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Over the last decade or so, reconstruction methods using $\ell_1$regularization, often categorized as compressed sensing (CS) algorithms, havesignificantly improved the capabilities of high fidelity imaging in electrontomography. The most popular $\ell_1$ regularization approach within electrontomography has been total variation (TV) regularization. In addition toreducing unwanted noise, TV regularization encourages a piecewise constantsolution with sparse boundary regions. In this paper we propose an alternative$\ell_1$ regularization approach for electron tomography based on higher ordertotal variation (HOTV). Like TV, the HOTV approach promotes solutions withsparse boundary regions. In smooth regions however, the solution is not limitedto piecewise constant behavior. We demonstrate that this allows for moreaccurate reconstruction of a broader class of images -- even those for which TVwas designed for -- particularly when dealing with pragmatic tomographicsampling patterns and very fine image features. We develop results for anelectron tomography data set as well as a phantom example, and we also makecomparisons with discrete tomography approaches.

Recovering Fine Details from Under-Resolved Electron Tomography Data using HOTV Regularization