TWO-DIMENSIONAL STATIONARY DYADIC WAVELET TRANSFORM, DECIMATED DYADIC DISCRETE WAVELET TRANSFORM AND THE FACE RECOGNITION APPLICATION

Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness.