Tomographic Reconstruction and Alignment Using Matrix Norm Minimization

Cryo electron tomography is the only imaging modality that can capture individual cellular structures in situ at nanometer resolution. By using subtomogram averaging, a technique for simultaneous alignment and clustering, high-resolution reconstructions of macromolecules can often be achieved. Two main challenges of subtomogram averaging are a low SNR and missing frequency components that can lead to distortions in random directions in the reconstructed macromolecules. To cope with these challenges, we explore formulating the subtomogram averaging problem as a low-rank matrix recovery problem subject to constraints on the misfit to the Radon measurements. The rank minimization problem is relaxed to a nuclear-norm minimization problem that simultaneously reconstructs the three-dimensional structures and recovers the alignment parameters. The resulting reconstructions using small synthetic 32 × 32 × 32 data sets are denoised and refined versions of the target structures which are clustered very accurately. However, due to the increased computational complexity, the method is currently not able to align larger data sets.