PHASE AND THE WREATH PRODUCT TRANSFORM: SOME APPLICATIONS
AND AN EXTENSION
Dissertation
Xuling Luo
April 2001
Dissertation (ps) /
The importance of phase in signals and in image representation has been
well recognized over the last two decades. In this dissertation we examine
the utility of phase information in the multiresolution spectrum
associated with the cyclic group-based Wreath Product Transform (WPT)
and the DFT-based complex lapped transform (DCLT). The DCLT is formulated
as an extension of the WPT from the filter bank point of view.
Perfect reconstruction conditions are derived for the complex lapped
transform, thus allowing the construction of filters with an unitary
matrix $Q$ and orthogonal projector matrix $P$. By choosing $Q$ to be
the inverse DFT matrix, a set of DCLTs can be constructed, where the WPT
is a special case. \newline
\newline
We use multiresolution phase information in the applications either
directly through consideration of only the angle information in the
spectrum or through employing the full complex spectrum.
Multiresolution WPT phase information is used in three applications:
image classification, block motion estimation and image segmentation.
The DCLT phase is applied to the image segmentation problem both in a
noisy and noiseless environment, and results
obtained are compared to those with the WPT and other lowpass
multiresolution transforms.