3D macromolecule structure reconstruction from electron micrograph by exploiting symmetry and sparsity

Single particle reconstruction is often employed for 3-D reconstruction of diverse macromolecules. However, the algorithm requires a good initial guess from a priori information to guarantee the convergence to the correct solution. This paper describes a novel model free 3-D reconstruction algorithm by employing the symmetry and sparsity of unknown structure. Especially, we develop an accurate and fully automatic iterative algorithm for 3D reconstruction of unknown helix structures. Because the macromolecule structure assumes only sparse supports in real space and the helical symmetry provides several symmetric views from a single micrograph, a reasonably quality 3-D reconstruction can be obtained from the limited views using the compressed sensing theory. Furthermore, the correct helix parameters usually provide the maximal variance of the reconstructed volume, facilitating the parameter estimation. Remarkably, the search space of helix parameter can be drastically reduced by exploiting the diffraction pattern. With the estimated helix parameter and additional 3-D registration, the multiple helix segments can be combined for the optimal quality reconstruction. Experimental results using synthetic and real helix data confirm that our algorithm provides superior reconstruction of 3-D helical structure.