3dcon: tomogram denoising by deconvolution

Cryo-electron tomography is an expanding technology for the study of macromolecules, viruses and cells. It is often applied to specimens that are too large or heterogeneous for methods based on 2D image averaging such as single-particle analysis, for example intracellular membranes or organelles. Current practice records a tilt series of projection images in rotation. Reconstruction is normally an ill-posed mathematical problem. Particularly for the under-determined case of sparse data, discrete tilt angles and a limited tilt range, characteristic artifacts appear in the reconstructed slices. Much of what appears as noise is in fact structural: the projection of contrast from different planes. Various schemes are employed to regularize the reconstruction, including machine-learning frameworks built on neural networks. To the extent that the noise is structural, based on the geometry of the tilt series, it might be suppressed by deconvolution with a suitable kernel. This was demonstrated and has been used regularly in cryo-STEM tomography of thick specimens where the under-sampling problem is particularly acute. Here, we present 3dcon as an open-source extension of the entropy-regularized deconvolution algorithm that had been adopted from fluorescence microscopy. It takes advantage of modern computing hardware for convenient and fast processing. Deconvolution is entirely algorithmic, meaning that successful processing of the data does not depend on the data itself. As such, it should be robust in a wide variety of applications.