Bayesian Estimation of Density via Multiple Sequential Inversions of Two-Dimensional Images With Application to Electron Microscopy

Resolution of the available image dictates the discretization length of the model; three models pertaining to distinct resolution classes (at micrometer to nanometer scale lengths) are developed. We develop priors on the material density, such that these priors adapt to the sparsity inherent in the density function. The likelihood is defined in terms of the distance between the convolution of the unknown functions and the image data.

The posterior probability density of the unknowns given the data is expressed using the developed priors on the density and priors on the microscopy correction function as elicited from the microscopy literature. We achieve posterior samples using an adaptive Metropolis-within-Gibbs inference scheme. The method is applied to learn the material density of a three-dimensional sample of a nano-structure, using real image data.

Illustrations on simulated image data of alloy samples are also included.