Homomorphic wavelet-based statistical despeckling of SAR images

In this paper, we introduce the homomorphic Gamma-WMAP (wavelet maximum a posteriori) filter, a wavelet-based statistical speckle filter equivalent to the well known Gamma-MAP filter. We perform a logarithmic transformation in order to make the speckle contribution additive and statistically independent of the radar cross section. Further, we propose to use the normal inverse Gaussian (NIG) distribution as a statistical model for the wavelet coefficients of both the reflectance image and the noise image. We show that the NIG distribution is an excellent statistical model for the wavelet coefficients of synthetic aperture radar images, and we present a method for estimating the parameters. We compare the homomorphic Gamma-WMAP filter with the Gamma-MAP filter and and the recently introduced Gamma-WMAP filter, which are both based on the same statistical assumptions. The homomorphic Gamma-WMAP filter is shown to have better performance with regard-to smoothing homogeneous regions. It may in some cases introduce a small bias, but in our studies it is always less than that introduced by the Gamma-MAP filter. Further, the speckle removed by the homomorphic Gamma-WMAP filter has statistics closer to the theoretical model than the speckle contribution removed with the other filters.