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An Improved Version of the Inverse Hyperanalytic Wavelet Transform

An Improved Version of the Inverse Hyperanalytic Wavelet Transform. Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher. Introduction. Wavelet techniques based on the Discrete Wavelet Transform (DWT) Advantages Sparsity of coefficients Disadvantages

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An Improved Version of the Inverse Hyperanalytic Wavelet Transform

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  1. An Improved Version of the Inverse Hyperanalytic Wavelet Transform Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher

  2. Introduction Wavelet techniques based on the Discrete Wavelet Transform (DWT) • Advantages • Sparsity of coefficients • Disadvantages • Shift-sensitivity (input signal shift → unpredictable change in the output coefficients) • Poor directional selectivity Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  3. Shift-Invariant Wavelet Transforms • One-Dimensional DWT (1D - DWT) • Undecimated DWT (UDWT) • Dual -Tree Complex Wavelet Transform (DT-CWT) • Analytical DWT • Two-Dimensional DWT (2D - DWT) • 2D UDWT • 2D DT-CWT • Hyperanalytical Wavelet Transform (HWT) Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  4. Advantage Shift-invariant Disadvantages High redundancy Reduced directional selectivity UDWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  5. Advantages Quasi shift-invariant Good directional selectivity Disadvantages Redundancy Filters from the 2nd branch can be only approximated DT-CWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  6. ADWT DWT at whose entry we apply the analytical signal defined as: xa=x+iH{x} where H{x} denotes the Hilbert transform of x Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  7. IADWT • The new implementation: Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  8. Simulation ResultsADWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  9. Objective Comparison • Degree of invariance: • Grad = 1 – d/m • d – standard deviation and • m – mean of the sequences of energies of a certain type of coefficients corresponding to 16 shifts Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  10. HWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  11. Simulation ResultsHWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

  12. Conclusion • The new implementation of the IHWT has a better shift-invariance • Its application in image denoising slightly improves the results obtained applying the old implementation of the IHWT Ioana Firoiu, Alexandru Isar, Jean-Marc Boucher, “An Improved Version of the Inverse Hyperanalytic Wavelet Transform”

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