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Related papers: 3-D Projected $ L_{1}$ inversion of gravity data

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Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here…

Geophysics · Physics 2026-04-07 Pankaj K Mishra , Sanni Laaksonen , Jochen Kamm , Anand Singh

In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…

Optimization and Control · Mathematics 2021-12-28 Guiyun Xiao , Zheng-Jian Bai

We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…

Optimization and Control · Mathematics 2025-09-03 Xiaoyu Luo , Chuanhou Gao

How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…

Computer Vision and Pattern Recognition · Computer Science 2020-11-17 Zhaoqun Li

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

Computer Vision and Pattern Recognition · Computer Science 2023-08-11 Iaroslav Koshelev , Stamatios Lefkimmiatis

The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…

Optimization and Control · Mathematics 2025-11-19 Yuyuan Ouyang , Kyle Yates

The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…

Numerical Analysis · Mathematics 2022-08-16 Saeed Vatankhah , Rosemary A Renaut , Vahid E Ardestani

In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…

Numerical Analysis · Mathematics 2026-01-27 Yuyuan Zhou , Lorenzo Audibert , Shixu Meng , Bo Zhang

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li

Iteratively Re-weighted Least Squares (IRLS) were used to simulate the $L_p$-norm approximation of the ballistic trajectory in absolute gravimeters. Two iterations of the IRLS delivered sufficient accuracy of the approximation without a…

Instrumentation and Detectors · Physics 2016-02-17 V. D. Nagornyi , S. Svitlov , A. Araya

Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine…

Machine Learning · Computer Science 2020-06-03 Hongwei Dong , Liming Yang

The open source MATLAB package IGUG for 3D inversion of gravity data is presented. It is based on methodology that was introduced by Bijani et al (2015), in which a homogeneous subsurface body is modeled by an ensemble of simple point…

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…

Machine Learning · Computer Science 2022-08-31 Xiaoxia Wu , Edgar Dobriban , Tongzheng Ren , Shanshan Wu , Zhiyuan Li , Suriya Gunasekar , Rachel Ward , Qiang Liu

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

Statistics Theory · Mathematics 2013-11-05 Samuel Vaiter , Charles Deledalle , Gabriel Peyré , Charles Dossal , Jalal Fadili

In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…

Optimization and Control · Mathematics 2025-11-10 Na Zhang , Hong Chen , Qia Li , Junpeng Zhou

We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can…

Numerical Analysis · Mathematics 2020-12-30 Andrea Aspri , Yury Korolev , Otmar Scherzer

It is proposed to revisit the inverse problem associated with Smoluchowski's coagulation equation. The objective is to reconstruct the functional form of the collision kernel from observations of the time evolution of the cluster size…

Statistical Mechanics · Physics 2015-05-27 Colm Connaughton , Peter P. Jones

The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use…

Methodology · Statistics 2021-07-08 Sheng Dai

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in…

Machine Learning · Statistics 2025-07-02 Sunay Joshi , Shayan Kiyani , George Pappas , Edgar Dobriban , Hamed Hassani