1 / 12

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

Download Presentation

An Improved Version of the Inverse Hyperanalytic Wavelet Transform

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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”

More Related