research-article

Nonnegative Tensor Patch Dictionary Approaches for Image Compression and Deblurring Applications

Authors:

Elizabeth Newman,

Misha E. KilmerAuthors Info & Claims

SIAM Journal on Imaging Sciences, Volume 13, Issue 3

Pages 1084 - 1112

https://doi.org/10.1137/19M1297026

Published: 01 January 2020 Publication History

Abstract

In recent work [S. Soltani, M. Kilmer, and P. C. Hansen, BIT, 56 (2016)], an algorithm for nonnegative tensor patch dictionary learning in the context of X-ray CT imaging and based on a tensor-tensor product called the t-product [M. E. Kilmer and C. D. Martin, Linear Algebra Appl., 435 (2011), pp. 641--658] was presented. Building on that work, in this paper, we use nonnegative tensor patch--based dictionaries trained on other data, such as facial image data, for the purpose of either compression or image deblurring. We begin with an analysis in which we address issues such as suitability of the tensor-based approach relative to a matrix-based approach, dictionary size, and patch size to balance computational efficiency and qualitative representations. Next, we develop an algorithm that is capable of recovering nonnegative tensor coefficients given a nonnegative tensor dictionary. The algorithm is based on a variant of the modified residual norm steepest descent method. We show how to augment the algorithm to enforce sparsity in the tensor coefficients and note that the approach has broader applicability since it can be applied to the matrix case as well. We illustrate the surprising result that dictionaries trained on image data from one class can be successfully used to represent and compress image data from different classes and across different resolutions. Finally, we address the use of nonnegative tensor dictionaries in image deblurring. We show that tensor treatment of the deblurring problem coupled with nonnegative tensor patch dictionaries can give superior restorations as compared to standard treatment of the nonnegativity constrained deblurring problem.

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Cited By

Mo CDing WWei Y(2024)Perturbation Analysis on T-Eigenvalues of Third-Order TensorsJournal of Optimization Theory and Applications10.1007/s10957-024-02444-z202:2(668-702)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s10957-024-02444-z
Liu YZeng XWang W(2023)Proximal gradient algorithm for nonconvex low tubal rank tensor recoveryBIT10.1007/s10543-023-00964-063:2Online publication date: 4-Apr-2023
https://dl.acm.org/doi/10.1007/s10543-023-00964-0

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cover image SIAM Journal on Imaging Sciences

SIAM Journal on Imaging Sciences Volume 13, Issue 3

EISSN:1936-4954

DOI:10.1137/sjisbi.13.3

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© 2020, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2020

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Cited By

Mo CDing WWei Y(2024)Perturbation Analysis on T-Eigenvalues of Third-Order TensorsJournal of Optimization Theory and Applications10.1007/s10957-024-02444-z202:2(668-702)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s10957-024-02444-z
Liu YZeng XWang W(2023)Proximal gradient algorithm for nonconvex low tubal rank tensor recoveryBIT10.1007/s10543-023-00964-063:2Online publication date: 4-Apr-2023
https://dl.acm.org/doi/10.1007/s10543-023-00964-0

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