Physics-Based Regularizer for Joint Soft Segmentation and Reconstruction of Electron Microscopy Images of Polycrystalline Microstructures

For Bayesian image reconstruction applications in which the measured image follows from physical considerations, it is desirable to incorporate the corresponding physics into the prior model. In this paper, we use a phase-field as the physicsbased prior model to implement the soft segmentation and reconstruction of noisy microstructural images of a polycrystalline, covalent material (SiC). The functional form of this prior is based on a coarse-grained Ginzburg-Landau free energy that embodies the underlying physics, and its phenomenological parameters are obtained from atomistic computer simulation. In particular, we compare an existing functional form developed by Fan and Chen for microstructural simulations with one developed here that is better suited to noise reduction in image reconstruction, and find that the latter form is indeed superior in this context. Numerical and experimental results demonstrate that the proposed method performs successful soft segmentation and reconstruction of microscopy images, even at very low signal levels. In addition, the superior performance of the proposed model for several case studies in comparison with state-of-the-art methods, such as BM3D and one using a MRF-based prior, is demonstrated.