On globally asymptotically stable continuous-time CNNs for adaptive smoothing of multidimensional signals

We present a theoretical framework from which an approach to nonlinear, locally-adaptive smoothing of multi-dimensional signals has been derived which exhibits properties favourable to any application: unique solution, data adaption, presentation of signal structure, continuous dependency of the result on both the input signal and few parameters, and effective control of parameters. We also show that i) the FEM discretisation nicely inherits the properties of the continuous notation, and that ii) the discretised version represents a globally asymptotically stable network. We then explicate the embedding of our approach in the continuous-time CNN paradigm of Roska and Chua (1992) and provide results from our simulations. Lastly we report on ongoing work towards CNN circuit design such as to render possible real-time processing in the future-a desideratum in computer vision system design.