The processing of large sets of data points in space arises nowadays in a wide range of fields – including image reconstruction, tomography, GIS and visualization – and results in the analysis of large-scale structured and unstructured data. A characteristic of such data is that points that are not necessarily in close spatial proximity may nevertheless show long-range (i.e. non-local) similarities which can be exploited for the overall data analysis. The question arises of how to develop model- and data-driven methods for analysing efficiently data in order to uncover information about spatially distant points and to analyse how they interact with each other.

This series contains theoretical and applied works by recognised researchers from mathematical science, computer vision and data science. The aim is to provide a mathematical description of the modelling, the analysis and the optimisation aspects of processing data that features complex and non-local relationships.

Areas of interest: Non-local partial differential equations and variational approaches on graphs; Linear and nonlinear flows; Neural networks; Mathematical image processing; Large-scale data analysis; Optimization