An Extended Field-Based Method for Noise Removal From Electron Tomographic Reconstructions.

Molecular structure determination is important for understanding functionalities and dynamics of macromolecules, such as proteins and nucleic acids. Cryo-electron tomography (ET) is a technique that can be used to determine the structures of individual macromolecules, thus providing the snapshots of their native conformations. Such 3-D reconstructions encounter several types of imperfections due to missing, corrupted, and low-contrast data. In this paper, we demonstrate that extending the reconstruction space, which increases the dimensionality of the linear system being solved during reconstruction, facilitates the separation of signal and noise. A considerable amount of the noise associated with collected projection data arises independently from the geometric constraint of image formation, whereas the solution to the reconstruction problem must satisfy such geometric constraints. Increasing the dimensionality thereby allows for a redistribution of such noise within the extended reconstruction space, while the geometrically constrained approximate solution stays in an effectively lower dimensional subspace. Employing various tomographic reconstruction methods with a regularization capability we performed extensive simulation and testing and observed that enhanced dimensionality significantly improves the accuracy of the reconstruction. Our results were validated with reconstructions of colloidal silica nanoparticles as well as P. falciparum erythrocyte membrane protein 1. Although the proposed method is used in the context of Cryo-ET, the method is general and can be extended to a variety of other tomographic modalities.