Efficient implementation of a filtered back-projection algorithm using a voxel-by-voxel approach

The large amount of image data necessary for high-resolution 3D reconstruction of macromolecular assemblies leads to significant increases in the computational time. One of the most time consuming operations is 3D density map reconstruction, and software optimization can greatly reduce the time required for any given structural study. The majority of algorithms proposed for improving the computational effectiveness of a 3D reconstruction are based on a ray-by-ray projection of each image into the reconstructed volume. In this paper, we propose a novel fast implementation of the “filtered back-projection” algorithm based on a voxel-by-voxel principle. Our version of this implementation has been exhaustively tested using both model and real data. We compared 3D reconstructions obtained by the new approach with results obtained by the filtered Back-Projections algorithm and the Fourier–Bessel algorithm commonly used for reconstructing icosahedral viruses. These computational experiments demonstrate the robustness, reliability, and efficiency of this approach.