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Title: Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ 1 regularization

Abstract

Over the last decade or so, reconstruction methods using ℓ 1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ 1 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 ℓ 1 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 Lab. (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:
Journal Article: 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. doi: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. doi: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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