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Image Processing with Complex Wavelets
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
You can always find the topics here!Topics: Signals, Wavelet analysis, Image processing, Coefficients, Quadrants, Image filters, Sampling rates, Design, Images of transformations, Supernova remnants
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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.
Philosophical Transactions: Mathematical, Physical and Engineering Sciences © 1999 Royal Society