Conferences Page Contents
IASTED SIP'99 Conference, Nassau, Bahamas, October, 1999
IASTED SIP'99 Tutorial on Wavelets. There will be a half-day tutorial on wavelets
and wavelet transforms presented by Carl Taswell at the IASTED SIP'99 Conference to be held October 1999 in the Bahamas.
The tutorial will provide a practical introduction emphasizing software demonstrations
of all concepts and methods. For additional details, refer to the course outline. Revisit this site prior to the conference
for any revisions to the course outline. Please note that IASTED Conferences do
not charge any extra fees for tutorials beyond the usual registration fee for the
conference.
C. Taswell, Randomized Signal Classes
for Evaluating the Performance of Wavelet Shrinkage Denoising Methods.
Paper #296-214, pages 352-355 in Proceedings of the IASTED SIP'99 Conference.
Previous simulation experiments for the comparison of wavelet shrinkage denoising
methods have used fixed signal classes defined by adding instances of noise
to a single test signal. New simulation experiments are reported here with randomized
signal classes defined by adding instances of noise to instances of randomized test
signals. As expected, significantly greater variability in the performance of the
denoising methods was observed. Statistically valid comparisons must be conducted
with respect to this variability. Use of randomized, rather than fixed, signal classes
should yield more realistic and meaningful results.
BMES-EMBS'99 Conference, Atlanta, Georgia, October, 1999
C. Taswell and J. Niederholz, Quality
Controlled Compression of Polysomnograms. Paper #10.3.1.4, page 944
in Proceedings of the
BMES-EMBS'99 Conference.
A novel compression algorithm incorporating the near-best wavelet packet transform
is introduced for multi-modal signals in low bitrate telemonitoring applications.
The method permits flexible control of the total bitrate subject to the constraints
of the channel, and the allocation of the total bitrate to each of the constituent
modes subject to the quality preferences of the observer. Its performance is demonstrated
using polysomnograms.
J. Niederholz and C. Taswell, Near-Best
WPT Compression of Polysomnograms. Paper #10.3.4.1, page 961 in Proceedings
of the BMES-EMBS'99
Conference.
Near-best and best wavelet packet transforms were compared with wavelet transforms
for the compression of polysomnograms in a low bitrate telemonitoring application.
Near-best wavelet packet transforms provided better overall performance with respect
to efficiency of computation and compression, and amenability for use in more sophisticated
quality-on-demand algorithms.
IEEE ICASSP'99 Conference, Phoenix, Arizona, March, 1999
C. Taswell, Least and Most Disjoint
Root Sets for Daubechies Wavelets. Paper #1164, Proceedings of IEEE
ICASSP'99 Conference. See CT-1998-08 for extended version with multicolor
figures.
A new set of wavelet filter families has been added to the systematized collection
of Daubechies wavelets. This new set includes complex and real, orthogonal and biorthogonal,
least and most disjoint families defined using constraints derived from the principle
of separably disjoint root sets in the complex z domain. All of the new families
are considered to be constraint selected without a search and without any
evaluation of filter properties such as time-domain regularity and frequency-domain
selectivity. In contrast, the older families in the collection are considered to
be search optimized for extremal properties. Some of the new families are
demonstrated to be equivalent to some of the older families, thereby obviating the
necessity for any search in their computation. A library that displays images of
all filter families in the collection is available at the FirWav
Page.
IASTED SIP'98 Conference, Las Vegas, Nevada, October, 1998
C. Taswell, Wavelet Transform Compression
of Functional Magnetic Resonance Image Sequences. Paper #281-162,
pages 725-728 in Proceedings of the IASTED SIP'98 Conference.
Image sequences from functional neuroimaging experiments with 3-D magnetic resonance
scans of the human brain were wavelet transformed using a variety of orthogonal
and biorthogonal wavelet filters with different treatments of the image borders.
Contrary to the expectation that higher-order wavelets with more sophisticated boundary
treatments would yield better compression, simple Haar wavelets without any boundary
treatment provided the best compression throughout the rate-distortion performance
curve.
IAAMSAD International SSCC'98 Conference, Durban, South Africa, September, 1998
C. Taswell, A Spectral-Factorization
Combinatorial-Search Algorithm Unifying the Systematized Collection of Daubechies
Wavelets. Invited Paper and Session Keynote Lecture, Paper #323 in
Proceedings of the
IAAMSAD International SSCC'98 Conference.
A spectral-factorization combinatorial-search algorithm has been developed for unifying
a systematized collection of Daubechies minimum length maximum flatness wavelet
filters optimized for a diverse assortment of criteria. This systematized collection
comprises real and complex orthogonal and biorthogonal wavelets in families within
which the filters are indexed by the number of roots at z = -1. The main algorithm
incorporates spectral factorization of the Daubechies polynomial with a combinatorial
search of spectral factor root sets indexed by binary codes. The selected spectral
factors are found by optimizing the desired criterion characterizing either the
filter roots or coefficients. Daubechies wavelet filter families have been systematized
to include those optimized for time domain regularity, frequency domain selectivity,
time frequency uncertainty, and phase nonlinearity. The latter criterion permits
construction of the orthogonal least and most asymmetric real and least and most
symmetric complex filters. Biorthogonal symmetric spline and balanced length filters
with linear phase are also computable by these methods.
8th IEEE DSP Workshop, Bryce Canyon, Utah, August, 1998
C. Taswell, Numerical Evaluation of Time-Domain
Moments and Regularity of Multirate Filter Banks. Paper #71 in Proceedings
of the 8th IEEE DSP Workshop.
Numerical methods are described for evaluating the time-domain moments and regularity
of multirate filter banks. Estimates of the Holder regularity are computed for the
continuous functions obtained from the iterated discrete filters. Estimates of the
centered moments are also computed for both the discrete filters and continuous
functions. These estimates are then used to obtain the vanishing moment numbers.
None of the methods require any preprocessing of the filters or a priori
information about them. Thus, the methods can serve as tests for the evaluation
of arbitrary filter banks. Results are presented for various examples.
ICSPAT'97 Conference, San Diego, California, September, 1997
C. Taswell, Computational Algorithms
for Daubechies Least-Asymmetric, Symmetric, and Most-Symmetric Wavelets,
pages 1834-1838 in Proceedings ICSPAT'97 Conference.
Computational algorithms have been developed for generating min-length max-flat
FIR filter coefficients for orthogonal and biorthogonal wavelets with varying degrees
of asymmetry or symmetry. These algorithms are based on spectral factorization of
the Daubechies polynomial with a combinatorial search of root sets selected by a
desired optimization criterion. Daubechies filter families were systematized to
include Real Orthogonal Least Asymmetric (DROLA), Real Biorthogonal symmetric balanced
Most Regular (DRBMR), Complex Orthogonal Least Asymmetric (DCOLA), and Complex Orthogonal
Most Symmetric (DCOMS). Total phase nonlinearity was the criterion minimized to
select the roots for the DROLA, DCOLA, and DCOMS filters. Time-domain regularity
was used to select the roots for the DRBMR filters (which have linear phase only).
New filters with distinguishing features are demonstrated with examples.
ICSPAT'96 Conference, Boston, Massachusetts, October, 1996
C. Taswell, Specifications and Standards
for Reproducibility of Wavelet Transforms, pages 1923-1927 in Proceedings
ICSPAT'96 Conference.
As the number of applications and use of wavelet transforms continues to grow, so
does the number of classes and variations of wavelet transform algorithms. All of
these algorithms incorporate a filter convolution in some implementation, typically,
as part of an iterated filter bank. In contrast to implementations of the classical
Fourier transform where there is at most a choice of sign and normalization constant
in the complex exponential kernel, for wavelet transform algorithms there are multiple
choices including both the signs and normalization constants of the wavelet kernels
as well as the phase delays or advances of each of the filters in the wavelet filter
bank. These algorithmic details, however, are usually not reported in the literature
albeit with certain exceptions such as the FBI fingerprint image compression standard.
Nevertheless, it is necessary to specify such details in order to insure the reproducibility
of results output by each algorithm regardless of its implementation by any programmer
working in any language or any engineer designing any DSP chip. This report itemizes
a list of choices that must be specified clearly in order to insure the reproducibility
of a sequence of transform coefficients generated by a specific wavelet transform
algorithm. Moreover, this report proposes a simple but novel solution to the phase
alignment problem for wavelet transforms. The general principles of this solution
apply in various specific forms to both non-subsampled and critically subsampled
wavelet transforms and to both symmetric and asymmetric wavelet filters.
IEEE ICASSP'96 Conference, Atlanta, Georgia, May, 1996
C. Taswell, Speech Compression with
Cosine and Wavelet Packet Near-Best Bases, pages 566-568 in Proceedings
ICASSP '96.
Compression of speech from the TIMIT corpus was investigated for several transform
domain methods coding near-best and best bases from cosine and wavelet packet transforms.
Satisficing (suboptimizing) search algorithms for selecting near-best bases were
compared with optimizing algorithms for best bases in these adaptive tree-structured
transforms. Experiments were performed on several hundred seconds of speech spoken
by both male and female speakers from all dialect regions of the TIMIT corpus. Near-best
bases provided rate-distortion performance effectively as good as that of best bases
but without the additional computational penalty. Cosine packet bases outperformed
wavelet packet bases.
SPIE Conference on Wavelet Applications, Orlando, Florida, April, 1995
C. Taswell, Image Compression by Parameterized-Model
Coding of Wavelet Packet Near-Best Bases pages 153-161 in Proceedings
SPIE Conference on Wavelet Applications, SPIE Press Volume 2491.
Top-down tree search algorithms with non-additive information cost comparisons as
decision criteria have recently been proposed by Taswell for the selection of near-best
bases in wavelet packet transforms. Advantages of top-down non-additive near-best
bases include faster computation speed, smaller memory requirement, and extensibility
to biorthogonal wavelets in addition to orthogonal wavelets. A new compression scheme
called parameterized-model coding was also proposed and demonstrated for one-dimensional
signals. These methods are extended here to two-dimensional signals and applied
to the compression of images. Significant improvement in compression while maintaining
comparable distortion is demonstrated for parameterized-model coding relative to
quantized-scalar coding. In general, the lossy compression scheme is applicable
for low bit rate coding of the M largest packets of wavelet packet decompositions
with wavelet packet basis libraries and the M atoms of matching pursuit decompositions
with time-frequency atom dictionaries.
Villard de Lans Conference Conference on Wavelet and Statistics, Villard de Lans,
France, November, 1994
C. Taswell, WavBox 4: A Software Toolbox
for Wavelet Transforms and Adaptive Wavelet Packet Decompositions
pages 361-375 in Wavelets and Statistics, Lecture Notes in Statistics Vol. 103,
edited by Antoniadis and Oppenheim, Springer Verlag, 1995.
WavBox provides both a function library and a computing environment for wavelet
transforms and adaptive wavelet packet decompositions. WavBox contains a collection
of these transforms, decompositions, and related functions that perform multiresolution
analyses of 1-D multichannel signals and 2-D images. The current version 4.1c includes
overscaled pyramid transforms, discrete wavelet transforms, and adaptive wavelet
and cosine packet decompositions by best level, best basis, and matching pursuit
as described by Mallat, Coifman, Wickerhauser, and other authors. WavBox also implements
Taswell's new search algorithms with decision criteria, called near-best basis and
non-additive information costs respectively, for selecting bases in wavelet packet
transforms, as well as Donoho and Johnstone's wavelet shrinkage denoising methods.
Various choices of filter classes (orthogonal, biorthogonal, etc), filter families
(Daubechies, Vetterli, etc), and convolution versions (interval, circular, extended,
etc) exist for each transform and decomposition. The software has been designed
for efficient automated computation, interactive exploratory data analysis, and
pedagogy. Essential features of the design include: perfect reconstruction for multiresolution
decomposition of data of arbitrary size not restricted to powers of 2; both command
line and graphical user interfaces with a comprehensive set of plots and visual
displays; an object property expert system with artificial intelligence for configuring
valid property combinations; heirarchical modules and switch-driven function suites;
vector-filter and matrix-operator implementations of convolutions; extensibility
for the inclusion of other wavelet filters, convolution versions, and transforms;
optional arguments with built-in defaults for most m-files; and extensive on-line
help and self-running tutorial demos.
C. Taswell, Top-Down and Bottom-Up
Tree Search Algorithms for Selecting Bases in Wavelet Packet Transforms
pages 345-359 in Wavelets and Statistics, Lecture Notes in Statistics Vol. 103,
edited by Antoniadis and Oppenheim, Springer Verlag, 1995.
Search algorithms for finding signal decompositions called near-best bases using
decision criteria called non-additive information costs have recently been proposed
by Taswell for selecting bases in wavelet packet transforms represented as binary
trees. These methods are extended here to distinguish between top-down and bottom-up
tree searches. Other new non-additive information cost functions are also proposed.
In particular, the near-best basis with the non-additive cost of the Shannon entropy
on probabilities is compared against the best basis with the additive cost of the
Coifman-Wickerhauser entropy on energies. All wavelet packet basis decompositions
are also compared with the nonorthogonal matching pursuit decomposition of Mallat
and Zhang and the orthogonal matching pursuit decomposition of Pati et al. Monte
Carlo experiments using a constant-bit-rate variable-distortion paradigm for lossy
compression suggest that the statistical performance of top-down near-best bases
with non-additive costs is superior to that of bottom-up best bases with additive
costs. Top-down near-best bases provide a significant increase in computational
efficiency with reductions in memory, flops, and time while nevertheless maintaining
similar coding efficiency with comparable reconstruction errors measured by l^p-norms.
Finally, a new compression scheme called parameterized model coding is introduced
and demonstrated with results showing better compression than standard scalar quantization
coding at comparable levels of distortion.
IEEE Intl Symposium on Time-Frequency Time-Scale Analysis, Philadelphia, Pennsylvania,
October, 1994
C. Taswell, Near-Best Basis Selection
Algorithms with Non-Additive Information Cost Functions pages 13-16
in Proceedings Symposium on Time-Frequency Time-Scale Analysis, IEEE Press Volume
94TH8007.
Search algorithms for finding signal decompositions called near-best bases using
decision criteria called non-additive information costs are proposed for selecting
bases in wavelet packet transforms. These new methods are compared with the best
bases and additive information costs of Coifman and Wickerhauser. All near-best
and best bases were also compared with the matching pursuit decomposition of Mallat
and Zhang. Preliminary experiments suggest that for the application of time-frequency
analysis, a wide variety of results can be obtained with the different methods,
and that for the application of data compression, the near-best basis selected with
non-additive costs may outperform the best basis selected with additive costs.
International Conference on Wavelets and Applications, Toulouse, France, June 1992
K. McGill and C. Taswell, Wavelet Transform Algorithms for Finite-Duration Discrete-Time
Signals pages 221-224 in Progress in Wavelet Analysis and Applications,
Proceedings of the International Conference on Wavelets and Applications, edited
by Meyer and Roques, Editions Frontieres, 1993.
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