Manifold Based Low-Rank Regularization for Image Restoration and Semi-Supervised Learning

Manifold Based Low-Rank Regularization for Image Restoration and Semi-Supervised Learning Low-rank structures play important roles in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold structure has been considered in many data processing problems. Inspired by this concept, we consider a manifold based low-rank regularization as a linear approximation of manifold dimension. This regularization is less restricted than the global low-rank regularization, and thus enjoy more flexibility to handle data with nonlinear structures. As applications, we demonstrate the proposed regularization to classical inverse problems in image sciences and data sciences including image inpainting, image super-resolution, X-ray computer tomography image reconstruction and semi-supervised learning. We conduct intensive numerical experiments in several image restoration problems and a semi-supervised learning problem of classifying handwritten digits using the MINST data. Our numerical tests demonstrate the effectiveness of the proposed methods and illustrate that the new regularization methods produce outstanding results by comparing with many existing methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

Manifold Based Low-Rank Regularization for Image Restoration and Semi-Supervised Learning

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0492-x
Publisher site
See Article on Publisher Site

Abstract

Low-rank structures play important roles in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold structure has been considered in many data processing problems. Inspired by this concept, we consider a manifold based low-rank regularization as a linear approximation of manifold dimension. This regularization is less restricted than the global low-rank regularization, and thus enjoy more flexibility to handle data with nonlinear structures. As applications, we demonstrate the proposed regularization to classical inverse problems in image sciences and data sciences including image inpainting, image super-resolution, X-ray computer tomography image reconstruction and semi-supervised learning. We conduct intensive numerical experiments in several image restoration problems and a semi-supervised learning problem of classifying handwritten digits using the MINST data. Our numerical tests demonstrate the effectiveness of the proposed methods and illustrate that the new regularization methods produce outstanding results by comparing with many existing methods.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jul 6, 2017

References

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