  We presented a new 3D refinement method for Cryo-EM single particle analysis
which can improve the resolution of final electron density map in this paper.
We proposed to enforce both sparsity and smoothness to improve the regularity
of electron density map in the refinement process. To achieve this goal, we
designed a novel type of real space penalty function and incorporated it into
the refinement process. We bridged the backprojection step with local kernel
regression, thus enabling us to embed the 3D model in reproducing kernel
Hilbert space using specific kernels. We also proposed a first order method to
solve the resulting optimization problem and implemented it efficiently with
CUDA. We compared the performance of our new method with respect to the
traditional method on real datasets using a set of widely used metrics for
Cryo-EM model validation. We demonstrated that our method outperforms the
traditional method in terms of those metrics. The implementation of our method
can be found at https://github.com/alncat/cryoem.
