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   -> Volume 6, Issue 5

Preprint: Recent wavelet/time-freq papers from the Rice DSP group
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PostPosted: Sun Apr 13, 1997 7:36 pm    
Subject: Preprint: Recent wavelet/time-freq papers from the Rice DSP group
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#1 Preprint: Recent wavelet/time-freq papers from the Rice DSP group


Matthew S. Crouse, Robert D. Nowak and Richard G. Baraniuk
Submitted to IEEE Transactions on Signal Processing, January 1997

Wavelet-based statistical signal processing techniques such as
denoising and detection typically model the wavelet coefficients as
independent or jointly Gaussian. These models are unrealistic for
many real-world signals. In this paper, we develop a new framework
for statistical signal processing based on wavelet-domain hidden
Markov models (HMMs). The framework enables us to concisely model the
statistical dependencies and nonGaussian statistics encountered with
real-world signals. Wavelet-domain HMMs are designed with the
intrinsic properties of the wavelet transform in mind and provide
powerful yet tractable probabilistic signal models. Efficient
Expectation Maximization algorithms are developed for fitting the HMMs
to observational signal data. The new framework is suitable for a
wide range of applications, including signal estimation, detection,
classification, prediction, and even synthesis. To demonstrate the
utility of wavelet-domain HMMs, we develop novel algorithms for signal
denoising, classification, and detection.


Robert D. Nowak and Richard G. Baraniuk
Submitted to IEEE Transactions on Image Processing, April 1997

Many imaging systems rely on photon detection as the basis of image
formation. One of the major sources of error in these systems is
Poisson noise due to the quantum nature of the photon detection
process. Unlike additive Gaussian noise, Poisson noise is
signal-dependent, and consequently separating signal from noise is a
very difficult task. In this paper, we develop a novel wavelet-domain
filtering procedure for noise removal in photon imaging systems. The
filter adapts to both the signal and the noise and balances the
trade-off between noise removal and excessive smoothing of image
details. Designed using the statistical method of cross-validation,
the filter is simultaneously optimal in a small-sample predictive sum
of squares sense and asymptotically optimal in the mean square error
sense. The filtering procedure has a simple interpretation as a joint
edge detection/estimation process. Moreover, we derive an efficient
algorithm for performing the filtering that has the same order of
complexity as the fast wavelet transform itself. The performance of
the new filter is assessed with simulated data experiments and tested
with actual nuclear medicine imagery.


Robert D. Nowak and Richard G. Baraniuk
Submitted to IEEE Transactions on Signal Processing, February 1997

Nonlinearities are often encountered in the analysis and processing of
real-world signals. In this paper, we introduce two new structures
for nonlinear signal processing. The new structures simplify the
analysis, design, and implementation of nonlinear filters and can be
applied to obtain more reliable estimates of higher-order statistics.
Both structures are based on a two-step decomposition consisting of a
linear orthogonal signal expansion followed by scalar polynomial
transformations of the resulting signal coefficients. Most existing
approaches to nonlinear signal processing characterize the
nonlinearity in the time domain or frequency domain; in our framework
any orthogonal signal expansion can be employed. In fact, there are
good reasons for characterizing nonlinearity using more general signal
representations like the wavelet transform. Wavelet expansions often
provide very concise signal representation and thereby can simplify
subsequent nonlinear analysis and processing. Wavelets also enable
local nonlinear analysis and processing in both time and frequency,
which can be advantageous in non-stationary problems. Moreover, we
show that the wavelet domain offers significant theoretical advantages
over classical time or frequency domain approaches to nonlinear signal
analysis and processing.


Robert D. Nowak and Richard G. Baraniuk
Submitted to IEEE Transactions on Image Processing, February 1996

In this paper, we propose a general framework for studying a class of
weighted highpass filters. Our framework, based on a multiscale
signal decomposition, allows us to study a wide class of filters and
to assess the merits of each. We derive an automatic procedure to
optimally tune a filter to the local structure of the image under
consideration. The entire algorithm is fully automatic and requires
no parameter specification from the user. Several simulations
demonstrate the efficacy of the method.


Martin Pasquier, Paulo Goncalves, Richard G. Baraniuk
Submitted to IEEE Transactions on Signal Processing, July 1996

We introduce a new method for the time-scale analysis of
non-stationary signals. Our work leverages the success of the
``time-frequency distribution series / cross-term deleted
representations" into the time-scale domain to match wide-band
signals that are better modeled in terms of time shifts and scale
changes than in terms of time and frequency shifts. Using a wavelet
decomposition and the Bertrand time-scale distribution, we locally
balance linearity and bilinearity in order to provide good resolution
while suppressing troublesome interference components. The theory of
frames provides a unifying perspective for cross-term deleted
representations in general.


Paulo Goncalves and Richard G. Baraniuk
Submitted to IEEE Transactions on Signal Processing, April 1996

In this paper, we introduce a new set of tools for time-varying
spectral analysis: the pseudo affine Wigner distributions. Based on
the affine Wigner distributions of J. and P. Bertrand, these new
time-scale distributions support efficient online operation at the
same computational cost as the continuous wavelet transform.
Moreover, they take advantage of the proportional bandwidth smoothing
inherent in the sliding structure of their implementation to suppress
cumbersome interference components. To formalize their place within
the echelon of the affine class of time-scale distributions, we
introduce and study an alternative set of generators for this class.


Matthew S. Crouse, Martin Pasquier, Richard G. Baraniuk
Department of Electrical and Computer Engineering
Rice University
Houston, TX 77005-1892

Robert D. Nowak
Department of Electrical Engineering
Michigan State University
East Lansing, MI 48824-1226

Paulo Goncalves:
INRIA Rocquencourt - Projet fractales
Domaine de Voluceau, B.P. 105
78153 Le Chesnay Cedex, France

This work was supported by the National Science Foundation, grant
no. MIP-9457438, and the Office of Naval Research, grant no.
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