Advanced prior modeling for 3D bright field electron tomography

Many important imaging problems in material science involve reconstruction of images containing repetitive non-local structures. Model-based iterative reconstruction (MBIR) could in principle exploit such redundancies through the selection of a log prior probability term. However, in practice, determining such a log prior term that accounts for the similarity between distant structures in the image is quite challenging. Much progress has been made in the development of denoising algorithms like non-local means and BM3D, and these are known to successfully capture non-local redundancies in images. But the fact that these denoising operations are not explicitly formulated as cost functions makes it unclear as to how to incorporate them in the MBIR framework. In this paper, we formulate a solution to bright field electron tomography by augmenting the existing bright field MBIR method to incorporate any non-local denoising operator as a prior model. We accomplish this using a framework we call plug-and-play priors that decouples the log likelihood and the log prior probability terms in the MBIR cost function. We specifically use 3D non-local means (NLM) as the prior model in the plug-and-play framework, and showcase high quality tomographic reconstructions of a simulated aluminum spheres dataset, and two real datasets of aluminum spheres and ferritin structures. We observe that streak and smear artifacts are visibly suppressed, and that edges are preserved. Also, we report lower RMSE values compared to the conventional MBIR reconstruction using qGGMRF as the prior model.