## 1 Introduction
The drawback of achieving focused targets is that speckle becomes spatially correlated in either range, azimuth, or both, depending on where the window is applied. While geometrically accurate targets are desirable, the autocorrelation function of speckle may induce an artificial increment of coherence in areas, mainly vegetated, affected by a temporal decorrelation of radar echoes. The coherence bias mainly depends on the missing local ergodicity of the data, originating from autocorrelation. High coherence values are the prerequisite for an accurate unwrapping of the phase field; thus, the coherence bias may result in erroneous detection of areas in which the phase is reliable and may be unwrapped. Although the frequency window may be enabled or disabled upon request, the two benefits of well-focused targets and spatially uncorrelated speckle cannot be jointly achieved. Coherent processing of temporal sequences of SLC images includes sea surface complex wind field estimations [15], measurements of interferometric coherence over time, e.g., to analyze changes in glaciers and snow cover [16], or rainforest mapping [17]. Generally speaking, temporal coherence analysis provides a valuable tool for investigating subtle variations in land cover, independent of the dielectric and geometric properties of the surface, and is related to the temporal correlation of detected speckle patterns in a sequence of images [18]. In fact, high coherence indicates not only that the reflectivity of the surface is unchanged but also that the spatial distribution of elementary scatterers within the resolution cell, approximately twice the pixel size, is unchanged. Another possible application of deconvolution for speckle whitening is in multi-baseline SAR tomography, stemming from interferometry. In this emerging technique, a stack of SLC images, acquired from slightly different antenna phase center positions in the vertical plane that constitute a cross-track array [10; 19], is processed in the baseline domain to obtain a synthetic beam in the elevation dimension to resolve the scattering distribution in full 3D [19; 20]. The most important current scenario for SAR tomography is the sensing and monitoring of forest structures and biomass, which is of great importance to the carbon cycle and global warming issues [20]. Benefits are expected from whitened speckle in tomographic processing, as well as in interferogram estimation, due to the increased number of effective looks [19; 20]. Exactly one decade ago, a viable strategy for \"whitening\" spatially correlated speckle in SLC data, without prior knowledge of the SAR system and the raw-data processor, was developed by one of the authors [6]. Spatially correlated speckle is perhaps the major reason for the mediocre despeckling performance achieved by advanced methods when single-look amplitude/intensity images [21] are processed for speckle reduction [22]. The procedure in [6] is fully unsupervised and carries out estimation and inversion of the frequency response of the SAR system, with preliminary detection based on percentile thresholding and separate processing of bright targets. In subsequent studies, the applicability of the whitening procedure to polarimetric speckle reduction [23] and polarimetric feature extraction [24] was addressed. Recently, it has been demonstrated that incoherent change detection from SAR images also takes significant advantage of the uncorrelatedness of speckle [25], even for methods that are slightly sensitive to speckle [26]. In this paper, we resume our earlier investigations [27] to determine whether the original procedure [6] can be used for coherent processing, where phase information is invaluable. This includes mainly InSAR but, in principle, also differential InSAR (DInSAR), and coherent change detection based on temporal coherence analysis [28]. Also, some suggestions for its possible application to SAR tomography [19] will be briefly discussed. The organization of this article is as follows.