KENBIKYO Vol.53▶No.3 2018

■Feature Articles: Electron Tomography for the Case of TEM, from Soft to Hard

A Non-Linear Discrete Reconstruction Method Based on a Gray-Level Quantization Unit

**Abstract: **In electron tomography the ‘missing wedge’ problem due to limited specimen tilt angles is crucial. In addition, reduction of the number of projection images is highly desired. In this article, a novel reconstruction method using an image gray-level quantization unit (QU) is described, which was devised to resolve the issues. A digital image consists of QUs which are stacked in each pixel for making a brightness. Therefore, it is thinkable that a tomography image is reconstructed by arranging discrete QUs in three-dimensionally, where the 3 axes are two for the image plane and one for the gray-level. Here, the total number of QUs can be approximately determined from the projection theory. Then, a solution which minimize an error calculated from a set of given projection data gives a unique one. As a result of computer model-based simulations and an experiment with a complex nano-particle, successful reconstruction images unaffected by missing wedge problem were obtained. Furthermore, even though a relatively small number of projection images were given to the method, almost the same images output.

**Key words: **electron tomography, non-linear reconstruction, missing wedge, gray-level quantization unit, inverse problem