Efficient, quantitative numerical methods for statistical image deconvolution and denoising

Abstract

We review the development of efficient numerical methods for statistical multi-resolution estimation of optical imaging experiments. In principle, this involves constrained linear deconvolution and denoising, and so these types of problems can be formulated as convex constrained, or even unconstrained, optimization. We address two main challenges: first of these is to quantify convergence of iterative algorithms; the second challenge is to develop efficient methods for these large-scale problems without sacrificing the quantification of convergence. We review the state of the art for these challenges. © The Author(s) 2020.