Why a Complex Valued Solution for a Real Domain Problem

An insight into the potential benefits of using complex valued models for real valued data is provided. The problem itself is not new; it is however timely and important to revisit this issue, due to a plethora of modern applications based on multidimensional and multichannel measurements which can be cast into an equivalent problem in the field of complex numbers C. The analysis and simulations highlight the duality between several classes of real domain problems and their complex valued representations. This is supported by case studies on image processing, modelling of point processes for brain prosthetics, and forecasting of vector fields.