A wavelet regularization method for diffuse radar-target imaging and speckle-noise reduction

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, τ), 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, τ). This approach offers the ability to capture significant components of ln S(f, τ) 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 trade-off. The regularization technique is applicable to a broad class of speckle-noise reduction problems.