Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Image Processing with Complex Wavelets

Nick Kingsbury
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 357, No. 1760, Wavelets: The Key to Intermittent Information? (Sep. 15, 1999), pp. 2543-2560
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/55178
Page Count: 18
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Image Processing with Complex Wavelets
Preview not available

Abstract

We first review how wavelets may be used for multi-resolution image processing, describing the filter-bank implementation of the discrete wavelet transform (DWT) and how it may be extended via separable filtering for processing images and other multi-dimensional signals. We then show that the condition for inversion of the DWT (perfect reconstruction) forces many commonly used wavelets to be similar in shape, and that this shape produces severe shift dependence (variation of DWT coefficient energy at any given scale with shift of the input signal). It is also shown that separable filtering with the DWT prevents the transform from providing directionally selective filters for diagonal image features. Complex wavelets can provide both shift invariance and good directional selectivity, with only modest increases in signal redundancy and computation load. However, development of a complex wavelet transform (CWT) with perfect reconstruction and good filter characteristics has proved difficult until recently. We now propose the dual-tree CWT as a solution to this problem, yielding a transform with attractive properties for a range of signal and image processing applications, including motion estimation, denoising, texture analysis and synthesis, and object segmentation.

Page Thumbnails

  • Thumbnail: Page 
2543
    2543
  • Thumbnail: Page 
2544
    2544
  • Thumbnail: Page 
2545
    2545
  • Thumbnail: Page 
2546
    2546
  • Thumbnail: Page 
2547
    2547
  • Thumbnail: Page 
2548
    2548
  • Thumbnail: Page 
2549
    2549
  • Thumbnail: Page 
2550
    2550
  • Thumbnail: Page 
2551
    2551
  • Thumbnail: Page 
2552
    2552
  • Thumbnail: Page 
2553
    2553
  • Thumbnail: Page 
2554
    2554
  • Thumbnail: Page 
2555
    2555
  • Thumbnail: Page 
2556
    2556
  • Thumbnail: Page 
2557
    2557
  • Thumbnail: Page 
2558
    2558
  • Thumbnail: Page 
2559
    2559
  • Thumbnail: Page 
2560
    2560