Abstract: A new directional multi-resolution ridgelet network (DMRN) is proposed based on the ridgelets frame theory, which uses the ridgelet as the activation function of the hidden layer. For some multi-resolution properties of the ridgelet in the direction besides the scale and the position, the DMRN has great capabilities to catch essential features of “direction-rich” data. It proves to be able to approximate any multivariate function in a more stable and efficient way, and it is optimal in approximating functions with spatial inhomogeneities. On the other hand, by using the binary ridgelet frame as the mathematical foundation in its construction, the DMRN is more flexible and simple structure. The construction and the learning algorithm for the proposed DMRN are given, with its approximation property also analyzed in detail. Possibilities of applications to regression and pattern recognition are included to demonstrate its superiority to other methods and its feasibility in practice. Both theoretical analysis and simulation results prove its efficiency.

Key words: ridgelet frame, directional multi-resolution, ridgelet network