Model-based iterative reconstruction for micro-scale and nano-scale imaging

Transmission electron microscopes (TEM) and synchrotron X-ray (SX) sources are widely being used to characterize materials at the nano-scale and micron-scale in two/three dimensions. While there has been significant progress in enhancing the hardware in these instruments to improve image quality, the algorithms used for image reconstruction have not fully exploited the statistical information in the data and the properties of the material being imaged to enhance the quality of the images. Model-based iterative reconstruction (MBIR) is an emerging theme for image reconstruction that combines a probabilistic model for the measurement system (forward model) with a probabilistic model for the image (prior model) to formulate the reconstruction as a high-dimensional estimation problem. In this dissertation, we propose MBIR algorithms for different imaging modalities used in a TEM and in SX imaging. First, we propose an MBIR algorithm for high angle annular dark field - scanning TEM (HAADF-STEM) tomography. Next, we present an MBIR algorithm for handling anomalous measurements encountered in bright field - electron tomography (BF-ET) of crystalline samples. Results on simulated as well as real data show significant improvements over the typical reconstruction approaches used for HAADFSTEM tomography and BF-ET. Furthermore, the proposed MBIR for BF-ET is also useful for SX tomography as it can handle anomalous measurements from saturated detector pixels. Finally, we propose a flexible optimization framework, termed Plug-and-Play priors, that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art denoising algorithms for MBIR. We will demonstrate how the Plug-and-Play priors can be used to mix and match a wide variety of denoising algorithms based on advanced image models with forward models encountered in TEM tomography, SX tomography and in sparse image reconstruction from STEM data, thus greatly expanding the range of possible problem solutions