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Register a new userGraph Signal Restoration Using Nested Deep Algorithm Unrolling
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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.
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We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we propose a hybrid neural architecture inspired by the algorithmic unfolding of the iterative weighted minimum mean squared error (WMMSE) method, that we denote as unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are parameterized using graph neural networks (GNNs), where the time-varying underlying graphs are given by the fading interference coefficients in the wireless network. These GNNs are trained through a gradient descent approach based on multiple instances of the power allocation problem. Once trained, UWMMSE achieves performance comparable to that of WMMSE while significantly reducing the computational complexity. This phenomenon is illustrated through numerical experiments along with the robustness and generalization to wireless networks of different densities and sizes.
In this chapter, we review biomedical applications and breakthroughs via leveraging algorithm unrolling, an important technique that bridges between traditional iterative algorithms and modern deep learning techniques. To provide context, we start by tracing the origin of algorithm unrolling and providing a comprehensive tutorial on how to unroll iterative algorithms into deep networks. We then extensively cover algorithm unrolling in a wide variety of biomedical imaging modalities and delve into several representative recent works in detail. Indeed, there is a rich history of iterative algorithms for biomedical image synthesis, which makes the field ripe for unrolling techniques. In addition, we put algorithm unrolling into a broad perspective, in order to understand why it is particularly effective and discuss recent trends. Finally, we conclude the chapter by discussing open challenges, and suggesting future research directions.
Massive access is a critical design challenge of Internet of Things (IoT) networks. In this paper, we consider the grant-free uplink transmission of an IoT network with a multiple-antenna base station (BS) and a large number of single-antenna IoT devices. Taking into account the sporadic nature of IoT devices, we formulate the joint activity detection and channel estimation (JADCE) problem as a group-sparse matrix estimation problem. This problem can be solved by applying the existing compressed sensing techniques, which however either suffer from high computational complexities or lack of algorithm robustness. To this end, we propose a novel algorithm unrolling framework based on the deep neural network to simultaneously achieve low computational complexity and high robustness for solving the JADCE problem. Specifically, we map the original iterative shrinkage thresholding algorithm (ISTA) into an unrolled recurrent neural network (RNN), thereby improving the convergence rate and computational efficiency through end-to-end training. Moreover, the proposed algorithm unrolling approach inherits the structure and domain knowledge of the ISTA, thereby maintaining the algorithm robustness, which can handle non-Gaussian preamble sequence matrix in massive access. With rigorous theoretical analysis, we further simplify the unrolled network structure by reducing the redundant training parameters. Furthermore, we prove that the simplified unrolled deep neural network structures enjoy a linear convergence rate. Extensive simulations based on various preamble signatures show that the proposed unrolled networks outperform the existing methods in terms of the convergence rate, robustness and estimation accuracy.
Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying graph structure, as in social, biological, and many other domains. This paper explores 1)how graph signal processing (GSP) can be used to extend CNN components to graphs in order to improve model performance; and 2)how to design the graph CNN architecture based on the topology or structure of the data graph.
While the depth of convolutional neural networks has attracted substantial attention in the deep learning research, the width of these networks has recently received greater interest. The width of networks, defined as the size of the receptive fields and the density of the channels, has demonstrated crucial importance in low-level vision tasks such as image denoising and restoration. However, the limited generalization ability, due to the increased width of networks, creates a bottleneck in designing wider networks. In this paper, we propose the Deep Regulated Convolutional Network (RC-Net), a deep network composed of regulated sub-network blocks cascaded by skip-connections, to overcome this bottleneck. Specifically, the Regulated Convolution block (RC-block), featured by a combination of large and small convolution filters, balances the effectiveness of prominent feature extraction and the generalization ability of the network. RC-Nets have several compelling advantages: they embrace diversified features through large-small filter combinations, alleviate the hazy boundary and blurred details in image denoising and super-resolution problems, and stabilize the learning process. Our proposed RC-Nets outperform state-of-the-art approaches with significant performance gains in various image restoration tasks while demonstrating promising generalization ability. The code is available at https://github.com/cswin/RC-Nets.
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