Angular Assignment Using the Visible Space and a Fast Wavelet Based Correction
Carlos Óscar Sanchez Sorzano, EPFL LIB

Test Run • 05 June 2003

Abstract
3D Electron Microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. This information is crucial in structural biology and provides key information about the way that macromolecules interact. 3D Electron Tomography computes the 3D reconstruction of a macromolecule based on the information provided by thounsands of 2D projections acquired with an electron microscope. One of the key parameters required to perform such a 3D reconstruction is the direction of projection of each projection image which is unknown a priori and must be determined using some algorithm. This information is usually coded with three Euler angles.
The visible space is defined as the subspace spanned by the set of projections that can be seen given a reference model. We propose to project experimental images onto the visible space and the use of wavelets in order to match the experimental projections with those obtained from a model volume used as reference. The use of projection onto the visible space prevents the algorithm from matching features that are not feasible given the reference model. On the other hand, the wavelet decomposition of the projection images provide a framework for a multiscale matching algorithm in which speed and robustness against noise is gained. Results obtained from computer simulations in terms of accuracy and speed encourages the use of this approach.