Denoiser-based projections for 2-D super-resolution multi-reference alignment

We study the 2-D 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 well-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 of images. In particular, we suggest to use denoisers as projections, and design two computational frameworks to estimate the image: projected expectation-maximization and projected method of moments. We provide an efficient GPU implementation, and demonstrate the effectiveness of these algorithms by extensive numerical experiments on a wide range of parameters and images.