Article
Automation & Control Systems
Xiaowei Li, Xuqi Zhang, Zhiguo Wang, Xiaojing Shen
Summary: This paper addresses the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. It proposes a consensus ADMM-based SMF algorithm to handle the state estimation constraints by transforming the nonlinear system into a linear one using a SIP approach. The proposed filter is shown to be effective through numerical examples.
Article
Engineering, Electrical & Electronic
Samad Wali, Chunming Li, Mudassar Imran, Abdul Shakoor, Abdul Basit
Summary: This paper analyzes and tests the efficiency of the alternating direction method of multipliers (ADMM) for level-set based image segmentation. The comparison with the classical gradient descent method shows the effectiveness and efficiency of the ADMM method. Experimental results on medical image segmentation demonstrate an average segmentation coefficient of 0.97 (Dice) and 0.92 (Jaccard), with an average running time of 1.70 seconds and average estimation values of 0.0932 (MAD), 0.993 (accuracy), 0.981 (sensitivity), and 0.964 (specificity).
Article
Mathematics, Applied
Arash Sarshar, Steven Roberts, Adrian Sandu
Summary: This paper presents a new ADI approach based on the partitioned General Linear Methods framework, which allows for the construction of high order ADI methods and alleviates the order reduction phenomenon seen with other schemes. Numerical experiments provide further insight into the accuracy, stability, and applicability of these new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Zhang-Lei Shi, Xiao Peng Li, Chi-Sing Leung, Hing Cheung So
Summary: This study introduces an algorithm for portfolio optimization that explicitly controls the cardinality of the portfolio through a non-convex optimization problem. Results on real-world datasets demonstrate the superiority of the proposed algorithm over several existing algorithms.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Engineering, Mechanical
Miantao Chao, Liqun Liu
Summary: In this paper, a dynamical ADMM is proposed for two-block separable optimization problems. The classical ADMM is obtained after discretizing the dynamical system in time. Under appropriate conditions, it is proved that the trajectory asymptotically converges to a saddle point of the Lagrangian function. When the coefficient matrices in the constraint are identity matrices, a worst-case O(1/t) convergence rate in the ergodic sense is proven.
NONLINEAR DYNAMICS
(2023)
Article
Multidisciplinary Sciences
Sofia Giuffre, Attilio Marciano
Summary: This paper deals with nonlinear monotone variational inequalities with gradient constraints. By using a new strong duality principle, the equivalence between the problem at hand and a suitable double obstacle problem is proven. Furthermore, the existence of L-2 Lagrange multipliers is achieved.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Optics
Roger Chiu, Carlos E. Castaneda, Onofre Orozco-Lopez, Didier Lopez-Mancilla, Edgar Villafana-Rauda
Summary: Keeping information hidden has always been crucial, and cryptography has been used for centuries, with various encryption methods and models proposed. The encryption method is a key challenge, as the security of the encryption system depends on how the process is conducted. In this study, we propose an encryption model based on convolution, which lacks a direct inversion process, making it difficult to restore encrypted data. The results demonstrate that this model is highly resistant to external attacks, making it a promising candidate for information encryption applications.
OPTICS AND LASER TECHNOLOGY
(2023)
Article
Engineering, Mechanical
Liang Yu, Jerome Antoni, Han Zhao, Qixin Guo, Rui Wang, Weikang Jiang
Summary: In this paper, a novel computational framework for acoustic imaging is proposed, which simplifies the algorithm to balance computation speed and accuracy by converting the problem into an inverse problem and dividing it into forward model and denoising model parts.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Operations Research & Management Science
Yunfei Qu, Wanbin Tong, Hongjin He, Yeong-Cheng Liou
Summary: The paper introduces a projection method for general variational inequalities, inspired by the spirit of the BB step size. Computational experiments show that this method is more efficient than existing state-of-the-art projection methods.
Article
Engineering, Multidisciplinary
Benxin Zhang, Guopu Zhu, Zhibin Zhu, Sam Kwong
Summary: This paper proposes a nonconvex log total variation model for image restoration, and presents a specific alternating direction method of multipliers to solve the model. Experimental results demonstrate that the proposed method is effective in image denoising, deblurring, computed tomography, magnetic resonance imaging, and image super-resolution.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Engineering, Electrical & Electronic
Feng Lin, Weiyu Li, Qing Ling
Summary: This paper addresses the problem of distributed learning under Byzantine attacks and proposes a Byzantine-robust stochastic ADMM method. The effectiveness of the proposed method is demonstrated through theoretical analysis and numerical experiments.
Article
Engineering, Electrical & Electronic
Ekin Nurbas, Emrah Onat, T. Engin Tuncer
Summary: The paper introduces a new method for DoA estimation in distributed sensor array networks using ADMM and SBL framework, showing improved performance in local arrays and reduction in transmitted parameters. Experimental results demonstrate that distributed use of ADMM efficiently enhances DoA estimation performance.
DIGITAL SIGNAL PROCESSING
(2022)
Article
Cell Biology
Aiye Wang, Zhuoqun Zhang, Siqi Wang, An Pan, Caiwen Ma, Baoli Yao
Summary: This paper introduces a method called ADMM-FPM which utilizes the concept of alternating direction method of multipliers to solve the phase retrieval problem in Fourier ptychographic microscopy (FPM). Compared to existing algorithms, ADMM-FPM shows better stability and robustness under noisy conditions.
Article
Operations Research & Management Science
Sedi Bartz, Ruben Campoy, Hung M. Phan
Summary: This paper proposes and studies an adaptive version of ADMM for the case where the objective function is the sum of a strongly convex function and a weakly convex function. By combining generalized notions of convexity and penalty parameters with the convexity constants of the functions, we prove convergence of the algorithm under natural assumptions.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Automation & Control Systems
Claus Danielson
Summary: This article presents an ADMM algorithm for solving large-scale MPC problems, reducing computational cost and memory usage through symmetry decomposition. In practical case studies, the symmetric algorithm significantly reduced computation time and memory usage, enabling previously unviable MPCs to run in real time on resource-limited embedded computers.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2021)
Article
Optics
Christian Brunner, Andreas Duensing, Christian Schroeder, Michael Mittermair, Vladimir Golkov, Maximilian Pollanka, Daniel Cremers, Reinhard Kienberger
Summary: In this study, deep neural networks are applied to solve the challenge of information extraction from spectrograms recorded with the attosecond streak camera in time-resolved photoelectron spectroscopy. Extensive benchmarking on simulated data shows that the deep neural networks exhibit competitive retrieval quality and superior tolerance against noisy data conditions.
Article
Robotics
Lukas von Stumberg, Daniel Cremers
Summary: We present a monocular visual-inertial odometry system based on delayed marginalization and pose graph bundle adjustment. By delaying marginalization, we can obtain updated marginalization prior and new linearization points, and inject IMU information into marginalized states. Our system outperforms existing techniques in visual-inertial odometry.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Article
Computer Science, Artificial Intelligence
Hartmut Bauermeister, Emanuel Laude, Thomas Moellenhoff, Michael Moeller, Daniel Cremers
Summary: Dual decomposition approaches in nonconvex optimization often encounter duality gaps. This paper eliminates the duality gap by reformulating the nonconvex task in the space of measures and approximating the infinite-dimensional problem using a piecewise polynomial discretization in the dual. The approach successfully reduces the duality gap and demonstrates scalability in the stereo matching problem.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Zhenzhang Ye, Bjoern Haefner, Yvain Queau, Thomas Moellenhoff, Daniel Cremers
Summary: This paper discusses the formulation of imaging and low-level vision problems as nonconvex variational problems and proposes convex relaxation methods to solve them. It extends a previous conference paper by introducing product-space relaxation and sublabel-accurate discretization, and demonstrates the use of a cutting-plane method to solve the resulting semi-infinite optimization problem. The journal version includes additional experiments, a more detailed algorithm outline, and a user-friendly introduction to functional lifting methods.
INTERNATIONAL JOURNAL OF COMPUTER VISION
(2023)
Editorial Material
Engineering, Electrical & Electronic
Subhadip Mukherjee, Andreas Hauptmann, Ozan Oktem, Marcelo Pereyra, Carola-Bibiane Schonlieb
Summary: In recent years, there has been significant progress in understanding the stability and convergence of data-driven methods for image reconstruction, despite concerns about their lack of robustness. This article introduces convergence concepts and presents a survey of learned methods with mathematically rigorous guarantees, such as input-convex neural networks (ICNNs) that combine deep learning with convex regularization theory. The article aims to provide valuable insights for methodological researchers and practitioners alike, by advancing the understanding and establishing a solid mathematical foundation for data-driven image reconstruction.
IEEE SIGNAL PROCESSING MAGAZINE
(2023)
Article
Engineering, Electrical & Electronic
Dongdong Chen, Mike Davies, Matthias J. Ehrhardt, Carola-Bibiane Schonlieb, Ferdia Sherry, Julian Tachella
Summary: From early image processing to modern computational imaging, successful models and algorithms have relied on the fundamental property of natural signals: symmetry. Symmetry, in the form of equivariance, can also be incorporated into deep neural networks (DNNs) for more data-efficient learning. However, computational imaging presents unique challenges for equivariant network solutions due to the observation of images through noisy and ill-conditioned operators. The emerging field of equivariant imaging (EI) provides improved generalization and new imaging opportunities, with links to acquisition physics, iterative reconstruction, blind compressed sensing, and self-supervised learning.
IEEE SIGNAL PROCESSING MAGAZINE
(2023)
Article
Mathematics, Applied
Carlos Esteve-Yague, Willem Diepeveen, Ozan Oktem, Carola-Bibiane Schonlieb
Summary: This paper presents the problem of reconstructing the three-dimensional atomic structure of a flexible macromolecule from a cryogenic electron microscopy (cryo-EM) dataset. By assuming that the macromolecule can be modeled as a chain or discrete curve, a method is introduced to estimate the deformation of the atomic model with respect to a given conformation. The method involves estimating the torsion and bond angles of the atomic model in each conformation as a linear combination of the eigenfunctions of the Laplace operator in the manifold of conformations.
Article
Computer Science, Artificial Intelligence
Qadeer Khan, Idil Sueloe, Melis Oecal, Daniel Cremers
Summary: Supervised deep learning methods using image data have shown promise in vehicle control, but suffer from the need for labeled training data and poor performance on out-of-distribution scenarios. To address these issues, we propose a framework that leverages visual odometry to determine vehicle trajectory and uses this to infer steering labels. Additionally, synthesized images from deviated trajectories are included in the training distribution for improved neural network robustness.
APPLIED INTELLIGENCE
(2023)
Article
Engineering, Biomedical
Malena Sabate Landman, Ander Biguri, Sepideh Hatamikia, Richard Boardman, John Aston, Carola-Bibiane Schonlieb
Summary: Krylov subspace methods are powerful iterative solvers for linear systems, commonly used in inverse problems. This work aims to bridge the gap between this field and applied medical physics and engineering, by providing a general framework for relevant Krylov subspace methods applied to 3D CT problems. Numerical results in synthetic and real-world CT applications are presented to showcase and compare the different methods.
PHYSICS IN MEDICINE AND BIOLOGY
(2023)
Article
Robotics
Simon Klenk, Lukas Koestler, Davide Scaramuzza, Daniel Cremers
Summary: Estimating neural radiance fields (NeRFs) from ideal images has been extensively studied. However, most methods assume optimal illumination and camera motion, which are often violated in robotic applications. To address this, we propose E-NeRF, the first method that estimates NeRFs from a fast-moving event camera.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yiran Wei, Xi Chen, Lei Zhu, Lipei Zhang, Carola-Bibiane Schonlieb, Stephen Price, Chao Li
Summary: The proposed study presents a multi-modal learning framework for predicting the genotype of glioma by integrating focal tumor image, tumor geometrics, and global brain network features. Experimental results demonstrate that the model outperforms baseline deep learning models, and the visualized interpretation aligns with clinical knowledge.
IEEE TRANSACTIONS ON MEDICAL IMAGING
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Lu Sang, Bjoern Haefner, Xingxing Zuo, Daniel Cremers
Summary: This paper presents a novel multi-view RGB-D based reconstruction method that utilizes a gradient signed distance field (gradient-SDF) to handle camera pose, lighting, albedo, and surface normal estimation. The proposed method optimizes the surface's quantities using its volumetric representation and validates two physically-based image formation models. Experimental results show that this method can recover high-quality surface geometry more accurately.
2023 IEEE/CVF WINTER CONFERENCE ON APPLICATIONS OF COMPUTER VISION (WACV)
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Florian Hofherr, Lukas Koestler, Florian Bernard, Daniel Cremers
Summary: We propose a method that combines neural implicit representations with neural ordinary differential equations to directly identify dynamic scene representations from visual observations. Our model requires less training data and has stronger generalization abilities than existing methods, and it can process high-resolution videos and synthesize photorealistic images. Additionally, our model can identify interpretable physical parameters and make long-term predictions.
2023 IEEE/CVF WINTER CONFERENCE ON APPLICATIONS OF COMPUTER VISION (WACV)
(2023)
Article
Computer Science, Information Systems
Lei Zhu, Xiaoqiang Wang, Ping Li, Xin Yang, Qing Zhang, Weiming Wang, Carola-Bibiane Schonlieb, C. L. Philip Chen
Summary: RGB-D salient object detection aims to detect visually distinctive objects or regions from a pair of the RGB image and the depth image. In this work, we propose a self-supervised self-ensembling network (S-3 Net) for semi-supervised RGB-D salient object detection by leveraging the unlabeled data and exploring a self-supervised learning mechanism. Experimental results demonstrate that our network outperforms the state-of-the-art methods on seven widely-used benchmark datasets.
IEEE TRANSACTIONS ON MULTIMEDIA
(2023)
Article
Computer Science, Artificial Intelligence
Philip Sellars, Angelica Aviles-Rivero, Carola-Bibiane Schonlieb
Summary: Semisupervised learning has gained attention for its ability to reduce the need for labeled data and improve deep semisupervised classification performance. This paper introduces the LaplaceNet framework, which utilizes graph-based pseudolabels and neural network training to achieve state-of-the-art results. The use of multisampling augmentation also enhances generalization.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
