A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An introduction to wavelets
Complex wavelet transforms with allpass filters
Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
Nonstationary signal analysis using the RI-Spline wavelet
Integrated Computer-Aided Engineering
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
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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.