Denoiser-Based Projections for 2D Super-Resolution MRA

We study the 2D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure determination problem for biological molecules. Since the SR-MRA problem is ill-posed without prior knowledge, accurate image estimation relies on designing priors that describe the statistics of the images of interest. In this work, we build on recent advances in image processing and harness the power of denoisers as priors for images. To estimate an image, we propose utilizing denoisers as projections and using them within two computational frameworks that we propose: projected expectation-maximization and projected method of moments. We provide an efficient GPU implementation and demonstrate the effectiveness of these algorithms through extensive numerical experiments on a wide range of parameters and images.