OpenMBIR

High Angle Annular Dark Field (HAADF)-Scanning Transmission Electron Microscope (STEM) data is increasingly being used in the physical sciences to study materials in 3D because it is free from the diffraction effects seen in Bright Field (BF) STEM data and produces a signal related to the atomic number of the region being probed. Typically, tomographic reconstructions are performed by directly applying either Filtered Back Projection (FBP) or the SIRT algorithm to the data without taking into account an explicit model for image formation. In particular, since HAADF-STEM tomography is a limited angle tomography modality with low SNR, these methods can result in significant artifacts in the reconstructed volume.

OpenMBIR is an open source project that implements a Model Based Iterative Reconstruction (MBIR) algorithm for HAADF- STEM tomography. First a model is developed for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a MAP estimation problem. The formulation also accounts for certain missing measurements like the transmission measurement, offsets and noise variance, treating them as nuisance parameters in the MAP estimation framework. We adapt the Iterative Coordinate Descent (ICD) algorithm to our application to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets, show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

More theory on the model and algorithm is outlined in the following paper
https://engineering.purdue.edu/~bouman/publications/pdf/ssp-2012.pdf