A fast mapping method in the ISAF reconstruction algorithm

ISAF (icosahedral symmetry-adapted functions) algorithm is the new high-resolution algorithm of icosahedral molecules. But its running speed is very slow because of the time-consuming operations of mapping sampling points into 3D space. In this paper, a fast mapping method is proposed to increase the running speed of this stage. First of all, the angle corresponding to one pixel arc in the maximum Fourier ring was taken as the sampling angle and the same angle sampling was applied in every rings. After that, the sampling points in ring R=1 were mapped into 3D space. Finally, the 3D spatial positions of radial sampling points in other rings were deduced according to the rotate angle invariability of radial sampling points. The simulated data of PSV-F (Penicillium stoloniferum virus F) and experimental Cryo-EM data of CPV (cytoplasmic polyhedrosis virus) were used for validating this method. The results show that the whole speedup reaches to an order of magnitude at the premise of assuring accuracy. In addition, the speedup is increasing with the increase of the maximum Fourier radius and the number of projections.