  Electron tomographic reconstruction is a method for obtaining a
three-dimensional image of a specimen with a series of two dimensional
microscope images taken from different viewing angles. Filtered backprojection,
one of the most popular tomographic reconstruction methods, does not work well
under the existence of image noises and missing wedges. This paper presents a
new approach to largely mitigate the effect of noises and missing wedges. We
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 iteration for mitigating the effect of missing wedges.
Our numerical study is presented to show the performance gain of the proposed
approach over the state-of-the-art.
