  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.
