Wavelet mother, selection

Chau and his co-workers have proposed some wavelet-based methods to compress UV-VIS spectra [24,37]. In their work, a UV-VIS spectrum was processed with the Daubechies wavelet function, Djfi. Then, all the Cj elements and selected Dj coefficients at different) resolution levels were stored as the compressed spectral data. A hard-thresholding method was adopted for the selection of coefficients from Dj. A compression ratio up to 83% was achieved. As mentioned in the previous section, the choice of mother wavelets is vast in WT, so one can select the best wavelet function for different applications. Flowever, most workers restrict their choices to the orthogonal wavelet bases such as Daubechies wavelet. Chau et al. chose the biorthogonal wavelet for UV VIS spectral data compression in another study [37]. Unlike the orthogonal case, which needs only one mother wavelet (p(t), the biorthogonal one requires two mother wavelets. (p(t) and (p(t), which satisfy the following biorthogonal property [38] ... 

Signal compression is gaining importance in biomedical engineering due to the potential applications in telemedicine. In this work, we propose a novel scheme of signal compression based on signal-dependent wavelets. To adapt the mother wavelet to the signal for the purpose of compression, it is necessary to define (1) a family of wavelets that depend on a set of parameters and (2) a quality criterion for wavelet selection (i.e., wavelet parameter optimization). We propose the use of an unconstrained parameterization of the wavelet for wavelet optimization. A natural performance... 

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