Speckle removal from SAR images in the undecimated wavelet domain

Speckle reduction is approached as a minimum mean-square error (MMSE) filtering performed in the undecimated wavelet domain by means of an adaptive rescaling of the detail coefficients, whose amplitude 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 variance and autocorrelation of the fading variable, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. On the test image Lena corrupted by synthetic speckle, the proposed method outperforms Kuan's local linear MMSE filtering by almost 3-dB signal-to-noise ratio. When true synthetic aperture radar (SAR) images are concerned, empirical criteria based on distributions of multiscale local coefficient of variation, calculated in the undecimated wavelet domain, are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle does not obey a fully developed model, to avoid blurring strong textures and point targets. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from optical images, demonstrate that the visual quality of the 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 typical impairments often introduced by critically subsampled wavelet-based denoising.