Multi-dimensional Wavelet Frames

Abstract

Peti & Krishnaprasad [1] first studied the connection between neural networks and wavelet transforms. Zhang & Benveniste [2] gave a different treatment of this connection. However, the problem of constructing multi-dimensional wavelet frames for use in neural networks has not been satisfactorily studied. In this report, one-dimensional wavelet frame is generalized to the multi-dimensional case by using single-scaling and multi-scaling parameters. The construction of multi-dimensional wavelet frames is also discussed. These results provide more insight on the use of wavelets in neural networks.