Havelková, Eva / Hnětynková, Iveta. Iterative hybrid regularization for extremely noisy full models in single particle analysis. 2023. Linear Algebra and its Applications, Vol. 656, p. 131-157
Cryo-electron microscopy single particle analysis (SPA) represents a vital tool for structure determination of macromolecules. Discrete inverse problems arising in this field are extremely large and seriously contaminated by noise. The model matrix is highly structured and can not be stored explicitly. Iterative regularization methods are used here only rarely, since it is believed that they are computationally expensive and require complicated stopping criteria. In this paper, we overcome these difficulties and demonstrate that Hybrid Krylov subspace methods can be used to solve SPA inverse problems efficiently. We propose an application-driven regularization parameter selection approach and present a matrix-free implementation of the hybrid solver for GPU computations in single precision arithmetic. In comparison to Fourier-based techniques, the hybrid approach allows to compute reconstructions from full (nonreduced) SPA models even for highly noisy data sets.