Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy

Recognizing that the microscope depth of field is a significant resolution-limiting factor in 3D cryoelectron microscopy, Jensen and Kornberg proposed a concept they called defocus-gradient corrected backprojection (DGCBP) and illustrated by computer simulations that DGCBP can effectively eliminate the depth of field limitation. They did not provide a mathematical justification for their concept. Our paper provides this, by showing (in the idealized case of noiseless data being available for all projection directions) that the reconstructions obtained based on DGCBP from data produced with distance-dependent blurring are essentially the same as what is obtained by a classical method of reconstruction of a 3D object from its line integrals. The approach is general enough to be applicable for correcting for any distance-dependent blurring during projection data collection. We present a new implementation of the DGCBP concept, one that closely follows the mathematics of its justifications, and illustrate it using mathematically described phantoms and their reconstructions from finitely many distance-dependently blurred projections.