  Over the last decade or so, reconstruction methods using $\ell_1$
regularization, often categorized as compressed sensing (CS) algorithms, have
significantly improved the capabilities of high fidelity imaging in electron
tomography. The most popular $\ell_1$ 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
$\ell_1$ 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. We develop results for an
electron tomography data set as well as a phantom example, and we also make
comparisons with discrete tomography approaches.
