25 papers · ranked by Valyu relevance
Martin Benning, Martin Burger
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo- )inverses feasible. In the last two decades interest has shifted from linear towards nonlinear regularization methods even for linear inverse problems.…
Cesare Molinari, Mathurin Massias, Lorenzo Rosasco, Silvia Villa
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms…
Simon Matet, Lorenzo Rosasco, Silvia Villa, Bang Long Vu
We consider the problem of designing efficient regularization algorithms when regularization is encoded by a (strongly) convex functional. Unlike classical penalization methods based on a relaxation approach, we propose an iterative method where regularization is achieved via early stopping. Our results show that the…
Silvia Gazzola, Per Christian Hansen, James G. Nagy
This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR TOOLS, serves two related purposes: we provide implementations of a range of iterative solvers, including several recently proposed methods…
Jingfeng Wu, Vladimir Braverman, Lin F. Yang
Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a single round of training takes significant amount of time. Very recently, Neu &…
Ali Punjani, Haowei Zhang, David J. Fleet
Single particle cryo-EM is a powerful method for studying proteins and other biological macromolecules. Many of these molecules comprise regions with varying structural properties including disorder, flexibility, and partial occupancy. These traits make computational 3D reconstruction from 2D images challenging.…
Nathaniel Mays, Zhong Ming
We propose and analyze an iterative refinement of a modified Lavrentiev regularization method for deconvolution of the discrete Helmholtz-type differential filter. The modification for the Lavrentiev regularization method exploits the properties of the Helmholtz filter, and we prove that the modification reduces the…
Beilei Tong
A weighted Bregman-Gradient Projection denoising method, based on the Bregman iterative regularization (BIR) method and Chambolle’s Gradient Projection method (or dual denoising method) is established. Some applications to image denoising on a 1-dimensional curve, 2-dimensional gray image and 3-dimensional color image…
Huanyu Xu, Quansen Sun, Nan Luo, Guo Cao + 2 more
In this paper, a Bregman iteration based total variation image restoration algorithm is proposed. Based on the Bregman iteration, the algorithm splits the original total variation problem into sub-problems that are easy to solve. Moreover, non-local regularization is introduced into the proposed algorithm, and a method…
Julianne Chung, Silvia Gazzola
In this paper we develop flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with an ℓ2 fit-to-data term and an ℓp penalization term, for p ≥ 1. First we approximate the p-norm penalization term as a sequence of 2-norm penalization terms using adaptive…
Quoc Tuan Nguyen Diep, Hoang Nhut Huynh, Thanh Ven Huynh, Minh Quan Cao Dinh + 2 more
'Minh Quan Cao Dinh' 'Anh Tu Tran' 'Trung Nghia Tran'] Title: Abstract Electrical Impedance Tomography (EIT) is a non-invasive method for imaging conductivity distributions within a target area. The inverse problem associated with EIT is nonlinear and ill-posed, leading to low spatial resolution reconstructions.…
S Crisci, M Piana, V Ruggiero, M Scussolini
Parametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. From a computational viewpoint, the realization of parametric images requires the pixel-wise numerical…
Holger Mohr, Hannes Ruge
In certain modeling approaches, activation analyses of task-based fMRI data can involve a relatively large number of predictors. For example, in the encoding model approach, complex stimuli are represented in a high-dimensional feature space, resulting in design matrices with many predictors. Similarly, single-trial…
Bin Jia, Xiaodong Wang
Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot…
Silvia Gazzola, Sebastian James Scott, Alastair Spence, Fabiana Zama + 1 more
'Elena Loli Piccolomini'] Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total…
Mauro Leidi, Yiwei Jia, Dominik Helbing, Jaime Barranco + 6 more
An open-source, user-friendly MATLAB framework for Magnetic Resonance Imaging (MRI) reconstruction was developed to simplify the reconstruction process, with a specific focus on non-Cartesian imaging and dynamic applications in the presence of motion. Monalisa is decomposing the reconstruction pipeline into clear…
Authors not listed
Collective variables (CVs) are essential for interpreting and accelerating rare events in molecular simulations. However, their design remains limited by the requirement of differentiability with respect to atomic coordinates. This constraint excludes many powerful structural descriptors that are routinely used for…
Navid Azizan, Sahin Lale, Babak Hassibi
Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization, such as "explicit regularization" (via weight decay), are often used to avoid…
Samuel Lippl, Benjamin Peters, Nikolaus Kriegeskorte, Xiao Luo
Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. However, principled methods for measuring and manipulating iterative…
Lippl Samuel, Peters Benjamin, Kriegeskorte Nikolaus
Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. Here we quantify the degree to which ResNets learn iterative solutions and…
Adeleke Maradesa, Baptiste Py, Ting Hei Wan, Mohammed B. Effat + 1 more
Electrochemical impedance spectroscopy (EIS) is a characterization technique used widely in electrochemistry. Obtaining EIS data is simple when modern electrochemical workstations are used; however, analyzing EIS spectra is still a considerable quandary. The distribution of relaxation times (DRT) has emerged as a…
Sanjar Adilov
Machine learning models for molecular-property prediction typically work with molecular representations in the form of fingerprints, descriptors, or graphs. In case of fingerprints and descriptors, molecular representations usually comprise thousands of features, which causes the curse of dimensionality for many…
Authors not listed
Electrochemical impedance spectroscopy (EIS) coupled with distribution of relaxation times (DRT) analysis is a robust framework for characterizing electrochemical systems. However, DRT deconvolution is often plagued by spurious peaks, hindering accurate process identification and quantitative parameter estimation. To…
Authors not listed
Plastic mechanical recycling is the conventional technological step towards circularity. In such aspects, complex mixtures of polyolefin blends are often fed into mechanical recycling systems, resulting in moulded products with uncertain quality. To add to the difficulty of heterogeneous feedstocks, the testing of…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…