Compressed sensing electron tomography using adaptive dictionaries: a simulation study

Electron tomography (ET) is an increasingly important technique for examining the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of 2D projection images to be reconstructed into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process this inverse problem is considered ill-posed (i.e., no unique solution exists). Furthermore reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Compressed sensing (CS) has recently been applied to ET and showed promising results for reducing missing wedge artifacts caused by limited angle sampling. CS uses a nonlinear reconstruction algorithm that employs image sparsity as a priori knowledge to improve the accuracy of density reconstruction from a relatively small number of projections compared to other reconstruction techniques. However, The performance of CS recovery depends heavily on the degree of sparsity of the reconstructed image in the selected transform domain. Prespecified transformations such as spatial gradients provide sparse image representation, while synthesising the sparsifying transform based on the properties of the particular specimen may give even sparser results and can extend the application of CS to specimens that can not be sparsely represented with other transforms such as Total variation (TV). In this work, we show that CS reconstruction in ET can be significantly improved by tailoring the sparsity representation using a sparse dictionary learning principle