Electron Tomographic Reconstruction with Sparse Noise Filter and Shape Priors

Abstract

Tomographic reconstruction is a method for obtaining a three dimensional image of a specimen with a series of two dimensional projection images of the specimen taken from different tilt or projection angles. There are mainly two factors that can affect the quality of a reconstruction. When the signal-to-noise ratio from the projection images is low, the tomographic reconstruction can be noisy. And due to the instrumental limitation, the projection images cannot be taken for certain angle ranges, which incurs missing wedge of information. Tomographic reconstruction with the missing wedge contains significant image blurring and image artifacts due to the missing wedge. This dissertation presents three new approaches to largely mitigate the effect of noise and missing wedge.

We first propose a novel filtered backprojection that optimizes the filter of the backprojection operator in terms of a reconstruction error. This data-dependent filter adaptively chooses the spectral domains of signals and noises, suppressing the noise frequency bands, so it is very effective in denoising. We also propose the new filtered backprojection embedded within the simultaneous iterative reconstruction technique for mitigating the effect of missing wedge. The third approach considers a number of possible shapes of a specimen and allows data to choose the most plausible shape through the proposed maximum likelihood modeling. The estimated object shape is used to infill the missing information, and the reconstruction can be then achieved with a combination of the estimated information and observed sinograms.

We present the numerical performance of the proposed approaches with various simulated scenarios and real data studies in electron tomographic reconstruction of nanoparticles and compare the results with other existing tomographic reconstruction methods. Our numerical studies show the performance gain of the proposed approaches over the state-of-the-art.