Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration

• URL: http://arxiv.org/abs/2312.15701v1
• Date: Mon, 25 Dec 2023 11:53:06 GMT
• Title: Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration
• Authors: Jiahong Fu, Qi Xie, Deyu Meng and Zongben Xu
• Abstract summary: We propose a high-accuracy rotation equivariant proximal network that embeds rotation symmetry priors into the deep unfolding framework. This study makes efforts to suggest a high-accuracy rotation equivariant proximal network that effectively embeds rotation symmetry priors into the deep unfolding framework.
• Score: 68.18203605110719
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The deep unfolding approach has attracted significant attention in computer vision tasks, which well connects conventional image processing modeling manners with more recent deep learning techniques. Specifically, by establishing a direct correspondence between algorithm operators at each implementation step and network modules within each layer, one can rationally construct an almost ``white box'' network architecture with high interpretability. In this architecture, only the predefined component of the proximal operator, known as a proximal network, needs manual configuration, enabling the network to automatically extract intrinsic image priors in a data-driven manner. In current deep unfolding methods, such a proximal network is generally designed as a CNN architecture, whose necessity has been proven by a recent theory. That is, CNN structure substantially delivers the translational invariant image prior, which is the most universally possessed structural prior across various types of images. However, standard CNN-based proximal networks have essential limitations in capturing the rotation symmetry prior, another universal structural prior underlying general images. This leaves a large room for further performance improvement in deep unfolding approaches. To address this issue, this study makes efforts to suggest a high-accuracy rotation equivariant proximal network that effectively embeds rotation symmetry priors into the deep unfolding framework. Especially, we deduce, for the first time, the theoretical equivariant error for such a designed proximal network with arbitrary layers under arbitrary rotation degrees. This analysis should be the most refined theoretical conclusion for such error evaluation to date and is also indispensable for supporting the rationale behind such networks with intrinsic interpretability requirements.

Related papers

• Principled Architecture-aware Scaling of Hyperparameters [69.98414153320894]
  Training a high-quality deep neural network requires choosing suitable hyperparameters, which is a non-trivial and expensive process. In this work, we precisely characterize the dependence of initializations and maximal learning rates on the network architecture. We demonstrate that network rankings can be easily changed by better training networks in benchmarks.
  arXiv  Detail & Related papers  (2024-02-27T11:52:49Z)
• Convergence Guarantees of Overparametrized Wide Deep Inverse Prior [1.5362025549031046]
  Inverse Priors is an unsupervised approach to transform a random input into an object whose image under the forward model matches the observation. We provide overparametrization bounds under which such network trained via continuous-time gradient descent will converge exponentially fast with high probability. This work is thus a first step towards a theoretical understanding of overparametrized DIP networks, and more broadly it participates to the theoretical understanding of neural networks in inverse problem settings.
  arXiv  Detail & Related papers  (2023-03-20T16:49:40Z)
• Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution [91.3781512926942]
  Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. This work investigates the potential of network pruning for super-resolution iteration to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. We propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly network at each and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly.
  arXiv  Detail & Related papers  (2023-03-16T21:06:13Z)
• Optimisation & Generalisation in Networks of Neurons [8.078758339149822]
  The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. A new theoretical framework is proposed for deriving architecture-dependent first-order optimisation algorithms. A new correspondence is proposed between ensembles of networks and individual networks.
  arXiv  Detail & Related papers  (2022-10-18T18:58:40Z)
• The Principles of Deep Learning Theory [19.33681537640272]
  This book develops an effective theory approach to understanding deep neural networks of practical relevance. We explain how these effectively-deep networks learn nontrivial representations from training. We show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks.
  arXiv  Detail & Related papers  (2021-06-18T15:00:00Z)
• Reframing Neural Networks: Deep Structure in Overcomplete Representations [41.84502123663809]
  We introduce deep frame approximation, a unifying framework for representation learning with structured overcomplete frames. We quantify structural differences with the deep frame potential, a data-independent measure of coherence linked to representation uniqueness and stability. This connection to the established theory of overcomplete representations suggests promising new directions for principled deep network architecture design.
  arXiv  Detail & Related papers  (2021-03-10T01:15:14Z)
• Deep Networks from the Principle of Rate Reduction [32.87280757001462]
  This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative ascent gradient scheme for optimizing the rate reduction of learned features naturally leads to a multi-layer deep network, one iteration per layer. All components of this "white box" network have precise optimization, statistical, and geometric interpretation.
  arXiv  Detail & Related papers  (2020-10-27T06:01:43Z)
• A Deep-Unfolded Reference-Based RPCA Network For Video Foreground-Background Separation [86.35434065681925]
  This paper proposes a new deep-unfolding-based network design for the problem of Robust Principal Component Analysis (RPCA) Unlike existing designs, our approach focuses on modeling the temporal correlation between the sparse representations of consecutive video frames. Experimentation using the moving MNIST dataset shows that the proposed network outperforms a recently proposed state-of-the-art RPCA network in the task of video foreground-background separation.
  arXiv  Detail & Related papers  (2020-10-02T11:40:09Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Network Adjustment: Channel Search Guided by FLOPs Utilization Ratio [101.84651388520584]
  This paper presents a new framework named network adjustment, which considers network accuracy as a function of FLOPs. Experiments on standard image classification datasets and a wide range of base networks demonstrate the effectiveness of our approach.
  arXiv  Detail & Related papers  (2020-04-06T15:51:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.