Ridgelets: Theory and Applications

Single hidden-layer feedforward neural networks have been proposed as an approach to bypass the curse of dimensionality and are now becoming widely applied to approximation or prediction in applied sciences. In that approach, one approximates a multivariate target function by a sum of ridge functions; this is similar to projection pursuit in the literature of statistics. This approach poses new and challenging questions both at a practical and theorectical level, ranging from the construction of neural networks to their efficiency and capability. The topic of this thesis is to show that ridgelets, a new set of functions, provide an elegant tool to answer some of these fundamental questions ...