Novel nonlinear reconstruction method with grey-level quantisation units for electron tomography.

We report a new computed tomography reconstruction method, named quantisation units reconstruction technique (QURT), applicable to electron and other fields of tomography. Conventional electron tomography methods such as filtered back projection, weighted back projection, simultaneous iterative reconstructed technique, etc. suffer from the 'missing wedge' problem due to the limited tilt-angle range. QURT demonstrates improvements to solve this problem by recovering a structural image blurred due to the missing wedge and substantially reconstructs the structure even if the number of projection images is small. QURT reconstructs a cross-section image by arranging grey-level quantisation units (QU pieces) in three-dimensional image space via unique discrete processing. Its viability is confirmed by model simulations and experimental results. An important difference from recently developed methods such as discrete algebraic reconstruction technique (DART), total variation regularisation-DART, and compressed sensing is that prior knowledge of the conditions regarding the specimen or the expected cross-section image is not necessary.