Abstract
Algebraic reconstruction techniques (ART) are iterative procedures for solving systems of linear equations. They have been used in tomography to recover objects from their projections. In this work we apply an ART approach in which the basis functions used to describe the objects are not based on voxels, but are much smoother functions named “blobs.” The data collection studied in this work follows the so-called “conical tilt geometry” that is commonly used in many applications of three-dimensional electron microscopy of biological macromolecules. The performance of ART with blobs is carefully compared with a currently well known 3D reconstruction algorithm (weighted backprojection or WBP) using a methodology which assigns a level of statistical significance to a claim of relative superiority of one algorithm over another for a particular task. The conclusion we reach is that ART with blobs produces high quality reconstructions and is, in particular, superior to WBP in recovering features along the “vertical” direction. For the exact implementation recommended in this paper, the computational costs of ART are almost an order of magnitude smaller than those of WBP, though ART has to solve an order of three million noisy equations in an order of 50,000 unknowns
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Marabini, R., Herman, G.T., Carazo, J.M. (1999). Fully Three-Dimensional Reconstruction in Electron Microscopy. In: Börgers, C., Natterer, F. (eds) Computational Radiology and Imaging. The IMA Volumes in Mathematics and its Applications, vol 110. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1550-9_12
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DOI: https://doi.org/10.1007/978-1-4612-1550-9_12
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