Non-uniform refinement: Adaptive regularization improves single particle cryo-EM reconstruction

Ali Punjani; Haowei Zhang; David J. Fleet

Another possible approach to local control of regularization is to formulate the problem in another basis. In most single particle EM reconstruction methods, the Fourier basis is chosen primarily because the Fourier Slice Theorem facilitates fast projection evaluation and reconstruction. Another natural choice are the closely related spherical harmonics that permit fast rotation [34] . Wavelet bases have also been suggested [30] , the basis functions of which are simultaneously localized in space and the Fourier domain. Indeed, wavelets are used in methods for local resolution estimation [2, 17, 29] . Kucukelbir et al [16] describe an interesting approach to iterative refinement with an adaptive wavelet basis and a sparsity prior. This approch is also similar in spirit to the goal in this work, but their model has a single regularization parameter for the entire 3D map. It is based on the noise variance estimated from the corners of particle images, which may not capture local variations in noise due to disorder, motion, or partial occupancy. Nevertheless, like the cross-validation approach here, the authors also find that with a data-driven approach they can largely avoid the need for manual parameter setting and the spatial masking that is needed with a Fourier basis.