Figure 1

The GENFIRE algorithm. GENFIRE first computes oversampled Fourier slices from a tilt series of 2D projections. The oversampled Fourier slices are used to accurately calculate a small fraction of points on a 3D Cartesian grid based on gridding interpolation. The algorithm then iterates between real and reciprocal space. The support and positivity constraints are enforced in real space, while the small fraction of grid points corresponding to the measured data are enforced in reciprocal space. Error metrics are used to monitor the convergence of the iterative process. After several hundred iterations, the algorithm converges to a 3D structure that is concurrently consistent with the measured data in reciprocal space and the physical constraints in real space.