A directional multi-resolution ridgelet network

In this paper, a directional multi-resolution ridgelet network (DMRN) is proposed based on ridgelet theory. By using ridgelet as the activation function, DMRN has great capabilities in catching essential features of "direction-rich" data for its multi-resolution property in direction besides scale and position. It proves to be able to approximate any multivariate function in a more stable and efficient way, and is optimal in approximating functions with spatial inhomogeneities. Using binary ridgelet frame for its design, DMRN is characteristic of more flexible structure. Possibilities of applications to regression and recognition are included to demonstrate its superiority.