Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation

TL;DR

This paper introduces a plug-and-play prior framework for electron tomography and sparse image interpolation that leverages non-local redundancy and modern denoising algorithms to improve reconstruction quality and convergence.

Contribution

It adapts the plug-and-play priors framework to electron tomography, providing a flexible method that incorporates advanced denoising algorithms and guarantees convergence.

Findings

Higher quality reconstructions on simulated data

Improved convergence over existing methods

Effective use of non-local means denoising

Abstract

Many material and biological samples in scientific imaging are characterized by non-local repeating structures. These are studied using scanning 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, can enable high speed data acquisition and minimize sample damage caused by the electron beam. In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the non-local redundancy in images. We adapt a framework, termed plug-and-play (P&P) priors, to solve these imaging problems in a regularized inversion setting. The power of the P&P approach is that it allows a wide array of modern denoising algorithms to be used as a "prior model" for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the P&P approach, and we use these insights to design a new non-local means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.