Advanced Prior Modeling for Nano-scale Imaging

Many material and biological samples in scientific imaging are characterized by non-local repeating structures. These are studied using scanning/transmission electron microscopy and electron tomography. Sparse sampling of individual pixels in a 2D image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, or low-resolution data acquisition can enable high speed data acquisition and minimize sample damage caused by the electron beam. However, accurate reconstructions from such sparse/low-resolution data is often challenging. In this work, we present algorithms for electron tomographic reconstruction, sparse image interpolation (or inpainting), and super-resolution that exploits the non-local redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a prior model for a variety of inverse problems. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new non-local means denoising algorithm. In the end, we look at 4x, 8x, and 16x super-resolution reconstruction using library-based non-local means (LB-NLM) denoiser as a prior model within plug-and-play, to accurately characterize high-resolution textures and edge features, using high-resolution library patches acquired over a small field-of-view of the microscopy sample. Finally, we demonstrate that our algorithms produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods