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Provable Super-Convergence With a Large Cyclical Learning Rate

IEEE SIGNAL PROCESSING LETTERS 2021年 28卷 1645-1649页

作者： Oymak, Samet Univ Calif Riverside Dept Elect Engn Riverside CA 92507 USA

Conventional wisdom dictates that learning rate should be in the stable regime so that gradient-based algorithms don't blow up. This letter introduces a simple scenario where an unstably large learning rate scheme leads to a super fast convergence, with the convergence rate depending only logarithmically on the condition number of the problem. Our scheme uses a Cyclical Learning Rate where we periodically take one large unstable step and several small stable steps to compensate for the instability. These findings also help explain the empirical observations of [Smith and Topin, 2019] where they show that CLR with a large maximum learning rate can dramatically accelerate learning and lead to so-called "super-convergence". We prove that our scheme excels in the problems where Hessian exhibits a bimodal spectrum and the eigenvalues can be grouped into two clusters (small and large). The unstably large step is the key to enabling fast convergence over the small eigen-spectrum.

关键词： Eigenvalues and eigenfunctions Convergence Jacobian matrices Standards Deep learning Signal processing algorithms Schedules Convergence of numerical methods iterative algorithms Gradient methods

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DTV-NET: An iterative Reconstruction Network for Incomplete Projections in Static CT

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Ma, Chunliang Wang, Yukang Zha, Keyang Li, Yunxiang Luo, Shouhua Southeast Univ Dept Biol Engn Nanjing 210096 Peoples R China Dept Nanovis Technol Beijing Co Ltd Beijing 100094 Peoples R China

The Nanovision static computed tomography (CT), a novel CT scanning system, employs a multisource array and a flat-panel detector array fixed on two parallel planes with a constant offset. Unlike conventional CT systems, this static CT acquires full projection views in axial scanning mode using a focus-shifting technique combined with small-angle gantry rotation. This unique scanning protocol limits the angular range of each source, enabling complete scan acquisition. However, the large cone angle between the sources and the detector, combined with the uneven clustering of projections inherent in multisource acquisition, leads to significantly incomplete projections. Consequently, significant cone-beam artifacts and uneven sparse-angle artifacts coexist, degrading the reconstructed image quality. To address these issues, this article proposes a deep iterative network based on directional total variation (DTV) regularization (DTV-Net). DTV-Net incorporates DTV as a regularization term within the fast iterative shrinkage-thresholding algorithm (FISTA) framework, achieving both artifact suppression and rapid convergence. Specifically, it employs an encoder-decoder architecture and a head attention block (HAB) module to adaptively adjust threshold parameters in the gradient space, effectively removing redundant gradient information corresponding to artifacts. During end-to-end training, we integrated the ASTRA toolbox with tensorized representations and introduced a tensorized projection operator (TPO) tailored for the multiflat-panel detector array, optimizing iterative forward and backward projections. Extensive experiments demonstrate that the proposed DTV-Net algorithm outperforms prior art solutions on both simulation and clinical data.

关键词： Image reconstruction Computed tomography Digital TV Detectors Mathematical models Deep learning Training iterative algorithms Feature extraction Convergence Cone beam reconstruction deep iterative network directional total variation (DTV) static computed tomography (CT)

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NONLINEARIZING TWO-PARAMETER EIGENVALUE PROBLEMS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2021年第2期42卷 775-799页

作者： Ringh, Emil Jarlebring, Elias KTH Royal Inst Technol SeRC Swedish E Sci Res Ctr Dept Math Lindstedtsvagen 25 SE-10044 Stockholm Sweden

We investigate a technique to transform a linear two-parameter eigenvalue problem into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original and the nonlinearized problem theoretically and show how to use the transformation computationally. Special cases of the transformation can be interpreted as a reversed companion linearization for polynomial eigenvalue problems, as well as a reversed (less known) linearization technique for certain algebraic eigenvalue problems with square-root terms. Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied. The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation. This situation arises naturally in domain decomposition techniques. A general error analysis is also carried out under the assumption that a backward stable eigensolver is used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation.

关键词： two-parameter eigenvalue problem nonlinear eigenvalue problem multiparameter eigenvalue problem iterative algorithms implicit function theorem

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iterative Field Reconstruction in Direct-Detection Receiver Using the Fienup Input-Output Algorithm

Iterative Field Reconstruction in Direct-Detection Receiver ...

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2022 IEEE Photonics Conference, IPC 2022

作者： Matsumoto, Masayuki Wakayama University Faculty of Systems Engineering 930 Sakaedani Wakayama-shi640-8510 Japan

iterative field reconstruction for dispersion compensation in IM/DD transmission systems is studied. Numerical simulation and a preliminary experiment show that the mixed use of Fienup input-output and Gerchberg-Saxto... 详细信息

ISBN: (数字)9781665434874

ISBN: (纸本)9781665434874

关键词： Numerical simulation iterative algorithms Optical receivers Dispersion Photonics Optical pulses

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A New Residual Generation-Based Fault Estimation Approach for Cyber-Physical Systems

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023年 72卷 1页

作者： Zhu, Jun-Wei Xia, Zhen-Hao Wang, Xin Zhejiang Univ Technol Inst Cyberspace Secur Coll Informat Engn Hangzhou 310023 Peoples R China Heilongjiang Univ Sch Math Sci Harbin 150080 Peoples R China Heilongjiang Univ Heilongjiang Prov Key Lab Theory & Computat Comple Harbin 150080 Peoples R China

This article investigates the problem of data-driven actuator fault estimation for cyber-physical systems (CPSs). First, a stable kernel representation (SKR)-based residual generator is constructed to achieve online detection for actuator fault using the system inputs-outputs (I/O) data. Then an iterative learning fault estimation (ILFE) algorithm is designed to reconstruct the actuator fault in real time. The proposed method realizes the actuator fault estimation when the model parameters are unknown, which avoids much time spent in the modeling process. Moreover, compared with the existing model-based approaches, the presented method still has better transient performance, steady-state performance, and computational efficiency, which is more suitable for the fault identification of practical control systems. Finally, the application to a servo motor demonstrates the superiority of the designed fault estimation method.

关键词： Estimation Generators Fault detection Data models Actuators iterative algorithms Servomotors Data-driven fault estimation iterative learning residual generator servo motor

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Hypersphere Fitting From Noisy Data Using an EM Algorithm

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IEEE SIGNAL PROCESSING LETTERS 2021年 28卷 314-318页

作者： Lesouple, Julien Pilastre, Barbara Alunann, Yoann Tourneret, Jean-Yves TeSA F-31500 Toulouse France Heriot Watt Univ Sch Engn Edinburgh EH14 4AS Midlothian Scotland Univ Toulouse F-31071 Toulouse France

This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.

关键词： Signal processing algorithms Maximum likelihood estimation Noise measurement Three-dimensional displays Fitting iterative algorithms Distributed databases Hypersphere Fitting Maximum Likelihood Estimation Expectation-Maximization Algorithm von Mises-Fisher distribution

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Comparison of the EM, CEM and SEM algorithms in the estimation of finite mixtures of linear mixed models: a simulation study

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COMPUTATIONAL STATISTICS 2021年第4期36卷 2507-2533页

作者： Novais, Luisa Faria, Susana Univ Minho Dept Math P-4800058 Guimaraes Portugal Univ Minho Ctr Mol & Environm Biol P-4800058 Guimaraes Portugal

Finite mixture models are a widely known method for modelling data that arise from a heterogeneous population. Within the family of mixtures of regression models, mixtures of linear mixed models have also been applied in different areas since, besides taking into consideration the heterogeneity in the population, they also allow to take into account the correlation between observations from the same individual. One of the main issues in mixture models concerns the estimation of the parameters. Maximum likelihood estimation is one of the most used methods in the estimation of the parameters for mixture models. However, the maximization of the log-likelihood function in mixture models is complex, producing in many cases infinite solutions whereby the maximum likelihood estimator may not exist, at least globally. For this reason, it is common to resort to iterative methods, in particular to the Expectation-Maximization (EM) algorithm. However, the slow convergence and the selection of initial values are two of biggest issues of the EM algorithm, the reason why some modified versions of this algorithm have been developed over the years. In this article we compare the performance of the EM, Classification EM (CEM) and Stochastic EM (SEM) algorithms in the estimation of the parameters for mixtures of linear mixed models. In order to evaluate their performance, we carry out a simulation study and a real data application. The results show that the CEM algorithm is the least computationally demanding algorithm, although the three algorithms provide similar maximum likelihood estimates for the parameters.

关键词： Mixture models Maximum likelihood estimation iterative algorithms

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Semiparametric regression with the U-shaped baseline hazard function in the additive hazards model under general censoring mechanisms

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2021年第16期91卷 3255-3282页

作者： Fani, Shabnam Shen, Hua Lu, Xuewen Wu, Jingjing Univ Calgary Dept Math & Stat Calgary AB Canada

When employing natural shape constraint knowledge obtained from prior studies in survival data analysis, both restrictions of parametric models and difficulties of nonparametric approaches, including the selection of bandwidth and tuning parameter, can be avoided. We use this technique to derive a nonparametric estimator of the U-shaped baseline hazard function in the semiparametric additive hazards regression model for partly general interval-censored data. An iterative algorithm is developed for computing estimators of the baseline hazard function and regression coefficients simultaneously. Numerical studies using simulation and real dataset are conducted to compare the performance of the proposed approach incorporating shape information with that of the B-spline and I-spline methods without using shape restriction. They show that the proposed method increases the efficiency of estimator for the baseline hazard function in terms of the mean Hellinger distance and performs better, or at least leads to competitive results for estimating regression coefficients.

关键词： Additive hazards model baseline hazard function iterative algorithms semiparametric methods shape-restricted estimation

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SPIE-DIR: Self-Prior Information Enhanced Deep iterative Reconstruction Using Two Complementary Limited-Angle Scans for DECT

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023年 72卷 1页

作者： Zhang, Yikun Hu, Dianlin Lyu, Tianling Quan, Guotao Xiang, Jun Coatrieux, Gouenou Luo, Shouhua Chen, Yang Southeast Univ Sch Comp Sci & Engn Lab Image Sci & Technol Nanjing 210096 Peoples R China Zhejiang Lab Hangzhou 311121 Peoples R China United Imaging Healthcare Ltd Co CT RPA Dept Shanghai 201807 Peoples R China United Imaging Healthcare Ltd Co Xray Dept Shanghai 201807 Peoples R China IMT Atlantique LaTIM UMR1101 INSERM F-29000 Brest France Southeast Univ Dept Biomed Engn Nanjing 210096 Peoples R China Southeast Univ Jiangsu Prov Joint Int Res Lab Med Informat Proc Nanjing 210096 Peoples R China

Dual-energy computed tomography (DECT) can simultaneously provide the anatomical structure and material-specific information of the scanned object, having many applications in industry and medicine. Different from conventional CT, DECT acquires two attenuation measurements of the same object at two different X-ray spectra, resulting in apparent redundant information. This article exploits this kind of redundancy to develop the self-prior information enhanced deep iterative reconstruction (SPIE-DIR) algorithm for limited-angle DECT. Unlike the routine practice in model-based deep learning (DL) algorithms, the SPIE-DIR method simultaneously performs constraints in the projection, residual, and image domains, corresponding to three modules: projection inpainting, residual correction, and image refinement. During this stage, the prior image and prior projection derived from two complementary limited-angle scans are used to improve the algorithm performance. Besides, to avoid the blurring effect caused by minimizing the Euclidean distance, the Wasserstein generative adversarial network with gradient penalty is adopted to enhance the visual perception of the generated results. Experiments on the simulated data and real rat data have demonstrated that the proposed SPIE-DIR algorithm has the potential to obtain high-quality DECT images from two limited-angle scans. Furthermore, visual and quantitative assessments have shown the promising performance of SPIE-DIR in artifact removal, structural fidelity, CT number preservation, and visual perception enhancement.

关键词： Image reconstruction Computed tomography Deep learning iterative algorithms X-ray imaging Reconstruction algorithms Neural networks Deep iterative reconstruction dual-energy computed tomography generative adversarial network limited-angle self-prior information

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Solution approaches to inverse heat transfer problems with and without phase changes: A state-of-the-art review

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ENERGY 2023年第PartB期278卷

作者： Zalesak, Martin Klimes, Lubomir Charvat, Pavel Cabalka, Matous Kudela, Jakub Mauder, Tomas Brno Univ Technol Energy Inst Tech 2869-2 Brno 61669 Czech Republic Brno Univ Technol Inst Math Tech 2869-2 Brno 61669 Czech Republic Brno Univ Technol Inst Automat & Comp Sci Tech 2869-2 Brno 61669 Czech Republic

Heat transfer problems (HTPs) with and without phase change are encountered in many areas of science and engineering. Some HTPs cannot be solved straightforwardly since certain heat transfer parameters are unknown. As a result, the need to find solutions to inverse HTPs arises. A number of approaches, methods, and algorithms for the solution of inverse HTPs have been developed and published in the past. Nonetheless, even the most recent handbooks dealing with inverse HTPs do not provide a comprehensive overview of the developments and advancements in this area (in particular the applications and comparisons of the methods). The present state-of-the-art review aims at filling this information gap and it also presents an overview of the most recent research works. Four classes of distinct methods and algorithms are addressed in detail;conventional (usually iterative and gradient-based) algorithms, nature-inspired meta-heuristic algorithms, techniques utilising artificial neural networks and machine learning, and algorithms based on fuzzy logic. The results obtained with the use of these methods are assessed and compared to each other. The intended contributions of the present review are twofold. Firstly, the review presents a comprehensive overview of the latest advancements and developments in the field of inverse HTPs, including cutting-edge research works. Secondly, it critically evaluates and compares the performance of different methods and algorithms, providing practical insights to researchers for the selection of suitable approaches to solve their specific inverse HTPs.

关键词： Inverse heat transfer Phase change Least square problem iterative algorithms Meta-heuristics Artificial neural networks Fuzzy logic

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