Algorithms For Orientation Estimation And 3D Reconstruction From Cryo-EM Images

The single particle reconstruction(SPR)using cryogenic electron microscopy(cryo-EM)has played a unique advantage in the study of the structure and function mechanism of biological macromolecules,and has become a widely used method to determine the structure of biological macromolecules.It is an advanced technique for determining the three-dimension(3D)structure of biological specimens from their two-dimension projection images,by freezing biological macromolecules with the homogeneous and dispersed identical sample particles at low temperature.There are some challenges to reconstruct the three dimension structure of biological specimens.First,the observed micrographs are contaminated by a huge amount of noise due to the limitations of the tolerable electron dose to avoid radiation damage to the vitrified biological particle.Second,the acquired images are modulated by a contrast transfer function(CTF)in order to improve the contrast in micrographs,while the CTF has zero values at some frequencies due to the oscillatory nature of the CTF,which leads to the loss of information of the observed micrographs.Third,the projection orientations of the particles are unknown due to random orientations and positions of the particles.In this thesis,two problems of orientation estimations of cryo-EM images and single particle reconstruction from cryo-EM are studied,aiming to develop fast and effective algorithms for these two problems.Since orientations of the microscopic images obtained from cryo-EM imaging are randomly unknown,it is necessary to determine orientation estimation of each microscopic image before three-dimensional reconstruction.The orientations estimation is based on the common line method.Mathematically,the projection orientation can be described by the rotation matrix.We established the rotation matrix estimation model.and further established the least squared model(LS)and the least unsquared deviations model(LUD)of the rotation matrix and the common line.Because the rotation matrix is an orthogonal matrix,the problem of orientation estimation can be transformed into an optimization problem based on orthogonal constraints,but the non-convexity of the orthogonal constraints causes numerical calculation difficulties for orientation estimation.From the two perspectives of Euclidean space constrained optimization and manifold optimization,we apply the generalized projection gradient descent method and the manifold proximal gradient method to solve the minimization problem with orthogonal constraints,respectively.This paper analyzes the convergence of the algorithm.Numerical experiments show the effectiveness of our proposed algorithms.After orientations between cryo-EM images have been determined,the problem of single particle reconstruction from cryo-EM can be mathematically expressed as a system of linear equations with disturbances.Regularization methods are usually used to stabilize the solution of the system.This paper considers Tikhonov and Total Variation(TV)regularization functions.The regularization parameter is determined by the discrepancy principle,that is,the data fitting item should not be greater than a certain value,which can be determined in advance by using the statistical characteristics of noise.When the Tikhonov regularization model is used,the optimization problem has an explicit solution.When using the total variational regularization model,in order to overcome the difficulty of numerical calculation caused by the zero gradient of the TV norm,we use the duality theory to express the dual form of TV norm,and convert the SPR problem into a minimax problem.First-order primal dual algorithm is used to solve the problem,and the convergence analysis of the algorithm is proved.The efficiency of our proposed methods are verified by testing on simulated datas.