Article
Geochemistry & Geophysics
Xiaocheng Yang, Chaodong Lu, Jingye Yan, Lin Wu, Mingfeng Jiang, Lin Li
Summary: Synthetic aperture imaging radiometers (SAIRs) are powerful tools for high-resolution imaging, but their reconstruction process faces an ill-posed inverse problem. This letter presents a reweighted total variation (RTV) method to address the reconstruction issue in SAIRs, and numerical simulation experiments demonstrate the effectiveness and performance of the proposed method.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2022)
Article
Operations Research & Management Science
Mohammad Eslannian
Summary: In this paper, we study the split common fixed point problem for a finite family of demimetric mappings and a finite family of Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem of Halpern's type iteration for finding a solution of the split common fixed point problem.
Article
Operations Research & Management Science
Simeon Reich, Truong Minh Tuyen
Summary: New cyclic projection algorithms based on Bregman distances are proposed for solving the split common fixed point problem for Bregman relatively nonexpansive operators and the split feasibility problem with multiple output sets in real reflexive Banach spaces.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Xiangfan Mu, Rui Shi, Geng Luo, Xianguo Tuo, Honglong Zheng
Summary: High spatial resolution tomographic gamma scanning (TGS) reconstruction is crucial for radioassay of drummed low-level radioactive waste. Sparse sampling and improved algorithms such as MLEM-TVM have been applied to achieve accurate imaging results in a shorter scanning time, enhancing radionuclide positioning and radioactivity reconstruction accuracy.
IEEE TRANSACTIONS ON NUCLEAR SCIENCE
(2021)
Article
Geochemistry & Geophysics
Minghua Wang, Qiang Wang, Jocelyn Chanussot, Dan Li
Summary: This study introduces a novel approach for removing mixed noise from hyperspectral images using a multidirectional low-rank modeling and spatial-spectral total variation model. By combining weighted nuclear norm and SSTV regularization, it can estimate LR tensor more accurately and effectively remove noise.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2021)
Article
Mathematics, Applied
Majed Alotaibi, Alessandro Buccini, Lothar Reichel
Summary: This paper investigates the possibility of projecting large-scale problems into a Krylov subspace of small dimension and solving the minimization problem using a split Bregman algorithm. The focus is on restoring images contaminated by blur and noise. Computed examples demonstrate that the projected split Bregman methods described are fast and yield high-quality solutions.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Thermodynamics
Benjamin A. Tourn, Juan C. Alvarez Hostos, Victor D. Fachinotti
Summary: This work proposes the extension of total variation regularization strategies to solve one-dimensional linear inverse heat conduction problems. Three solution procedures are tested and compared in terms of their performance, showing that the staircase effect dominates the reconstructions. Despite deteriorating the quality in some cases, it does not prevent the appropriate fulfillment of the reconstruction task. This study demonstrates the suitability and reliability of extending total variation approaches as a novel alternative to standard procedures in solving linear inverse heat conduction problems involving the estimation of surface heat fluxes.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2021)
Article
Computer Science, Software Engineering
P. S. Baiju, Sherin Lisa Antony, Sudhish N. George
Summary: An optimization framework is proposed to efficiently estimate the scene transmission map for effective dehazing, introducing low-rank approximation and total variation regularization to enhance dehazing effects. The inclusion of l(1) norm minimization enhances details, resulting in dehazing results surpassing state-of-the-art methods.
Article
Mathematics, Applied
E. C. Godwin, T. O. Alakoya, O. T. Mewomo, J. C. Yao
Summary: In this paper, a split minimization problem with multiple output sets is introduced and studied. A new iterative method is proposed for solving the problem, using the inertial Halpern approximation technique in p-uniformly convex and uniformly smooth Banach spaces. The method does not require prior knowledge of the operators norm, and a strong convergence result is proven under mild conditions. Applications and numerical examples are presented to demonstrate the efficiency and applicability of the algorithm. The results in this paper unify and complement existing research in the literature.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Fariba Kazemi Golbaghi, M. R. Eslahchi, Mansoor Rezghi
Summary: In this paper, a novel variable-order total fractional variation model is proposed for image denoising, which automatically allocates the order of fractional derivative for each pixel based on the context of the image, capturing both the edges and texture of the image simultaneously. The efficiency of the model is demonstrated through good visual effects and a better signal-to-noise ratio.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Operations Research & Management Science
Hamid Gazmeh, Eskandar Naraghirad
Summary: This paper discusses the split common null point problem in two Banach spaces and proves strong convergence theorems using the Bregman generalized resolvents of maximal monotone operators. A new technique based on the Bregman distance induced by a Bregman function is introduced, improving and extending many recent results in the literature.
Article
Physics, Multidisciplinary
Aobing Chi, Chengbi Zeng, Yufu Guo, Hong Miao
Summary: This paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor-Fourier coefficients in a multi-frequency dynamic phasor model. It transforms the phasor problem into a compressive sensing model based on the regularity and sparsity of the dynamic harmonic signal distribution, and derives an optimized hybrid regularization algorithm with the Bregman split method to improve the estimation accuracy.
Article
Mathematics, Applied
Godwin Chidi Ugwunnadi, Chinedu Izuchukwu, Abdul Rahim Khan
Summary: This article studies the split common fixed point problem for Bregman demigeneralized type mappings in the context of two real Banach spaces. A new self-adaptive method is proposed and proven to strongly converge to a solution of this problem. As a consequence, new self-adaptive methods for solving split feasibility problem, split common null point problem, and split equilibrium problem are proposed using dynamical stepsize techniques, allowing these methods to be easily implemented without prior knowledge of the norm of the bounded linear operator. Numerical experiments are performed to demonstrate the implementation and efficiency of the methods.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Evelyn Cueva, Alexander Meaney, Samuli Siltanen, Matthias J. Ehrhardt
Summary: This work discusses synergistic multi-spectral CT reconstruction that combines information from all energy channels to enhance reconstruction of each individual channel. By fusing available data to obtain a polyenergetic image and using directional total variation as prior information, improvements in image quality and computational speed are observed. The study also analyzes the use of directional total variation in variational regularization and iterative regularization processes.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Computer Science, Software Engineering
Chunxue Wang, Huayan Zhang, Ligang Liu
Summary: This paper introduces a reflectance and illumination decomposition model for the Retinex problem using total generalized variation regularization and H1 decomposition. Experimental results show that the proposed model is comparable both quantitatively and qualitatively with several state-of-the-art methods.
Article
Chemistry, Physical
Kristopher K. Barr, Naihao Chiang, Andrea L. Bertozzi, Jerome Gilles, Stanley J. Osher, Paul S. Weiss
Summary: Scanning probe techniques have been enhanced by improving data acquisition and image processing algorithms, enabling more detailed analysis of surfaces and interfaces, including image segmentation by domains, detection of dipole direction, and hydrogen-bonding interactions. The computational algorithms used in these techniques are continually evolving, with the incorporation of machine learning to the next level of iteration. However, real-time adjustments during data recording are still a challenge for significantly enhancing microscopy and spectroscopic imaging methods.
JOURNAL OF PHYSICAL CHEMISTRY C
(2022)
Article
Chemistry, Multidisciplinary
Joseph de Rutte, Robert Dimatteo, Maani M. Archang, Mark van Zee, Doyeon Koo, Sohyung Lee, Allison C. Sharrow, Patrick J. Krohl, Michael Mellody, Sheldon Zhu, James Eichenbaum, Monika Kizerwetter, Shreya Udani, Kyung Ha, Richard C. Willson, Andrea L. Bertozzi, Jamie B. Spangler, Robert Damoiseaux, Dino Di Carlo
Summary: Techniques to analyze and sort single cells based on functional outputs have the potential to transform cellular biology and accelerate the development of cell and antibody therapies. This study describes a method to fabricate chemically functionalized microcontainers, called nanovials, for sorting single cells based on their secreted products. The nanovials can be easily used with commonly accessible laboratory infrastructure and allow high-throughput screening of cells.
Article
Engineering, Multidisciplinary
Kyung Ha, Joseph de Rutte, Dino Di Carlo, Andrea L. Bertozzi
Summary: This paper introduces a new method to create templated droplets using amphiphilic microparticles and presents a mathematical model to explain the key properties of droplet formation.
JOURNAL OF ENGINEERING MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Bao Wang, Tan Nguyen, Tao Sun, Andrea L. Bertozzi, Richard G. Baraniuk, Stanley J. Osher
Summary: This paper proposes a new DNN training scheme called scheduled restart SGD (SRSGD), which replaces the constant momentum in SGD with increasing momentum and stabilizes the iterations by resetting the momentum to zero according to a schedule. Experimental results demonstrate that SRSGD significantly improves the convergence and generalization of DNNs across various models and benchmarks.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Oncology
Hangjie Ji, Kyle Lafata, Yvonne Mowery, David Brizel, Andrea L. Bertozzi, Fang-Fang Yin, Chunhao Wang
Summary: A biologically guided deep learning method was developed to predict post-radiation (18)FDG-PET image outcome based on pre-radiation images and radiotherapy dose information. The method incorporates a novel biological model and a 7-layer CNN to generate predicted images with breakdown biological components. The results showed good agreement with ground-truth and can be used for adaptive radiotherapy decision-making.
FRONTIERS IN ONCOLOGY
(2022)
Article
Mathematics, Applied
Marcelo Bongarti, Luke Diego Galvan, Lawford Hatcher, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi
Summary: In this paper, two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of infectious diseases are proposed using modified versions of the SIAR model. The first modification assumes a known proportion of the population does not comply with government mandates, while the second modification treats non-compliant behavior as a social contagion. The paper also explores different scenarios and provides local and asymptotic analyses for both models.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yifan Hua, Kevin Miller, Andrea L. Bertozzi, Chen Qian, Bao Wang
Summary: This paper proposes near-optimal overlay networks based on d-regular expander graphs for accelerating decentralized federated learning and improving its generalization. By integrating spectral graph theory and the theoretical convergence and generalization bounds for DFL, the proposed overlay networks provide theoretical guarantees for accelerated convergence, improved generalization, and enhanced robustness to client failures in DFL. Additionally, an efficient algorithm is presented to convert a given graph into a practical overlay network and maintain the network topology after potential client failures. Numerical experiments demonstrate the advantages of DFL with the proposed networks on various benchmark tasks involving hundreds of clients.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Dominic Yang, Yurun Ge, Thien Nguyen, Denali Molitor, Jacob D. Moorman, Andrea L. Bertozzi
Summary: Symmetry is important in subgraph matching and affects both the graph description and the search process. This work quantifies the effects of symmetry and proposes using it to improve subgraph isomorphism algorithms' efficiency. The authors define structural equivalence and establish conditions for safely generating more solutions. They demonstrate how to modify search routines to utilize symmetries and efficiently describe the solution space. The methods are tested on a benchmark set and extended to multiplex graphs with results from transportation systems, social media, adversarial attacks, and knowledge graphs.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2023)
Article
Criminology & Penology
Jiaoying Ren, Karina Santoso, David Hyde, Andrea L. Bertozzi, P. Jeffrey Brantingham
Summary: This paper examines the impact of COVID-19 on the activities of front-line workers in the City of Los Angeles Mayor's Office of Gang Reduction and Youth Development (GRYD), and finds that proactive peacemaking and violence interruption activities either remained stable or increased with the onset of the lockdown. However, the causal connection between these activities and gang-related crime needs further evaluation.
JOURNAL OF AGGRESSION CONFLICT AND PEACE RESEARCH
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Jason Brown, Riley O'Neill, Jeff Calder, Andrea L. Bertozzi
Summary: By using data augmentations specific to SAR imagery, this paper develops a contrastive SimCLR framework for feature extraction from MSTAR images. The results show that our contrastive embedding performs better than the autoencoder embedding in automatic target recognition on the MSTAR dataset.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXX
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Joshua Enwright, Harris Hardiman-Mostow, Jeff Calder, Andrea Bertozzi
Summary: This article introduces two new methods for classifying SAR data. The first method involves using Convolutional Neural Network (CNN) for feature extraction and combining with graph-based semi-supervised learning techniques to improve classification performance in small labeled datasets. The second method involves using Pseudo Label Propagation Neural Networks (PsLaPN Networks) to enhance training signal and address overconfidence and poor model calibration in neural networks. In experiments, both methods outperform the previous state-of-the-art on the OpenSARShip dataset.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXX
(2023)
Proceedings Paper
Acoustics
Harlin Lee, Andrea L. Bertozzi, Jelena Kovacevic, Yuejie Chi
Summary: This study investigates multi-task learning and proposes a fusion framework for federated multi-task linear regression. The proposed method combines local estimates and achieves improved performance in terms of mean squared error. Experimental results show the effectiveness of the method on real-world data.
2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
(2022)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Kevin Miller, Jack Mauro, Jason Setiadi, Xoaquin Baca, Zhan Shi, Jeff Calder, Andrea L. Bertozzi
Summary: The article presents a novel method for classifying Synthetic Aperture Radar (SAR) data using a combination of graph-based learning and neural network methods. The method uses a Convolutional Neural Network Variational Autoencoder (CNNVAE) to embed SAR data into a feature space, and then constructs a similarity graph for classification. The method reduces overfitting and improves generalization performance, and can be easily combined with human-in-the-loop active learning.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXIX
(2022)
Article
Automation & Control Systems
Karthik Elamvazhuthi, Bahman Gharesifard, Andrea L. Bertozzi, Stanley Osher
Summary: The controllability problem of the continuity equation corresponding to neural ordinary differential equations is explored, showing strong controllability properties. Specifically, given solutions of the continuity equation define trajectories on sets of probability measures. The study establishes the approximate controllability of the continuity equation of the neural ODE on sets of compactly supported probability measures.
IEEE CONTROL SYSTEMS LETTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xia Li, Chuntian Wang, Hao Li, Andrea L. Bertozzi
Summary: Deterministic compartmental models can provide the mean behavior of stochastic agent-based models, but they may significantly deviate from the mean in finite size populations due to chance variations. In this article, a martingale formulation is derived for the stochastic Susceptible-Infected-Recovered (SIR) model, consisting of a deterministic part coinciding with the classical SIR model and an upper bound for the stochastic part. Theoretical explanation of finite size effects is provided through analysis of the stochastic component depending on varying population size, supported by quantitative and direct numerical simulations.
NETWORKS AND HETEROGENEOUS MEDIA
(2022)
