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New lifting based structure for undecimated wavelet transform

New lifting based structure for undecimated wavelet transform

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A new structure for the undecimated wavelet transform (UWT) is introduced. This structure combines the stationary wavelet transform with a lifting scheme and its design is based on a polyphase structure. The suggested structure inherits the simplicity of the lifting scheme, such that the inverse transform is easily implemented. The proposed performance of the UWT is verified on a signal denoising application.

Inspec keywords: signal representation; wavelet transforms; white noise; Gaussian noise

Other keywords: stationary wavelet transform; undecimated wavelet transform; polyphase structure; signal denoising application; inverse transform; lifting based structure

Subjects: Signal processing theory; Integral transforms in numerical analysis; Signal processing and detection; Integral transforms in numerical analysis

References

    1. 1)
      • R.R. Coifman , D. Donoho . (1995) Translation-invariant de-noising, Wavelets and Statistics, vol. 103 of Lecture Notes in Statistics.
    2. 2)
      • Nason, G.P., Silverman, B.W.: `Stationary wavelet transform and some statistical applications', Technical Report, 1995.
    3. 3)
      • S.C. Burrus . (1998) Introduction to wavelets and wavelet transforms.
    4. 4)
      • D. Donoho . De-noising by soft-thresholding. IEEE Trans. Inf. Theory , 613 - 627
    5. 5)
      • W. Sweldens . The lifting scheme: A custom-design construction of biorthogonal wavelets. J. Appl. Comp. Harm. Anal. , 2 , 186 - 200
    6. 6)
      • I. Daubechies , W. Sweldens . Factoring wavelet transforms into lifting steps. J. Fourier Anal. Appl. , 3 , 247 - 269
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