title: Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1regularization.
abstract: Over the last decade or so, reconstruction methods using ℓ1regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ1regularization 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 ℓ1regularization 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. 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.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, United States. Electronic address: toby.sanders@asu.edu.
authors.forename: Toby
authors.initials: T
authors.lastname: Sanders
authors.affiliation: Department of Mathematics, Dartmouth College, United States.
authors.forename: Anne
authors.initials: A
authors.lastname: Gelb
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, United States.
authors.forename: Rodrigo B
authors.initials: RB
authors.lastname: Platte
authors.affiliation: Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, United States.
authors.forename: Ilke
authors.initials: I
authors.lastname: Arslan
authors.affiliation: Department of Chemistry, Lehigh University, United States.
authors.forename: Kai
authors.initials: K
authors.lastname: Landskron