Fast wavelet-packet-based shift-invariant feature extraction

Wavelet and wavelet packet decompositions have been proven to be very effective in analyzing various types of signals and images. One useful type of analysis is image and texture classification. Such processing requires the analysis framework to be invariant to changes in scale, translation and other types of deformations. We deal in this context with the shift variance of the discrete wavelet transform. Several methods have been proposed to cope with this problem. We extend the shift invariant wavelet frame method, described in previous studies, to ldquoshift invariant wavelet frame packetsrdquo, and greatly reduce its computational complexity. In the one-dimensional case, our method maintains O(ND) computation steps (where D is the decomposition depth and N is signal length), when either traditional or wavelet packet decomposition tree is used, instead of O(ND) and O(N2^D) respectively.