Abstract
Synthetic aperture radar (SAR) images are widely used for Earth observation to complement optical imaging. By combining information on the polarization and the phase shift of the radar echos, SAR images offer high sensitivity to the geometry and materials that compose a scene. This information richness comes with a drawback inherent to all coherent imaging modalities: a strong signal-dependent noise called “speckle.” This paper addresses the mathematical issues of performing speckle reduction in a transformed domain: the matrix-log domain. Rather than directly estimating noiseless covariance matrices, recasting the denoising problem in terms of the matrix-log of the covariance matrices stabilizes noise fluctuations and makes it possible to apply off-the-shelf denoising algorithms. We refine the method MuLoG by replacing heuristic procedures with exact expressions and improving the estimation strategy. This corrects a bias of the original method and should facilitate and encourage the adaptation of general-purpose processing methods to SAR imaging.
Highlights
Synthetic aperture radar (SAR) imaging is a key technology in airborne and satellite remote sensing
The residuals Zobtained with the modified MuLoG algorithm are comparable to the true residuals Z: no geometrical structure from the image is noticeable in the residuals, which indicates that contrasted features where not removed from the image by the despeckling processing
In order to perform a more quantitative comparison of the residuals, we report in Figure 7 the symmetrical Kullback-Leibler divergence (KLD) between the distribution of the residuals Σ and Σfor different numbers of looks ranging from L = 1 to 100
Summary
SAR imaging is a key technology in airborne and satellite remote sensing. This active imaging technique based on time-of-flight measurement and coherent processing (the so-called aperture synthesis) has a night and day capability and can produce images through clouds [30]. – PolSAR denotes multi-channel polarimetric images: each pixel k contains a vector vk = (vk, vk2, vk3) ∈ C3 of 3 complex amplitudes backscattered by the scene under different polarizations (horizontally or vertically linearly polarized components at emission or reception, see Figure 1(a));. Where ∗ denotes the conjugate transpose, and the complex-valued covariance matrix Σk carries all the information about the backscattering process: in SAR imaging (D = 1), Σk corresponds to the reflectivity at pixel k, in PolSAR Σk ∈ C3×3 characterizes the reflectivity in each polarimetric channel We introduce several modifications and show that they suppress the bias of the original method Beyond their use in MuLoG’s generic framework, these mathematical developments can benefit other variational methods for the restoration or segmentation of multi-channel SAR images, as well as hybrid methods that combine deep learning and an explicit statistical model of speckle by algorithm unrolling [29]
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