A variational framework with composite sparse regularization for cryo-electron tomography reconstruction

Motivation: Cryogenic electron tomography (cryo-ET) enables in situ visualization of macromolecular and cellular structures from tilt-series projections. Reconstruction quality is often compromised by extremely low signal-to-noise ratio (SNR) and vignetting artifacts arising from detector truncation under constrained acquisition geometries. In practice, existing methods frequently struggle to balance noise robustness, computational efficiency, and stability under these conditions. Results: We propose a robust, scalable, and parallelizable variational reconstruction framework that integrates a geometrically consistent data fidelity term with an implicit boundary-handling mechanism to mitigate truncation-induced artifacts without volume padding. A composite sparse regularizer integrating anisotropic total variation and curvelet-domain sparsity is employed to preserve structural boundaries and multiscale directional features. The resulting optimization problem is efficiently solved using the primal-dual hybrid gradient (PDHG) algorithm without nested inner iterations, for which we provide rigorous theoretical guarantees of stability and convergence. Experiments on simulated and experimental cryo-ET datasets demonstrate substantial noise suppression and contrast enhancement while preserving fine structural details under realistic, severely noise-limited and truncated acquisition conditions. These improvements lead to enhanced interpretability and facilitate downstream structural analysis, while achieving significantly reduced runtime compared to existing methods at comparable reconstruction quality. Availability and implementation: Our code available at https://github.com/icthrm/CSRT. The real datasets used in this study are publicly available from EMPIAR and the Caltech Electron Tomography Database.