Heterogeneity-sensitive adaptive speckle reduction in a translation-invariant wavelet domain

In this paper, LLMMSE filtering is performed in the undecimated wavelet domain by means of an adaptive rescaling of detail coefficients. The amplitude of each coefficient is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the speckle variance, and the wavelet filters only, without assuming any model to describe the underlying backscatter. Empirical criteria based on distributions of multiresolution C_v calculated in the undecimated wavelet domain are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle is not fully developed, to definitely avoid the slight blurring noticed in some textures and the perceivable smearing of point targets. Experiments carried out on SAR images demonstrate that the visual quality of results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids the typical impairments produced by critically-subsampled wavelet-based denoising.