In Nondestructive testing there is a variety of applications in Material Science, where the specimen is imaged by an Electron Microscope and then by image inversion, information
is extracted for the material interior. This type of information might contain noise either by the imaging procedure or by the numerical part of the inversion. We present a method that can improve the interior density results of an inversed material from a series of Scanning Electron Microscope (SEM) images. For this method, the material density can contain some discontinuity, such as regions where it is dense and regions where there are voids.
The proposed method directly stands on the Bayesian learning framework, adopting Gaussian Stochastic Processes (GSPs). Two test sample cases that contain some discontinuities in the density are tested. We also provide a comparison between two different GSP modelling approaches; one is a typical GSP and the other accounts for discontinuity, by introducing hyperparameters. The GSP method gives reconstructed data in reasonable agreement with the known original density distribution, giving confidence that the method can be applied to experimentally obtained SEM images.