Abstract
This chapter presents a new regularization method for inverse and imaging problems, called data-informed (DI) regularization, that implicitly avoids regularizing the data-informed directions. Our approach is inspired by and has a rigorous root in disintegration theory. We shall, however, present an elementary and constructive path using the classical truncated SVD and Tikhonov regularization methods. Deterministic and statistical properties of the DI approach are rigorously discussed, and numerical results for image deblurring, image denoising, and X-ray tomography are presented to verify our findings.
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This work was partially funded by the National Science Foundation awards NSF-1808576 and NSF-CAREER-1845799; by the Defense Threat Reduction Agency award DTRA-M1802962; by the Department of Energy award DE-SC0018147; by KAUST; by 2018 ConTex award; and by 2018 UT-Portugal CoLab award. The authors are grateful to the supports.
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Wittmer, J., Bui-Thanh, T. (2023). Data-Informed Regularization for Inverse and Imaging Problems. In: Chen, K., Schönlieb, CB., Tai, XC., Younes, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-98661-2_77
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