リフティングスキームによる複素数離散ウェーブレット変換の高速化に関する研究

抄録

It is well known that the Lifting Scheme (LS) allows us to design the fast calculation method of the Discrete Wavelet Transform (DWT). However, unfortunately, the LS can be only adopted for the wavelets having a compact support. For example, Meyer wavelet, which is a famous orthonormal wavelet basis, has no compact support. Additionally, the Complex Discrete Wavelet Transform (CDWT) is steady and useful for many signal processing applications, however, its imaginary part is constructed from the wavelets having no compact support. Therefore, we cannot adopt the LS for these analyses. In this study, we propose the design method of the LS filters for all the orthonormal wavelet bases without relation to having a compact support or not. We adopt our proposed method for the CDWTs using Meyer wavelet and Daubechies 6 wavelet, and confirm their steady analyses and fast calculation speeds.