GENFIRE, for GENeralized Fourier Iterative REconstruction, is a robust, Fourier-based reconstruction algorithm that is capable of using a limited set of input projections to generate a 3D reconstruction while also partially retrieving missing projection information. It does this by iterating between real and reciprocal space and applying simple constraints in each to find an optimal solution that correlates with the input projections while simultaneously obeying real space conditions such as positivity and support.The result is a more consistent and faithful reconstruction with superior contrast and, in many cases, resolution when compared with more traditional 3D reconstruction algorithms such as Filtered Back-Projection (FBP) or the Algebraic Reconstruction Technique (ART).

References: 

1. GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

2. GENFIRE package (github.com)