# IEEE EMBS'95 Time-Freq, Wavelets, Wavelet Packets in Biomed Engr.

Bill Thompson wgthom at gandalf.rutgers.edu
Wed Apr 19 21:04:44 EST 1995

 ANNOUNCEMENT:

Dear Colleague:

In the upcoming International Conference of the IEEE Engineering in
Medicine and Biology Society (EMBS) in Montreal, September 20-23, 1995, a
1 1/2 days workshop on NEW ADVANCES IN BIOMEDICAL SIGNAL AND IMAGE PROCESSING
will be held before the conference to discuss and present new advances in
biomedical signal and image processing methods and recent applications
of these emerging technologies including Time-Frequency, Wavelet Transform,
and Wavelet Packets.

by prominent experts in engineering, medicine, computer science and
applied mathematics.

The cost for each attendee will be:
1. $100 for IEEE student member 2.$200 IEEE members,
3. $300 non IEEE members. If you are interested in joining us at Montreal, and have any questions about the workshop and registrations, please contact me at Rutgers (908-445-4096) or e-mail (akay at gandalf.rutgers.edu). Sincerely, Metin Akay, Ph.D. Workshop Chair 17th Annual International Conference of IEEE EMBS WORKSHOP NEW ADVANCES IN BIOMEDICAL SIGNAL AND IMAGE PROCESSING Time-Frequency, Wavelets, Wavelet Packets in Biomedical Engineering Organizing Committee Tom Brotherton Patrick Flandrin Dennis Healy Andrew Laine Mohsine Karrakchou Yves Meyer Janet Rutledge Banu Onaral Tim Olson Malvin Teich Ahmed Tewfik Nitish Thakor Michael Unser Victor Wickerhaus William Williams Andrew Yagle In this workshop, we will focus on the tutorial presentations of advanced signal and image processing methods. These will include new advances in time-frequency and wavelet transform and wavelet packets. In addition, biomedical and image processing applications will be presented. The invited speakers are experts in the areas of signal processing, medical imaging, computers science and applied mathematics. We encourage engineers, medical researchers, computers scientists and applied mathematicians to learn about recent developments in signal and image processing and their applications in biomedical engineering. FUTURE TOPICS AND INVITED SPEAKERS 1. Time-Frequency and Wavelets in Signal and Image Processing: Algorithms and Implementations Yves Meyer 2. The generalized sampling and the design of discrete/continuous signal processing algorithms Michael Unser 3. The survey of the time-frequency analysis method from Wigner to the Modern approaches William Williams 4. The recent advances in quadratic time-frequency analysis methods Patrick Flandrin 5. Epileptic Seizure Detection Based on Wavelet Analysis of EEG Banu Onaral 6. Wavelet and Point-Process Analysis of Fractal Neural Firing Patterns in Audition and Vision Malvin Teich 7. Modern Methods in Neurological Signal Processing Applications to Detection of Brain Injury Nitish Thakor 8. Wavelets and Neural Networks in Maturation Metin Akay 9. The adapted waveform de-noising for medical signals and images Victor Wickerhauser 10. The noise reductions and spectral shaping as a combined processing strategy for hearing aids Janet Rutledge 11. New Signal Processing Techniques for Physiological Data Analysis Mohsine Karrakchou 12. Multiscale wavelet frames for contrast enhancement of digital radiographs Andrew Laine 13. Waveform and beamform design for range and 2-D Doppler ultrasound imaging Ahmed Tewfik 14. Reducing the imaging time in MRI Dennis Healy 15. Non-linear stabilization of ill-conditioned linear inverse problems via adaptive subspace decomposition Tim Olson 16. Inversion of the radon transform under wavelet constraints Andrew Yagle 17. The Application of Wavelets and Fuzzy Logic Based Neural Nets to Medical Data and Image Processing Problems Tom Brotherton ABSTRACTS: 1. Time-Frequency and Wavelets in Signal and Image Processing Algorithms and Implementations Yves Meyer Y.M. will provide a panorama on a variety of tools in image and signal processing, ranging from time-scale algorithms (i.e. traditional wavelets) to time-frequency algorithms like the Wigner distribution and the so-called "Malvar-Wilson bases". A new and unexpected result is the fact that, in many cases, using a Wigner distribution amounts to decomposing the signal (or image) into orthonormal localized chirps. The location of these atoms in the time frequency plane yields a crucial information displayed in a geometric picture. 2. Generalized sampling and the design of discrete/continuous signal processing algorithms Michael Unser Biomedical Engineering and Instrumentation Program, National Institutes of Health, Bethesda MD 20892-5766 Sampling is the process of representing continuous-time (or space) functions by sequences of numbers (discrete signal representation). Traditionally, both the signal and its representation are assumed to be bandlimited. Here, we lift this hypothesis and present a general procedure for the approximation of arbitrary finite energy signals from their sampled measurements at the output a given analog prefilter (e.g., non-ideal acquisition device). The approximation spaces that we consider are generated by translation of a generating kernel$\phi$, a special case being the conventional sinc interpolator. This function may also correspond to the impulse response of a display device, or may be selected to specify a certain spline or wavelet representation space. We show that a consistent signal approximation can be obtained by appropriate digital filtering of the discrete measurements. This approximation is essentially equivalent to the initial signal in the sense that it would result in exactly the same measurements if it was re-injected into the system. We present the conditions under which this scheme yields the optimal least squares solution and provide general error bounds. The theory is illustrated with the design of two algorithms. The first is a spline-based procedure the minimum error scale-conversion of images (with an arbitrary scaling factor). The second is a digital filtering algorithm for the improvement of image display. 3. Time-Frequency Signal Analysis from Wigner to the Modern Approaches W. J. Williams, Professor of EECS University of Michigan Time frequency signal analysis will be presented from classical representations such as the Wigner distribution and the spectrogram. The concepts of Cohen's class of distributions will be introduced and used as guides in developing and understanding a variety of new time-frequency analysis tools which have appeared during the past five years. The original concept of design for reduced interference distributions (RIDs) will be presented. It will be shown how high resolution in both time and frequency with sharp reductions in the often troublesome interference terms associated with the Wigner distribution can be achieved. A number of modern approaches which provide improved results and avoid the window trade-offs inherent in spectrograms will be discussed. The desirable properties of time-frequency distributions such as proper time and frequency marginals, proper time and frequency support among others will be discussed in terms of their realizability and the tradeoffs inherent in gaining these properties. Adaptive time-frequency distributions will be discussed in terms of their benefits and computational complexity. Discrete practical time frequency distributions such as the Binomial distribution will be discussed and guidelines for practical realizations of real-time applications will be presented. Time-frequency filtering and signal inversion from time-frequency distributions will be discussed briefly. Finally, similarities and differences between Cohen's class of distributions and wavelet transforms will be highlighted. 4. Some recent advances in quadratic time-frequency/scale signal analysis and processing. P. Flandrin* ENS Lyon, France Two families of results will be presented, which are believed to give new motivations for using quadratic (Wigner-type) time-frequency/scale representations in signal analysis and processing, and which are both based on an interpretation in terms of 'distributions' or 'densities'. First, a mechanical analogy will be used for constructing sharply localized representations which circumvent the usual trade-off between joint resolution and cross-terms level. (The approach relies on the concept of 'reassignment', associated to displacement operators on the plane.) Second, a probabilistic analogy will be put forward for attaching information and dissimilarity measures to representations, thus allowing to compare signals from their time-frequency content. *results to be presented will summarize joint works with F. Auger, R.G. Baraniuk and O. Michel. 5. Epileptic Seizure Detection Based on Wavelet Analysis of EEG Samir Mehta, Richard W. Koser, Banu Onaral Scaling Signals and Systems Laboratory Biomedical Engineering and Science Institute & Electrical and Computer Engineering Department, Drexel University College of Engineering 32nd and Chestnut Streets Philadelphia, Pennsylvania 19104 Phone:215-895-2247 Fax: 215-895-1695 Banu_Onaral at cbis.ECE.Drexel.EDU The inverse power-law attenuation of the normal EEG spectrum suggests that EEG exhibits self-similar fluctuations over a multiplicity of scales. Such behavior is best characterized by measures which capture the scale-invariant nature of the signal. We investigate the use of discrete wavelet transform as a multi-scale decomposition tool to monitor the statistical scale-invariant properties of the EEG in long-term monitoring aimed to localize epileptic foci. The objective is to detect the onset of seizure marked by loss of scale-invariance over clinically relevant scales. We develop a scheme which monitors changes in the scaling properties of EEG independent of waveform morphology. Results obtained by processing clinical data are presented. 6. WAVELET AND POINT-PROCESS ANALYSIS OF FRACTAL NEURAL FIRING PATTERNS IN AUDITION AND VISION Malvin C. Teich Columbia University New York, New York The existence of long-duration temporal correlation (i.e., memory) in the spike trains of peripheral auditory neurons is well established. Such correlation, extending to time scales at least five orders of magnitude greater than the refractory period, has been shown to be present in all primary afferent auditory neurons of the cat, chinchilla, and chicken. The upper limit of the observed correlation time is imposed by the duration of the recording. More proximally, correlation has also been found in the firing patterns of lateral superior olivary auditory neurons inthe cat. Recently, we have examined the response variability and correlation properties of spontaneous and stimulated spike trains at three loci in the cat visual system: retinal-ganglion cells, lateral-geniculate-nucleus cells in the thalamus, and striate-cortex neurons. We have also investigated the response of an insect visual interneuron, the descending contralateral movement detector of the locust. The Fano-factor time curves, and wavelet analysis, reveal that long-duration temporal correlation is also present in the firing patterns of these visual-system neurons. The spike trains generated by all of the visual-system neurons, as well as those generated by primary auditory neurons, can be discribed by a refractoriness-modified fractal stochastic point process. Malvin C. Teich, Professor Department of Electrical Engineering Columbia University 500 West 120 Street New York, New York 10027, USA Tel: (212) 854-3117 FAX: (212) 932-9421 EMAIL: mct2 at columbia.edu 7. Modern Methods in Neurological Signal Processing: Applications to Detection of Brain Injury Nitish V. Thakor, Xuan Kong, David Sherman Biomedical Engineering Department Johns Hopkins School of Medicine Baltimore, MD 21205, USA Tel: 410-955-7093; Fax: 410-955-0549 email: nthakor at bme.jhu.edu Brain injury resulting from events such as hypoxia or ischemia have important clinical correlates such as asphyxic injury in neotates and stroke in adults. Similarly, in high risk neurological surgeries or neurological critical care unit there is a need to rapidly detect possible incidence of brain injury. This presentation will review the origins and responses of neurological signals such as electroencephalogram and evoked potentials during experimental studies of brain injury. Four different methods of analysis of neurological signals will be presented. Results obtained using five methods (adaptive Fourier series modeling, adaptive coherence analysis, wavelet analysis, time-frequency analysis, and bispectral analysis) will be presented. Theoretical innovations and new experimental results will be discussed. 8. WAVELETS AND NNs in MATURATION Metin Akay Dept. of Biomedical Engineering, Rutgers University, Piscataway, NJ 08855 Spontaneous breathing movements in the fetus tend to occur intermittently and do not become continuous until after birth. In both the primate and the ovine species, breathing movements have been observed with a high degree of variability in instantaneous breathing rates. Previously, the analysis of fetal breath signals is limited to statistical description of the time intervals, or a measure of short-term and long-term fluctuations using the fast Fourier transform. In this study, use of the matching pursuit and NNs revealed that fluctuations in instantaneous fetal breathing rates were much more complicated than previously thought. The most interesting finding is the presence of sinusoidal-like activities which were indicated by the long horizontal structures in the energy distribution. Although fast Fourier transform had indicated substantial slow modulation in breathing rates, it was not apparent that there were sinusoidal-like activities. 9. Adapted Waveform De-Noising for Medical Signals and Images Ronald R. Coifman Mladen Victor Wickerhauser Yale University Washington University We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new wavelet packet'' and localized trigonometric'' libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect. 10. Noise Reduction and Spectral Shaping as a Combined Processing Strategy for Hearing Aids Janet C. Rutledge Assistant Professor EECS Department Northwestern University 2145 Sheridan Road Evanston, IL 60208-3118 Persons suffering from sensorineural hearing loss experience an elevated threshold of hearing and reduced dynamic range of hearing. Therefore hearing aids must incorporate amplification plus some sort of amplitude limiting. In addition, frequency and temporal resolution are normally reduced which causes an increased sensitivity to background noise. Hearing aids, which generally amplify all incoming sounds, exacerbate this problem. Techniques employing multi-channel amplitude compression have been proposed to compensate for the elevated threshold and reduced dynamic range of hearing. We show that wavelet parameterization methods can be used for time-varying, frequency-dependent amplitude compression which adapts to the incoming signal on a frame-by-frame basis. In addition, we propose a wavelet-based noise reduction system which distinguishes between speech and noise using a single-microphone input that can be used as a front end to this amplitude compression system. 11. New Signal Processing Techniques for Physiological Data Analysis Mohsine Karrakchou Ecole Polytechnique Federale de Lausanne Tel:(4121) 693 26 05 Signal Processing Lab Fax:(4121) 693 76 00 Swiss Federal Institute of Technology e-mail: mohsine at ltssg3.epfl.ch CH-1015 Lausanne Switzerland www: http://ltswww.epfl.ch/ The aim of this paper is to present and validate algorithms allowing the bedside estimation of the effective pulmonary capillary pressure. The method should be automatic, i.e. should require no user intervention beyond inflating the balloon. It should be usable even if the pulmonary arterial pressure signal is distorted by respiratory pressure variations, (provided that the distortions are not massive). In this way, the estimation of$P_{mv}$will no longer require that the patient be paralyzed and apneic, thus it will be more generally applicable. To achieve these requirements, three points are intensively investigated, namely, the cancellation of respiratory interference, the determination of the occlusion point and finally the estimation of the model parameters. New algorithms have been developed for each of these different topics. For the cancellation of respiratory interference, the approach consists in using an adaptive interference canceller scheme in which the auxiliary signal employed is the right atrial pressure signal. The latter can be recorded simultaneously with pulmonary artery pressure using the same catheter. New structures for subband adaptive filtering based on wavelet packets have been developed for this purpose For the determination of the starting point or more generally for singularity detection, the continuous wavelet transform as well as the orthogonal wavelet transform have been investigated. An original nonlinear scheme for multiscale analysis has been proposed to achieve the same objective improving the performance. The latter is inspired from continuous wavelet transform and is based on morphological operators. Concerning the parameter estimation, the underlying model of a double exponential and the peculiar nature of the present artifacts made the classical least square fitting method inappropriate. Therefore, an entirely new method for estimating the parameters of a linear combination of decaying exponentials has been developed. The core of the method is the Hough transform usually used in image processing. The developed algorithms were tested and validated on AO data obtained in an experimental model of lung injury and in intensive care patients presenting pulmonary hypertension. Excellent results have been obtained for the estimation of$P_{mv}$. Beside the important step forward that has been made for the$P_{mv}\$ estimation, the newly
developed algorithms are not only useful for the present application
but also for many others.

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12. Multiscale Wavelet Frames for Contrast Enhancement of Digital Radiographs

Andrew Laine
Computer and Information Sciences Department
301 Computer Science and Engineering Builiding
P.0. Box 116120
University of Florida
Gainesville, FL  32611

Email: laine at cis.ufl.edu
Phone/Fax: (904) 392-1239

This talk shall describe a novel approach for accomplishing mammographic
feature analysis by overcomplete multiresolution representations.
We show that efficient  representations may be identified  within a
continuum of scale-space and used to enhance  features of importance to
mammography. We present methods of contrast enhancement based on three
multiscale representations: (1) The dyadic wavelet transform
(separable), (2) The phi-transform (non-separable, non-orthogonal),
and (3) The hexagonal wavelet transform (non-separable).

Multiscale features identified within distinct levels of transform space
provide local support for image enhancement. Mammograms are reconstructed
from wavelet coefficients modified at one or more levels by local and global
non-linear operators. In each case, multiscale edges and gain parameters
are selected adaptively by a measure of energy within each level of
scale-space.
We show quantitatively that transform coefficients, modified within each
level by adaptive non-linear operators, can make more obvious unseen or
Our results are compared with traditional image enhancement techniques by
measuring the local contrast of known mammographic features.

13. Waveform and Beamform Design for range and 2-D Doppler
Ultrasound Imaging

Y. Kadah and A. H. Tewfik
Dept. Of Electrical Engineering, Univ. Of Minnesota

We consider the problem of producing an "optimal" range- 2-D
Doppler image in a finite amount of time. A range- 2-D Doppler
provides estimates of  the transverse and line-of-sight flows as a
function of range. By optimal image, we mean the closest image in a
2-norm sense to the actual the transverse and line-of-sight flows
distribution as a function of range. We show that to obtain that
optimal image we need to adjust both the beamform and waveform
of the transmitted ultrasound field to the flow distribution. We
propose a beamform and waveform selection strategy that leads to a
progressive refinement of resolution of the produced image along
the range, line-of-sight and transverse flow axes. In this approach,
the operator can at each step select the parameter for which
maximum improvement will occur. We discuss imaging scenarios in
which the returns due to the optimal beamforms and waveforms can
be "synthesized" from those corresponding to a  standard beamform
and waveform and scenarios where one actually needs to generate
different beamforms and waveforms to improve the quality of the
final image.

We have developed a solution to thsi problem that allows simultaneous
estimation of both components by properly selecting a sequence of
waveforms (which happen to be wavelets in the frequency domain).

14.     Reducing the Imaging Time in Magnetic Resonance Imaging

Dennis Healy
Dartmouth College

I will describe two approaches to the problem of reducing
imaging time in Magnetic Resonance Imaging (MRI).
Karhunen-Loeve (K-L) expansion of a training set of images to reduce the
number of encodes required for a Magnetic Resonance (MR) image of a new object.
We evaluate the error likely to be achieved as a function of the number of
encodes and two technical problems: reduced SNR in the images and
smoothing of theK-L functions in practice.  We propose the use of localized
trigonometric bases developed by Coifman et. al. as an alternative to the
K-L basis.  The localized trigonometric bases approach the error
achieved by the K-L basis, but they are easier to use with existing methods
for fast acquisition.

Next I'll summarize some recent work concerning the imaging of time-varying
objects from a sequence of projections taken during the evolution
of the object. Reconstruction of coarse features, corresponding to low
spatial-frequency data, can be made nearly instantaneously in time from the
evolving data. A temporal sequence of these low spatial-frequency
reconstructions can be used to estimate the motion of the object.
Once the motion is estimated, we may use the estimate to compensate for
some of the motion of fine scale features.
This enables accurate reconstructions of the time varying fine structure in
several cases. The algorithm is demonstrated for a joint motion case study.
In general, this technique shows promise for a wide variety of applications
in MRI, and fast imaging using x-ray CT.

Clinical applications should include both functional MRI such as
dynamic imaging of oxygen usage and blood flow in the brain, and
motion imaging of joints, angiography in the lungs, and heart imaging.

15. Non-linear stabilization of ill-conditioned linear
inverse problems via adaptive subspace decomposition"

Tim Olson
Dartmouth College

We will investigate methods to stabilize ill-conditioned
linear inverse problems.  These methods will utilize
non-linear constraints, and subspace decompositions which
preserve the non-linear constraints to stabilize ill-conditioned
linear problems.  One application of these methods is to
limited angle tomography.

16. Inversion of the Radon Transform under Wavelet Constraints

Berkman Sahiner and Andrew E. Yagle
The University of Michigan, Ann Arbor

We investigate two applications of the wavelet transform to the problem of
image reconstruction from projections.  The first application is nonlinear and
spatially-varying filtering of reconstructed noisy images.  We constrain
wavelet coefficients of the reconstructed noisy image to be zero in
certain regions of the time-scale plane, and compute the minimum
mean-square estimate of the image given the statistics of the additive
noise and the constraints.

We also discuss how the constraints may be obtained from the noise-corrupted
image.  The second application is image restoration in a limited-angle
reconstruction problem.  We propose a wavelet-based restoration algorithm
given some approximate a priori knowledge about the edges that lie
parallel to the missing view angles.  We use this approximate partial edge
knowledge to restore certain affected high-resolution wavelet domain images.
The low-resolution image is restored using interpolation, and the
wavelet transform is used to combine the low-resolution
and high-resolution images into a complete reconstructed image.
Numerical examples illustrate the improvement achieved in both applications.

17. The Application of Wavelets and Fuzzy Logic Based Neural Nets to
Medical Data and Image Processing Problems

Tom Brotherton
Pat Simpson
ORINCON Corporation

Fuzzy logic and neural network techniques have been gaining popularity in the
processing of medical data.  Presented here is the application of general
approach which uses a hierarchy of neural nets coupled with advanced feature
processing, such as wavelet transformations, to solve medical signal and image
processing problems.  These include the determination of the degree of
stenosis in the carotid artery using a single channel of Doppler ultrasound
where both FFT and wavelet transforms are used to characterize the data for
input to the nets; the determination of the severity of coronary artery
disease in stress test ECG wave forms; and the determination of cardiac
tissues and structures in echocardiogram images.  The presentation will focus
primarily on neural nets but will also discuss the relationship of frequency
transformations and wavelet processing to form inputs to neural nets for the
development of signal and image classification systems.  The neural networks
that we use, called Fuzzy Min-Max (FMM) neural networks are based on fuzzy
sets.  The use of fuzzy logic based neural nets is particularly relevant for
medical applications as they have nearest neighbor properties that allow the
user to determine "why" a network gave the results it did and thus have
explanatory capabilities that allow the user to determine where test patterns
did or did not overlap with training patterns.