Graph Signal Processing: History, development, impact, and outlook

Signal processing (SP) excels at analyzing, processing, and inferring information defined over regular (first continuous, later discrete) domains such as time or space. Indeed, the last 75 years have shown how SP has made an impact in areas such as communications, acoustics, sensing, image processing, and control, to name a few. With the digitalization of the modern world and the increasing pervasiveness of data-collection mechanisms, information of interest in current applications oftentimes arises in non-Euclidean, irregular domains. Graph SP (GSP) generalizes SP tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to interpret, and endowed with a corpus of mathematical results, rendering them natural candidates to serve as the basis for a theory of processing signals in more irregular domains.