Electron tomography image reconstruction using data-driven adaptive compressed sensing

Electron tomography (ET) is an increasingly important technique for the study of the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of two-dimensional projection images, followed by the reconstruction into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process, this inverse problem is ill-posed (i.e., a unique solution may not exist). Furthermore, reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Recently, compressed sensing (CS) has been applied to ET and showed promising results for reducing missing wedge artifacts. This uses image sparsity as a priori knowledge to improve the accuracy of reconstruction, and can require fewer projections than other reconstruction techniques. The performance of CS relies heavily on the degree of sparsity in the selected transform domain and this depends essentially on the choice of sparsifying transform. We propose a new image reconstruction algorithm for ET that learns the sparsifying transform adaptively using a dictionary-based approach. We demonstrate quantitatively using simulations from complex phantoms that this new approach reconstructs the morphology with higher fidelity than either analytically based CS reconstruction algorithms or traditional weighted back projection from the same dataset. SCANNING 38:251-276, 2016. © 2015 Wiley Periodicals, Inc.