## 1 Introduction  
Thanks to their all-weather and nighttime operational capabilities, synthetic aperture radar (SAR) satellite systems are very attractive and thus are widely used for a number of applications concerning environmental monitoring, frequently increasingly in synergy with artificial intelligence tools [1]. The fusion of SAR and optical data constitutes a unique chance to merge the complementary abilities of the two types of data [2,3]. SAR images, however, are corrupted by speckle, which is a signal-dependent noise peculiar to all coherent imaging systems that severely impairs the appearance of images and drastically reducesthe performance of automated analysis tools. Fully developed speckle is modeled in the spatial frequency domain as a white process. However, in the complex spatial domain of in-phase and quadrature components, speckle is modeled as a spatially uncorrelated, multiplicative random process, independent of the underlying radar reflectivity, described by a zero-mean circular Gaussian probability density function (PDF) [4]. However, when the raw SAR data are processed to synthesize an image, the validity of this assumption may be violated. Before the SAR processor, the raw data are slightly oversampled and weighted in the Fourier domain, where the deconvolution process of the system's point-spread function (PSF) is performed, to avoid two-dimensional Gibbs effects around bright targets. As a consequence of the use of frequency windows (mostly Hamming or Kaiser) along both range and azimuth, speckle becomes autocorrelated. Hence, the single-look complex (SLC) image is synthesized with speckle that is spatially correlated. This problem was first noticed by some authors who adjusted their post-processing in order to tackle correlated speckle [5; 6], and later by many others, e.g., [7; 8]. Although incoherent multilooking is usually performed, when phase information is unnecessary, the reduced spatial correlation achieved through multilooking implies a degraded spatial resolution; such a loss of information may not be tolerated in several application contexts. SAR interferometry (InSAR) exploits the phase differences of two or more complex-valued images relative to the same geographic area and taken from slightly different positions and/or at different times [9]. The information extracted from the phase difference is utilized for the estimation of topography [10] and the measurement of millimetric ground deformations (subsidence) for environmental risk monitoring and security applications. Also, analyses of ocean surface currents benefit from an interferometric approach [11]. Angular, or baseline, decorrelation, induced by spatial diversity of orbits, and temporal decorrelation, induced by changes in the dielectric properties of the scene, are the main factors that influence the dependability of the interferometric phase. Point targets and strongly textured regions play a fundamental role, as their distribution of elementary scatterers does not change over time. In contrast, areas covered by vegetation may exhibit temporal decorrelation, which impairs the measurements of the interferometric phase [12]. Coherent spatial multilooking of the complex interferogram is generally utilized to counteract the decorrelation effects induced by scattering mechanisms affecting a wide number of pixels. The interferometric coherence, estimated through the coherent multilooking of the normalized interferogram, is inversely related to the noise of the interferometric phase [13; 14]. When coherence is equal to one, speckle patterns in the two images are identical, and the interferometric phase is noise-free. The transfer function of the SAR system in the spatial frequency domain, referred to as the spatial frequency response (hereafter, the frequency response), may induce a spatial correlation of the speckle if frequency-domain filtering, e.g., achieved through a Hamming window, is introduced in the SAR processor that focuses the raw data into an SLC image.