Less is more: how compressed sensing is transforming metrology in chemistry

Mathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways. With the advent of the digital age, the subject of information theory has grown hugely in importance. In particular, over the last two decades significant advances in our understanding of sampling and function reconstruction have culminated in the development of an idea known as compressed sensing. What seems like an abstract idea is now having a profound impact throughout the scientific world-from enabling high-resolution imaging of pediatric patients in clinical medicine through to advancing 3D electron tomography images of nanoparticle catalysts and NMR spectroscopy studies of proteins. In this Minireview, we summarize these applications and provide an outlook on how the principles of compressed sensing are leading to entirely new approaches to measurement throughout the physical and life sciences.