Graph Signal Restoration Using Nested Deep Algorithm Unrolling

• URL: http://arxiv.org/abs/2106.15910v1
• Date: Wed, 30 Jun 2021 08:57:01 GMT
• Title: Graph Signal Restoration Using Nested Deep Algorithm Unrolling
• Authors: Masatoshi Nagahama, Koki Yamada, Yuichi Tanaka, Stanley H. Chan, Yonina C. Eldar
• Abstract summary: Graph signal processing is a ubiquitous task in many applications such as sensor, social transportation brain networks, point cloud processing, and graph networks. We propose two restoration methods based on convexindependent deep ADMM (ADMM) parameters in the proposed restoration methods are trainable in an end-to-end manner.
• Score: 85.53158261016331
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Graph signals are often corrupted through sensing processes, and need to be restored for the above applications. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then propose a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second method, the unrolled ADMM-based denoiser is incorporated as a submodule. Therefore, our restoration method has a nested DAU structure. Thanks to DAU, parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Since the proposed restoration methods are based on iterations of a (convex) optimization algorithm, the method is interpretable and keeps the number of parameters small because we only need to tune graph-independent regularization parameters. We solve two main problems in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements to several existing methods in terms of root mean squared error in both tasks.

Related papers

• Online Proximal ADMM for Graph Learning from Streaming Smooth Signals [9.34612743192798]
  We develop a novel algorithm for online graph learning using observation streams, assumed to be smooth on the latent graph. Our modus operandi is to process graph signals sequentially and thus keep memory and computational costs in check. The proposed approach also exhibits better tracking performance (in terms of suboptimality) when compared to state-of-the-art online graph learning baselines.
  arXiv  Detail & Related papers  (2024-09-19T17:12:03Z)
• Graph Signal Sampling for Inductive One-Bit Matrix Completion: a Closed-form Solution [112.3443939502313]
  We propose a unified graph signal sampling framework which enjoys the benefits of graph signal analysis and processing. The key idea is to transform each user's ratings on the items to a function (signal) on the vertices of an item-item graph. For the online setting, we develop a Bayesian extension, i.e., BGS-IMC which considers continuous random Gaussian noise in the graph Fourier domain.
  arXiv  Detail & Related papers  (2023-02-08T08:17:43Z)
• Graph Reinforcement Learning for Radio Resource Allocation [13.290246410488727]
  We resort to graph reinforcement learning for exploiting two kinds of relational priors inherent in many problems in wireless communications. To design graph reinforcement learning framework systematically, we first conceive a method to transform state matrix into state graph. We then propose a general method for graph neural networks to satisfy desirable permutation properties.
  arXiv  Detail & Related papers  (2022-03-08T08:02:54Z)
• Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals [8.140698535149042]
  We propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix. We show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.
  arXiv  Detail & Related papers  (2022-02-06T17:06:13Z)
• An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations [68.8204255655161]
  Filtering equations play a central role in many real-life applications, including numerical weather prediction, finance and engineering. One of the classical approaches to approximate the solution of the filtering equations is to use a PDE inspired method, called the splitting-up method. We combine this method with a neural network representation to produce an approximation of the unnormalised conditional distribution of the signal process.
  arXiv  Detail & Related papers  (2022-01-10T11:01:36Z)
• Message Passing Descent for Efficient Machine Learning [4.416484585765027]
  We propose a new iterative optimization method for the bf Data-Fitting (DF) problem in Machine Learning. The approach relies on bf Graphical Model representation of the DF problem. We suggest the bf Message Passage Descent algorithm which relies on the piece-wise-polynomial representation of the model DF function.
  arXiv  Detail & Related papers  (2021-02-16T12:22:54Z)
• Solving Sparse Linear Inverse Problems in Communication Systems: A Deep Learning Approach With Adaptive Depth [51.40441097625201]
  We propose an end-to-end trainable deep learning architecture for sparse signal recovery problems. The proposed method learns how many layers to execute to emit an output, and the network depth is dynamically adjusted for each task in the inference phase.
  arXiv  Detail & Related papers  (2020-10-29T06:32:53Z)
• Unrolling of Deep Graph Total Variation for Image Denoising [106.93258903150702]
  In this paper, we combine classical graph signal filtering with deep feature learning into a competitive hybrid design. We employ interpretable analytical low-pass graph filters and employ 80% fewer network parameters than state-of-the-art DL denoising scheme DnCNN.
  arXiv  Detail & Related papers  (2020-10-21T20:04:22Z)
• Learning to solve TV regularized problems with unrolled algorithms [18.241062505073234]
  Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals. We develop and characterize two approaches to do so, describe their benefits and limitations, and discuss the regime where they can actually improve over iterative procedures.
  arXiv  Detail & Related papers  (2020-10-19T14:19:02Z)
• Activation Relaxation: A Local Dynamical Approximation to Backpropagation in the Brain [62.997667081978825]
  Activation Relaxation (AR) is motivated by constructing the backpropagation gradient as the equilibrium point of a dynamical system. Our algorithm converges rapidly and robustly to the correct backpropagation gradients, requires only a single type of computational unit, and can operate on arbitrary computation graphs.
  arXiv  Detail & Related papers  (2020-09-11T11:56:34Z)

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.