Spatial Regression With Partial Differential Equation Regularisation

This work gives an overview of innovative class methods for the analysis spatial and functional data observed over complicated two-dimensional domains. is based on regression with regularising terms involving partial differential equations. The associated estimation problems are solved resorting to advanced numerical techniques. synergical interplay approaches from statistics, applied mathematics engineering endows important advantages respect available techniques, makes them able accurately deal structures which classical techniques unfit. Spatial regularisation illustrated via applications eco-colour doppler measurements blood-flow velocity, magnetic resonance imaging signals neural connectivity in cerebral cortex.