A Wavelet Regularization Method for
Diffuse Radar-Target Imaging and Speckle-Noise Reduction

by Pierre Moulin

We consider the problem of forming radar images under a diffuse-target
statistical model for the reflections off a target surface.
The desired image is the scattering function $S(f,^tau )$, which describes the
second-order statistics of target reflectivity in delay-Doppler coordinates.
Our estimation approach is obtained by application of the maximum-likelihood
principle and a regularization procedure based on a wavelet representation
for the logarithm of $S(f,^tau )$.
This approach offers the ability to capture significant components
of $ln S(f,^tau )$ at different resolution levels and guarantees
nonnegativity of the scattering function estimates.
We show that the radar imaging problem can be set up as a problem of inference
on the wavelet coefficients of an image corrupted by additive noise.
A simple hypothesis-testing technique for solving the problem at
a prespecified significance level is studied.
The significance level of the test is selected according to the desired
noise/resolution tradeoff.
The regularization technique is applicable to a broad class of speckle-noise
reduction problems.