Article
Mathematics
Bo Jiang, Yuming Huang, Ashkan Panahi, Yiyi Yu, Hamid Krim, Spencer L. Smith
Summary: The paper aims to infer a dynamic graph as a global model of time-varying measurements at network nodes, capturing both pairwise and higher order interactions. Through optimization and gradient-projection scheme, a model that efficiently captures brain functionality is proposed and shown to be viable in experiments.
Article
Engineering, Electrical & Electronic
Arian Eamaz, Farhang Yeganegi, Mojtaba Soltanalian
Summary: The classical problem of phase retrieval has various applications in optics, imaging, and signal processing. This paper investigates the phase retrieval problem in a one-bit setting using one-bit ADCs. The results demonstrate that the often encountered matrix semi-definiteness and rank constraints become redundant with the increasing number of samples, leading to improved efficiency.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Automation & Control Systems
Pierre Humbert, Batiste Le Bars, Laurent Oudre, Argyris Kalogeratos, Nicolas Vayatis
Summary: This paper introduces two algorithms, IGL-3SR and FGL-3SR, for learning graph structures from multivariate signals. These algorithms show superior performance in numerical computations and scalability compared to existing methods, with lower complexity.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Engineering, Electrical & Electronic
Feng Yang, Shiwen Yang, Yikai Chen, Shiwei Qu, Jun Hu
Summary: In this letter, an effective optimization method is proposed for synthesizing sparse antenna arrays subject to directivity constraints. The method involves a real-value mixed integer programming problem and an iterative convex optimization method to minimize the number of elements while meeting specified constraints. The integration of weighted l(1)-norm minimization and element position expansion and contraction strategies allows for flexibility in controlling the search space and convergence speed.
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Xiang Zhang, Lei Yu, Gang Zheng, Yonina C. C. Eldar
Summary: This paper proposes an adaptive version of spiking-based sparse recovery (A-SSR) algorithm to optimize non-convex regularized sparse recovery problems. The superiority of A-SSR is validated through synthetic simulations and real applications, showing significant improvement in recovery accuracy by avoiding systematic underestimation. Moreover, A-SSR maintains energy efficiency in hardware implementation.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Automation & Control Systems
Yan Shuo Tan, Roman Vershynin
Summary: The paper presents a two-step procedure for solving the phase retrieval problem and proves the convergence of an online stochastic gradient descent algorithm under certain conditions. It also introduces new concepts and methods related to non-convex optimization.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
Article
Automation & Control Systems
Michael R. Metel, Akiko Takeda
Summary: This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. The authors present the first non-asymptotic convergence bounds for this class of problem and compare their algorithms with the current state-of-the-art deterministic algorithm, finding superior convergence in a numerical experiment.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Engineering, Mechanical
Junjiang Liu, Baijie Qiao, Yanan Wang, Weifeng He, Xuefeng Chen
Summary: In this paper, a non-convex sparse regularization method is proposed to promote sparsity and improve solution accuracy. The Alternating Direction Method of Multipliers (ADMM) algorithm is used to solve the non-convex optimization problem. The proposed method outperforms the standard e'1 regularization in both localization accuracy and time-history reconstruction accuracy.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Automation & Control Systems
Rishabh Dixit, Amrit Singh Bedi, Ketan Rajawat
Summary: This paper addresses the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph, and proposes a distributed algorithm capable of handling nondifferentiable regularization penalties. Through analysis and testing, the algorithm shows good performance on the problem of distributed dynamic sparse recovery.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Engineering, Aerospace
Tom Tirer, Oded Bialer
Summary: The article focuses on the problem of estimating the direction of arrival (DOA) of sources in aerospace and vehicular communication, localization, and radar. It proposes an optimization scheme based on joint sparse and low-rank matrices to solve the problem, utilizing the alternating direction method of multipliers and the accelerated proximal gradient techniques. The article also demonstrates the advantages of estimating the subarrays' phase shifts and applying a coherent DOA estimation method.
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
(2022)
Article
Mathematics, Applied
Jian-Feng Cai, Jingyang Li, Juntao You
Summary: We study the problem of recovering a sparse signal of length n with s non-zero entries from m magnitude-only measurements. Two-stage non-convex approaches have gained considerable attention in recent studies. Despite being non-convex, many two-stage algorithms converge linearly to the underlying solution when properly initialized. However, the bottleneck for these algorithms with Gaussian random measurements lies in the initialization stage. We propose a truncated power method to replace the widely used spectral initialization in order to reduce the number of measurements.
Article
Computer Science, Information Systems
Ming-Hsun Yang, Y-W Peter Hong, Jwo-Yuh Wu
Summary: This paper proposes a novel approach that uses the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The method relies on support identification and exact recovery of nonzero signal entries. It can be extended to scenarios with sparse noise and non-sparse bounded noise, ensuring support identification and exact signal recovery under certain conditions.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Artificial Intelligence
Cheng Yang, Gene Cheung, Wei Hu
Summary: In this paper, we propose a fast metric learning framework that is entirely projection-free. The framework is based on the generalized graph Laplacian matrices and the Gershgorin disc perfect alignment theorem. By replacing the PD cone constraint with linear constraints and solving the optimization problem using alternating optimization, we achieve significant speed improvements compared to cone-projection schemes while maintaining competitive classification performance.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2022)
Article
Mathematics, Applied
Paul Hand, Oscar Leong, Vladislav Voroninski
Summary: This study focuses on recovering a real-valued n-dimensional signal from phaseless, linear measurements and analyzes the amplitude-based non-smooth least squares objective. Through the use of concentration methods, it is shown that subgradient descent algorithm can linearly converge to the true solution under proper initialization conditions, ensuring local convergence in the case of Gaussian measurements.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2021)
Article
Engineering, Electrical & Electronic
Zongyu Li, Kenneth Lange, Jeffrey A. Fessler
Summary: This paper proposes novel phase retrieval algorithms for maximum likelihood estimation in low-count scenarios with independent Poisson-distributed measurements. The algorithms utilize a modified Wirtinger flow with step sizes based on observed Fisher information and a novel curvature for majorize-minimize algorithms. Simulation experiments demonstrate that the proposed algorithms outperform existing optimization methods in terms of reconstruction quality and convergence speed.
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2022)
