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multi-parameter regularization method for atmospheric remote sensing

COMPUTER PHYSICS COMMUNICATIONS 2005年第1期165卷 1-9页

作者： Doicu, A Schreier, F Hilgers, S Hess, M DLR Remote Sensing Technol Inst D-82234 Wessling Germany

The iteratively regularized Gauss-Newton algorithm with simple bounds on the variables is extended to the multi-parameter case. The global regularization matrix is computed by using the L-curve method for a sequence of one-parameter regularization problems. Numerical results concerning the joint retrieval of O-3 and NO2 profiles using the scattered light from the limb of the atmosphere are presented. (C) 2004 Elsevier B.V. All rights reserved.

关键词： inverse problems nonlinear least squares multi-parameter regularization atmospheric spectroscopy remote sensing

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multi-parameter regularization methods for high-resolution image reconstruction with displacement errors

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2007年第8期54卷 1788-1799页

作者： Lu, Yao Shen, Lixin Xu, Yuesheng Syracuse Univ Dept Math Syracuse NY 13244 USA

We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization. parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.

关键词： multi-parameter regularization high-resolution image reconstruction wavelets framelets

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A multi-parameter regularization Model for Deblurring Images Corrupted by Impulsive Noise

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2017年第9期36卷 3702-3730页

作者： Jiang, Dandan Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China

This article considers image deblurring in the presence of impulse noise and proposes a new multi-parameter regularization model for image deblurring based on total variation (TV) and wavelet frame (WF), along with an efficient and effective solving algorithm for this restoring model. On the one hand, it is well known that the TV regularization-based Rudin-Osher-Fatemi model is very effective in preserving sharp edges and object boundaries which are generally the most important features to recover. On the other hand, WF-based approaches for image restoration have proven to be very successful in adaptively exploiting the regularity of natural images. By combining TV regularization and WF regularization, a novel multi-parameter regularization model is proposed for deblurring images in the presence of impulse noise. Numerically, the alternative direction method of multiplier (ADMM) with an adaptive scheme for choosing regularization parameters is provided and applied to this multi-parameter regularization model. Moreover, the convergence analysis of the ADMM is shown in the "Appendix." Furthermore, numerical experiments involving images corrupted by various types of blurring kernels and different levels of noises indicate that the proposed model and algorithm outperform several state-of-the-art approaches in terms of the restoration quality, especially the ability to mitigate staircasing effects while preserving important features in images.

关键词： TV Framelet Deblurring Impulse noise multi-parameter regularization ADMM

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A multi-parameter regularization model for image restoration

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SIGNAL PROCESSING 2015年 114卷 131-142页

作者： Fan, Qibin Jiang, Dandan Jiao, Yuling Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China

This paper presents a new multi-parameter regularization model for image restoration (IR) based on total variation (TV) and wavelet frame (WF). On one hand, the Rudin-Osher-Fatemi (ROF) model using TV as the regularization term has been proven to be very effective in preserving sharp edges and object boundaries which are usually the most important features to recover. On the other hand, adaptively exploiting the regularity of natural images has led to the successful WF approaches for IR. In this paper, we propose a novel model that combines these two approaches together to restore images from blurry, noisy and partial observations. Computationally, we use the alternative direction method of multiplier (ADMM) to solve the new model and provide its convergence analysis in the appendix. Numerical experiments on a set of IR benchmark problems show that the proposed model and algorithm outperform several state-of-the-art approaches in terms of the restoration quality. (C) 2015 Elsevier B.V. All rights reserved.

关键词： TV Framelet Denoising Deblurring multi-parameter regularization

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multi-parameter regularization Method for Synthetic Aperture Imaging Radiometers

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REMOTE SENSING 2021年第3期13卷 382-382页

作者： Yang, Xiaocheng Yang, Zhenyi Yan, Jingye Wu, Lin Jiang, Mingfeng Zhejiang Sci Tech Univ Sch Informat Sci & Technol Hangzhou 310018 Peoples R China Chinese Acad Sci Natl Space Sci Ctr Beijing 100190 Peoples R China

Synthetic aperture imaging radiometers (SAIRs) are powerful passive microwave systems for high-resolution imaging by use of synthetic aperture technique. However, the ill-posed inverse problem for SAIRs makes it difficult to reconstruct the high-precision brightness temperature map. The traditional regularization methods add a unique penalty to all the frequency bands of the solution, which may cause the reconstructed result to be too smooth to retain certain features of the original brightness temperature map such as the edge information. In this paper, a multi-parameter regularization method is proposed to reconstruct SAIR brightness temperature distribution. Different from classical single-parameter regularization, the multi-parameter regularization adds multiple different penalties which can exhibit multi-scale characteristics of the original distribution. multiple regularization parameters are selected by use of the simplified multi-dimensional generalized cross-validation method. The experimental results show that, compared with the conventional total variation, Tikhonov, and band-limited regularization methods, the multi-parameter regularization method can retain more detailed information and better improve the accuracy of the reconstructed brightness temperature distribution, and exhibit superior noise suppression, demonstrating the effectiveness and the robustness of the proposed method.

关键词： imaging radiometry synthetic aperture reconstruction method multi-parameter regularization

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Discrepancy curves for multi-parameter regularization

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JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2010年第6期18卷 655-676页

作者： Lu, Shuai Pereverzev, Sergei V. Shao, Yuanyuan Tautenhahn, Ulrich Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China Univ Appl Sci Zittau Gorlitz Dept Math D-02755 Zittau Germany

For solving linear ill-posed problems regularization methods are required when the right-hand side is with some noise. In the present paper regularized solutions are obtained by multi-parameter regularization and the regularization parameters are chosen by a multi-parameter discrepancy principle. Under certain smoothness assumptions we provide order optimal error bounds that characterize the accuracy of the regularized solutions. For the computation of the regularization parameters fast algorithms of Newton type are applied which are based on special transformations. These algorithms are globally and monotonically convergent. Some of our theoretical results are illustrated by numerical experiments. We also show how the proposed approach may be employed for multi-task approximation.

关键词： Ill-posed problems inverse problems noisy right-hand side Tikhonov regularization multi-parameter regularization discrepancy principle order optimal error bounds Newton's method global convergence monotone convergence

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multi-parameter TIKHONOV regularization FOR LINEAR ILL-POSED OPERATOR EQUATIONS

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Journal of Computational Mathematics 2008年第1期26卷 37-55页

作者： Zhongying Chen Yao Lu Yuesheng Xu Hongqi Yang Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China Department of Mathematics Syracuse University Syracuse NY 13244-1150 USA

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.

关键词： Ill-posed problems Tikhonov regularization multi-parameter regularization

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multi-parameter Tikhonov regularization—An Augmented Approach

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Chinese Annals of Mathematics,Series B 2014年第3期35卷 383-398页

作者： Kazufumi ITO Bangti JIN Tomoya TAKEUCHI Center for Research in Scientific Computation & Department of Mathematics North Carolina State University Department of Mathematics University of California Riverside 900 University Ave.Riverside CA92521 USA. Collaborative Research Center for Innovative Mathematical Modelling Institute of Industrial ScienceThe University of Tokyo 4-6-1-Cw601 Komaba Meguro-ku Tokyo 153-8505 Japan.

We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.

关键词： multi-parameter regularization Augmented Tikhonov regularization Balanced discrepancy principle

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2DNMR data inversion using locally adapted multi-penalty regularization

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COMPUTATIONAL GEOSCIENCES 2021年第3期25卷 1215-1228页

作者： Bortolotti, Villiam Landi, Germana Zama, Fabiana Univ Bologna Dept Civil Chem Environm & Mat Engn Bologna Italy Univ Bologna Dept Math Bologna Italy

Geologists and Reservoir Engineers routinely use time-domain nuclear magnetic resonance (NMR) to learn about the porous structure of rocks that hold underground fluids. In particular, two-dimensional NMR (2DNMR) technique is now gaining importance in a wide variety of applications. Crucial issue in 2DNMR analysis are the speed, robustness and accuracy of the data inversion process. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion of 2DNMR data. The method solves an unconstrained optimization problem whose objective function contains a data-fitting term, a single L1 penalty parameter and a multiple parameter L2 penalty. We propose an adaptation of the Fast Iterative Shrinkage and Thresholding (FISTA) method to solve the multi-penalty minimization problem, and an automatic procedure to compute all the penalty parameters. This procedure generalizes the Uniform Penalty principle introduced in [Bortolotti et al., Inverse Problems, 33(1), 2016]. The proposed approach allows us to obtain accurate 2D relaxation time distributions while keeping short the computation time. Results of numerical experiments on synthetic and real data prove that the proposed method is efficient and effective in reconstructing the peaks and the flat regions that usually characterize 2DNMR relaxation time distributions.

关键词： NMR relaxometry multi-parameter regularization multi-penalty regularization UPEN2D FISTA

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A Golub-Kahan-Type Reduction Method for Matrix Pairs

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JOURNAL OF SCIENTIFIC COMPUTING 2015年第2期65卷 767-789页

作者： Hochstenbach, Michiel E. Reichel, Lothar Yu, Xuebo Eindhoven Univ Technol Dept Math & Comp Sci NL-5600 MB Eindhoven Netherlands Kent State Univ Dept Math Sci Kent OH 44242 USA

We describe a novel method for reducing a pair of large matrices to a pair of small matrices . The method is an extension of Golub-Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large linear discrete ill-posed problems are described. In these problems the matrix A represents a discretization of a compact integral operator and B is a regularization matrix.

关键词： Generalized Golub-Kahan bidiagonalization Generalized Lanczos bidiagonalization Generalized Krylov method Matrix pair decomposition Ill-posed problem Tikhonov regularization multi-parameter regularization

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