Rotationally-invariant non-local means for image denoising and tomography

Many samples imaged in structural biology and material science contain several similar particles at random locations and orientations. Model-based iterative reconstruction (MBIR) methods can in principle be used to exploit such redundancies in images through log prior probabilities that accurately account for non-local similarity between the particles. However, determining such a log prior term can be challenging. Several denoising algorithms like non-local means (NLM) successfully capture such non-local redundancies, but the problem is two-fold: NLM is not explicitly formulated as a cost function, and neither can it capture similarity between randomly oriented particles. In this paper, we propose a rotationally-invariant nonlocal means (RINLM) algorithm, and describe a method to implement RINLM as a prior model using a novel framework that we call plug-and-play priors. We introduce the idea of patch pre-rotation to make RINLM computationally tractable. Finally, we showcase image denoising and 2D tomography results, using the proposed RINLM algorithm, as we highlight high reconstruction quality, image sharpness, and artifact suppression.