According to Equation (23), the reconstruction of an image leads to solving the inverse problem. Most of the solutions to Equation (23) in the literature use an optimization solution [ 14 , 21 ], for example:

where K —set of feasible solutions;

—regulizer;

regularization parameter. …”

Section: Inpainted Image Recognition and Reconstruction As An Inverse...mentioning

confidence: 99%

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Citko

Sienko

2022

Sensors

View full text Add to dashboard Cite

This paper considers the use of a machine learning system for the reconstruction and recognition of distorted or damaged patterns, in particular, images of faces partially covered with masks. The most up-to-date image reconstruction structures are based on constrained optimization algorithms and suitable regularizers. In contrast with the above-mentioned image processing methods, the machine learning system presented in this paper employs the superposition of system vectors setting up asymptotic centers of attraction. The structure of the system is implemented using Hopfield-type neural network-based biorthogonal transformations. The reconstruction property gives rise to a superposition processor and reversible computations. Moreover, this paper’s distorted image reconstruction sets up associative memories where images stored in memory are retrieved by distorted/inpainted key images.

show abstract

“…It has been shown that the combination of proximal algorithms with advanced denoisers, such as BM3D [15] or DnCNN [16], leads to the state-of-the-art performance for various imaging problems. Remarkably, the heuristic of using denoisers within iterative algorithms exhibited great empirical success [13,[17][18][19][20] and inspired a significant follow up work on the so-called model-based deep learning method that include RED, denoising-based approximate message passing (D-AMP), deep unfolding (DU), and deep equilibrium models (DEQ) [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…and contractiveness, are used to ensure convergence of other related frameworks, such as PnP and DEQ [9,26]. Thus, while our focus is on RED, our approach can be applied to develop more stable variants of other related frameworks.…”

Section: Introductionmentioning

confidence: 99%

Monotonically Convergent Regularization by Denoising

Hu¹,

Liu²,

Xu³

et al. 2022

Preprint

View full text Add to dashboard Cite

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED algorithm diverges.

show abstract

Deep Equilibrium Architectures for Inverse Problems in Imaging

Cited by 91 publications

References 34 publications

NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems

NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Monotonically Convergent Regularization by Denoising

Contact Info

Product

Resources

About