Affiliations: [a] Department of Production Systems Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tanpaku-cho, Toyohashi-shi 441-8580, Japan | [b] Faculty of Computer Science and System Engineering, Okayama Prefecture University, 111 Kuboki, 5301 Haga, Soja 719-1197, Japan
Correspondence:
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Corresponding author: Zhong Zhang, Department of Production System Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tanpaku-cho, Toyohashi-shi 441-8580, Japan. Tel.: +81 532 44 6711; Fax: +81 532 44 6690; E-mail: [email protected].
Abstract: In our first report, we have proposed a complex type wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet) for the continuous wavelet transform and demonstrated the advantages of our approach. In this study, we develop our RI-Spline wavelet for the Discrete Wavelet Transform (DWT) that uses a fast algorithm based on Multi-resolution analysis. The DWT has a translation variance problem, so it can not catch features of the signals exactly although it has been widely used in signal analysis. In order to overcome this translation variance problem, we first develop a Complex Discrete Wavelet Transform (CDWT) using the RI-Spline wavelet and propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet without increasing the computational cost very much. Then we apply this translation invariant CDWT to translation invariant de-noising. Experimental results show that our method, when applied to ECG data and music data, can obtain better de-noising results than conventional Wavelet Shrinkage.
