Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization
Abstract
Over the last decade or so, reconstruction methods using ℓ1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. In conclusion, we develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.
- Authors:
-
- Arizona State Univ., Tempe, AZ (United States). School of Mathematical and Statistical Sciences
- Dartmouth College, Hanover, NH (United States). Department of Mathematics
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Fundamental and Computational Sciences Directorate
- Lehigh Univ., Bethlehem, PA (United States). Department of Chemistry
- Publication Date:
- Research Org.:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1341752
- Report Number(s):
- PNNL-SA-123416
Journal ID: ISSN 0304-3991; PII: S0304399116301474
- Grant/Contract Number:
- AC05-76RL01830
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Ultramicroscopy
- Additional Journal Information:
- Journal Volume: 174; Journal ID: ISSN 0304-3991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 47 OTHER INSTRUMENTATION
Citation Formats
Sanders, Toby, Gelb, Anne, Platte, Rodrigo B., Arslan, Ilke, and Landskron, Kai. Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization. United States: N. p., 2017.
Web. doi:10.1016/J.ULTRAMIC.2016.12.020.
Sanders, Toby, Gelb, Anne, Platte, Rodrigo B., Arslan, Ilke, & Landskron, Kai. Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization. United States. https://doi.org/10.1016/J.ULTRAMIC.2016.12.020
Sanders, Toby, Gelb, Anne, Platte, Rodrigo B., Arslan, Ilke, and Landskron, Kai. Tue .
"Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization". United States. https://doi.org/10.1016/J.ULTRAMIC.2016.12.020. https://www.osti.gov/servlets/purl/1341752.
@article{osti_1341752,
title = {Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization},
author = {Sanders, Toby and Gelb, Anne and Platte, Rodrigo B. and Arslan, Ilke and Landskron, Kai},
abstractNote = {Over the last decade or so, reconstruction methods using ℓ1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. In conclusion, we develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.},
doi = {10.1016/J.ULTRAMIC.2016.12.020},
journal = {Ultramicroscopy},
number = ,
volume = 174,
place = {United States},
year = {Tue Jan 03 00:00:00 EST 2017},
month = {Tue Jan 03 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
journal, January 2005
- Archibald, Rick; Gelb, Anne; Yoon, Jungho
- SIAM Journal on Numerical Analysis, Vol. 43, Issue 1
Reducing the missing wedge: High-resolution dual axis tomography of inorganic materials
journal, October 2006
- Arslan, Ilke; Tong, Jenna R.; Midgley, Paul A.
- Ultramicroscopy, Vol. 106, Issue 11-12
3D imaging of nanomaterials by discrete tomography
journal, May 2009
- Batenburg, K. J.; Bals, S.; Sijbers, J.
- Ultramicroscopy, Vol. 109, Issue 6
Total Generalized Variation
journal, January 2010
- Bredies, Kristian; Kunisch, Karl; Pock, Thomas
- SIAM Journal on Imaging Sciences, Vol. 3, Issue 3
Sparsity and incoherence in compressive sampling
journal, April 2007
- Candès, Emmanuel; Romberg, Justin
- Inverse Problems, Vol. 23, Issue 3, p. 969-985
High-Order Total Variation-Based Image Restoration
journal, January 2000
- Chan, Tony; Marquina, Antonio; Mulet, Pep
- SIAM Journal on Scientific Computing, Vol. 22, Issue 2
Deterministic constructions of compressed sensing matrices
journal, August 2007
- DeVore, Ronald A.
- Journal of Complexity, Vol. 23, Issue 4-6
The Split Bregman Method for L1-Regularized Problems
journal, January 2009
- Goldstein, Tom; Osher, Stanley
- SIAM Journal on Imaging Sciences, Vol. 2, Issue 2
Electron tomography based on a total variation minimization reconstruction technique
journal, February 2012
- Goris, B.; Van den Broek, W.; Batenburg, K. J.
- Ultramicroscopy, Vol. 113
Advanced reconstruction algorithms for electron tomography: From comparison to combination
journal, April 2013
- Goris, B.; Roelandts, T.; Batenburg, K. J.
- Ultramicroscopy, Vol. 127
3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography: Prospects of atomic resolution electron tomography
journal, May 2008
- Jinschek, J. R.; Batenburg, K. J.; Calderon, H. A.
- Ultramicroscopy, Vol. 108, Issue 6
Compressed sensing electron tomography
journal, August 2013
- Leary, Rowan; Saghi, Zineb; Midgley, Paul A.
- Ultramicroscopy, Vol. 131
Finite Difference Methods for Ordinary and Partial Differential Equations
book, January 2007
- LeVeque, Randall J.
An efficient augmented Lagrangian method with applications to total variation minimization
journal, July 2013
- Li, Chengbo; Yin, Wotao; Jiang, Hong
- Computational Optimization and Applications, Vol. 56, Issue 3
Poisson noise removal from high-resolution STEM images based on periodic block matching
journal, March 2015
- Mevenkamp, Niklas; Binev, Peter; Dahmen, Wolfgang
- Advanced Structural and Chemical Imaging, Vol. 1, Issue 1
Reduced-dose and high-speed acquisition strategies for multi-dimensional electron microscopy
journal, May 2015
- Saghi, Zineb; Benning, Martin; Leary, Rowan
- Advanced Structural and Chemical Imaging, Vol. 1, Issue 1
Discrete Iterative Partial Segmentation Technique (DIPS) for Tomographic Reconstruction
journal, March 2016
- Sanders, Toby
- IEEE Transactions on Computational Imaging, Vol. 2, Issue 1
Physically motivated global alignment method for electron tomography
journal, April 2015
- Sanders, Toby; Prange, Micah; Akatay, Cem
- Advanced Structural and Chemical Imaging, Vol. 1, Issue 1
Improved Total Variation-Type Regularization Using Higher Order Edge Detectors
journal, January 2010
- Stefan, W.; Renaut, R. A.; Gelb, A.
- SIAM Journal on Imaging Sciences, Vol. 3, Issue 2
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
journal, January 2008
- Wang, Yilun; Yang, Junfeng; Yin, Wotao
- SIAM Journal on Imaging Sciences, Vol. 1, Issue 3
TVR-DART: A More Robust Algorithm for Discrete Tomography From Limited Projection Data With Automated Gray Value Estimation
journal, January 2016
- Zhuge, Xiaodong; Palenstijn, Willem Jan; Batenburg, Kees Joost
- IEEE Transactions on Image Processing, Vol. 25, Issue 1
Works referencing / citing this record:
Reconstruction of catadioptric omnidirectional images using dual alternating total variation minimization
journal, November 2018
- Zenati, Soraya; Boukrouche, Abdelhani; Boubchir, Larbi
- Evolving Systems, Vol. 10, Issue 4
Multiscale higher-order TV operators for L1 regularization
journal, October 2018
- Sanders, Toby; Platte, Rodrigo B.
- Advanced Structural and Chemical Imaging, Vol. 4, Issue 1