Evolutionary Models for Signal Enhancement and Approximation

This thesis deals with nature-inspired evolution processes for the purpose of signal enhancement and approximation. The focus lies on mathematical models which originate from the description of swarm behaviour. We extend existing approaches and show the potential of swarming processes as a modelling tool in image processing. In our work, we discuss the use cases of grey scale quantisation, contrast enhancement, line detection, and coherence enhancement. Furthermore, we propose a new and purely repulsive model of swarming that turns out to describe a specific type of backward diffusion process. It is remarkable that our model provides extensive stability guarantees which even support the utilisation of standard numerics. In experiments, we demonstrate its applicability to global and local contrast enhancement of digital images. In addition, we study the problem of one-dimensional signal approximation with limited resources using an adaptive sampling approach including tonal optimisation. We suggest a direct energy minimisation strategy and validate its efficacy in experiments. Moreover, we show that our approximation model can outperform a method recently proposed by Dar and Bruckstein