WAVELET-BASED TRANSFORMATIONS FOR NONLINEAR SIGNAL PROCESSING


Robert D. Nowak and Richard G. Baraniuk

Department of Electrical Engineering
Michigan State University
East Lansing, MI  48824-1226
Email:    rnowak@egr.msu.edu

Department of Electrical and Computer Engineering
Rice University
Houston, TX  77005-1892
Email:   richb@rice.edu

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.