We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.
Variational Regularization of Inverse Problems for Manifold-Valued Data
Image Analysis and Learning Group, Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Germany（图像分析与学习组，跨学科科学计算中心，海德堡大学，德国）；Department of Mathematics and Natural Sciences, Hochschule Darmstadt, and Institute of Computational Biology, Helmholtz Zentrum München, Germany（数学与自然科学系，达姆施塔特应用科学大学，以及计算生物学研究所，海德堡研究中心，德国）
Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging
Institute of Applied Mathematics, University of Bonn, Germany（波恩大学应用数学研究所）；Euler Institute, Università della svizzera italiana, Switzerland（瑞士意大利欧拉研究所；格拉茨大学数学与计算科学系）；Department of Mathematics and Scientific Computing, University of Graz, Austria（波恩心脏中心，第二内科部，波恩大学医院）；Heart Center Bonn, Department of Internal Medicine II, University Hospital Bonn, Germany（特伦托大学数学系）；Department of Mathematics, University of Trento, Italy
DARE: A Deformable Adaptive Regularization Estimator for Learning-Based Medical Image Registration
Department of Mathematics, University of Innsbruck（数学系，因斯布鲁克大学）；Department of Radiology, Medical University of Innsbruck（放射学系，因斯布鲁克医学院）；Neuroimaging Research Core Facility, Medical University of Innsbruck（神经影像研究核心设施，因斯布鲁克医学院）
