research-article

A tensor-based dictionary learning approach to tomographic image reconstruction

Authors:

Misha E. Kilmer,

Per Christian HansenAuthors Info & Claims

Volume 56, Issue 4

Pages 1425 - 1454

https://doi.org/10.1007/s10543-016-0607-z

Published: 01 December 2016 Publication History

Abstract

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.

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A tensor-based dictionary learning approach to tomographic image reconstruction

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cover image BIT

BIT Volume 56, Issue 4

Dec 2016

352 pages

ISSN:0006-3835

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Copyright © 2016 Springer Science+Business Media Dordrecht.

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BIT Computer Science and Numerical Mathematics

United States

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Published: 01 December 2016

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Cited By

Huang GZhong S(2024)Tensor randomized extended Kaczmarz methods for large inconsistent tensor linear equations with t-productNumerical Algorithms10.1007/s11075-023-01684-w96:4(1755-1778)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s11075-023-01684-w
Han FMiao YSun ZWei Y(2023)T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network Based on Tensor T-product OperatorNeural Processing Letters10.1007/s11063-023-11361-755:8(10993-11016)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s11063-023-11361-7
Wang XWei PWei Y(2023)A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity ProblemsJournal of Optimization Theory and Applications10.1007/s10957-023-02169-5197:1(334-357)Online publication date: 13-Feb-2023
https://dl.acm.org/doi/10.1007/s10957-023-02169-5
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
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Liao YLu T(2022)On Greedy Kaczmarz Method with Uniform Sampling for Consistent Tensor Linear Systems Based on T-ProductProceedings of the 6th International Conference on Advances in Image Processing10.1145/3577117.3577127(158-166)Online publication date: 18-Nov-2022
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Ma AMolitor D(2022)Randomized Kaczmarz for tensor linear systemsBIT10.1007/s10543-021-00877-w62:1(171-194)Online publication date: 1-Mar-2022
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Zheng MHuang ZWang Y(2021)T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programmingComputational Optimization and Applications10.1007/s10589-020-00231-w78:1(239-272)Online publication date: 1-Jan-2021
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