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Title: 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:
 [1];  [2];  [1];  [3];  [4]
  1. Arizona State Univ., Tempe, AZ (United States). School of Mathematical and Statistical Sciences
  2. Dartmouth College, Hanover, NH (United States). Department of Mathematics
  3. Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Fundamental and Computational Sciences Directorate
  4. 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}
}

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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
  • DOI: 10.1137/S0036142903435259

Reducing the missing wedge: High-resolution dual axis tomography of inorganic materials
journal, October 2006


3D imaging of nanomaterials by discrete tomography
journal, May 2009


Total Generalized Variation
journal, January 2010

  • Bredies, Kristian; Kunisch, Karl; Pock, Thomas
  • SIAM Journal on Imaging Sciences, Vol. 3, Issue 3
  • DOI: 10.1137/090769521

Sparsity and incoherence in compressive sampling
journal, April 2007


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
  • DOI: 10.1137/S1064827598344169

Deterministic constructions of compressed sensing matrices
journal, August 2007


The Split Bregman Method for L1-Regularized Problems
journal, January 2009

  • Goldstein, Tom; Osher, Stanley
  • SIAM Journal on Imaging Sciences, Vol. 2, Issue 2
  • DOI: 10.1137/080725891

Electron tomography based on a total variation minimization reconstruction technique
journal, February 2012


Advanced reconstruction algorithms for electron tomography: From comparison to combination
journal, April 2013


Compressed sensing electron tomography
journal, August 2013


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
  • DOI: 10.1007/s10589-013-9576-1

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
  • DOI: 10.1186/s40679-015-0004-8

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
  • DOI: 10.1186/s40679-015-0007-5

Discrete Iterative Partial Segmentation Technique (DIPS) for Tomographic Reconstruction
journal, March 2016


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
  • DOI: 10.1186/s40679-015-0005-7

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
  • DOI: 10.1137/080730251

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
  • DOI: 10.1137/080724265

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
  • DOI: 10.1109/TIP.2015.2504869

Works referencing / citing this record:

Reconstruction of catadioptric omnidirectional images using dual alternating total variation minimization
journal, November 2018


Multiscale higher-order TV operators for L1 regularization
journal, October 2018