Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization

Sanders, Toby; Gelb, Anne; Platte, Rodrigo B.; Arslan, Ilke; Landskron, Kai

doi:10.1016/J.ULTRAMIC.2016.12.020

Title: Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ₁ regularization

Journal Article · Tue Jan 03 00:00:00 EST 2017 · Ultramicroscopy

DOI:https://doi.org/10.1016/J.ULTRAMIC.2016.12.020· OSTI ID:1341752

Sanders, Toby ^[1]; Gelb, Anne ^[2]; Platte, Rodrigo B. ^[1]; Arslan, Ilke ^[3]; Landskron, Kai ^[4]

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

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.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1341752

Report Number(s):: PNNL-SA-123416; PII: S0304399116301474

Journal Information:: Ultramicroscopy, Vol. 174; ISSN 0304-3991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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Cited By (2)

Reconstruction of catadioptric omnidirectional images using dual alternating total variation minimization Zenati, Soraya; Boukrouche, Abdelhani; Boubchir, Larbi Evolving Systems, Vol. 10, Issue 4 https://doi.org/10.1007/s12530-018-9257-5	journal	November 2018
Multiscale higher-order TV operators for L1 regularization Sanders, Toby; Platte, Rodrigo B. Advanced Structural and Chemical Imaging, Vol. 4, Issue 1 https://doi.org/10.1186/s40679-018-0061-x	journal	October 2018

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