Optimising Big Images

Abstract

We take a look at big data challenges in image processing. Real-life photographs and other images, such ones from medical imaging modalities, consist of tens of million data points. Mathematically based models for their improvement— due to noise, camera shake, physical and technical limitations, etc.—are moreover often highly non-smooth and increasingly often non-convex. This creates significant optimisation challenges for the application of the models in quasi-real-time software packages, as opposed to more ad hoc approaches whose reliability is not as easily proven as that of mathematically based variational models. After introducing a general framework for mathematical image processing, we take a look at the current state-of-the-art in optimisation methods for solving such problems, and discuss future possibilities and challenges.