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Title: Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing

Abstract

In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selectionmore » and sorting of high-similarity atoms during an analysis or identification phase.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Naval Research Lab. (NRL), Washington, DC (United States)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1573320
Report Number(s):
PNNL-SA-148884
Journal ID: ISSN 1057-7149
Grant/Contract Number:  
AC05-76RL01830
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Transactions on Image Processing
Additional Journal Information:
Journal Volume: 29; Journal ID: ISSN 1057-7149
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; matching pursuit; path augmentation; image denoising; image reconstruction; k-sparse

Citation Formats

Emerson, Tegan H., Olson, Colin C., and Doster, Timothy. Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing. United States: N. p., 2020. Web. doi:10.1109/TIP.2019.2927331.
Emerson, Tegan H., Olson, Colin C., & Doster, Timothy. Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing. United States. doi:10.1109/TIP.2019.2927331.
Emerson, Tegan H., Olson, Colin C., and Doster, Timothy. Wed . "Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing". United States. doi:10.1109/TIP.2019.2927331.
@article{osti_1573320,
title = {Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing},
author = {Emerson, Tegan H. and Olson, Colin C. and Doster, Timothy},
abstractNote = {In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.},
doi = {10.1109/TIP.2019.2927331},
journal = {IEEE Transactions on Image Processing},
number = ,
volume = 29,
place = {United States},
year = {2020},
month = {7}
}

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This content will become publicly available on July 15, 2020
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