ECG Compression Using The Lifting Wavelet Transforms

Wavelet transforms overcome the shortcomings of Fourier-based techniquesbecause of wavelet's advantage on flexible time-frequency windows. Wavelet has beenwidely applied in numerical analysis, signal processing, and image processing. Atpresent, lifting scheme is new method for constructing wavelets and performing wavelettransform. This thesis focuses on wavelets, lifting schemes and their application algorithms onECG signal compressing. What the main results this thesis has delivered are as follows: First, this thesis describes the basic theory of wavelet in length and the generalizedorthonormal formula is presented as well. Second, this thesis presents the lifting scheme of dyadic single wavelet, includingthe lifting process, lifting factorization of wavelet transform and the reversibleinteger-to-integer lifting wavelet transform. Moreover, a necessary condition of definingwhether two pair of filters have the lifting relation and an efficient method for ECG datacompression are proposed. Third, the Multiwavelet and TST(Two-Scale similiary Transform) are discussedand examples are presented to account for these algorithms. Fourth, this thesis puts forward the lifting scheme, lifting factorization ofmultiwavelet and makes a discuss on the algorithm for raising approximation order ofmultiwavelets through lifting. The author also makes a comparison between liftingscheme and TST and find that lifting produces a complete new multiwavelet and usesno matrix division or singular matrixes and generally produces shorter new masks thanthe TST algotithm. So we choose lifting as our method to improve the multiwavelet'sproperty. Finally, the author argues that prefiltering a discrete signal is a necessary stepbefore using unbalanced multiwavelets. In this thesis, the author applies orthonormalperfiltered and first-order balanced multiwavelet to the compression of ECG datarespectively. By using orthonormal perfiltered we can acquire a better result than byusing first-order balanced multiwavelet or by using single wavelet.