Wavelet Frame Based Algorithm for 3D Reconstruction in Electron Microscopy

In electron microscopy, 3D reconstruction is one key component in many computer-ized techniques for solving 3D structures of large protein assemblies using electron microscopy imagesof particles. Main challenges in 3D reconstruction include very low signal-to-noise ratio and very largescale of data sets involved in the computation. Motivated by the recent advances of sparsity-basedregularization in wavelet frame domain for solving various linear inverse problems in imaging science,we proposed a wavelet tight frame based 3D reconstruction approach that exploits the sparsity ofthe 3D density map in wavelet tight frame system. The proposed approach not only runs efficientlyin terms of CPU time, but also requires a much lower memory footprint than existing framelet-basedregularization methods. The convergence of the proposed iterative scheme and the functional it min-imizes is also examined, together with the connection to existing wavelet frame based regularizations.The numerical experiments showed good performance of the proposed method when being used intwo electron microscopy techniques: single particle method and electron tomography.