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

Ali Punjani; Haowei Zhang; David J. Fleet

In the standard cryo-EM 3D reconstruction problem set up [12, 22, 26] , a generative model describes the formation of images of a target protein in an electron microscope. According to the model, the unobserved protein structure, represented by a 3D density, is rotated by a 3D pose and projected along the direction of the electron beam. The resulting 2D projection is translated in the plane, modulated by the microscope CTF, and corrupted by additive noise, under a certain noise model. The 3D density map m is typically parameterized as a real-space 3D array with density at each voxel, in a Cartesian grid of box size N , and a corresponding discrete Fourier representation,m = F m. The goal of reconstruction is to infer the unobserved 3D densities of the voxel array, called model parameters. Representing the 3D density, 2D projections, observed images, and the noise model in the Fourier domain is common practice for computational efficiency, exploiting the well-known convolution and Fourier-slice theorems [1, 12, 22, 26] . The unobserved pose variables for each image are latent variables.