## 3 Results
### TerraSAR-X/TanDEM-X Dataset  
The second test site consists of images collected by the X-band TerraSAR-X/TanDEM-X twin satellites (TSX-TDX) operated by DLR, the German Aerospace Center, in the area of Euskirchen, Germany. The images depict an agricultural region surrounding an urban settlement. Each image is in StripMap mode (3 m resolution). Here, temporal decorrelation is also low for vegetated areas, thanks to an extremely low temporal distance between acquisitions. The SAR processor employs a Hamming frequency window, which introduces a pronounced spatial correlation, particularly noticeable on the modulus of the unfiltered interferogram, as shown in Figure 7.  
Figure 4: Interferometric pair of images of Pomigliano, master image: (**a**) processed without a Hamming window; (**b**) processed with a Hamming window; (**c**) processed with a Hamming window and subsequently whitened. Figure 5: Coherence maps of Pomigliano estimated using 3 \(\times\) 3 boxcar filtering: (**a**) SLC pair processed without a Hamming window; (**b**) SLC pair processed with a Hamming window; (**c**) SLC pair processed with a Hamming window and subsequently whitened. Figure 6: Maps of the interferometric phase of Pomigliano estimated using a 3 \(\times\) 3 sliding window: (**a**) SLC pair processed without a Hamming window; (**b**) SLC pair processed with a Hamming window; (**c**) SLC pair processed with a Hamming window and subsequently whitened. The interferograms calculated from the original and whitened SLC image pairs were processed using the NL-InSAR algorithm [46], which is a modified version of the PPB [45] and is suitable for filtering SAR interferograms. Figure 8 displays the moduli of the filtered interferograms for the original and whitened data. In the latter case, filtering is more aggressive in vegetated areas than in built-up areas, where the detail preservation accuracy of NL-InSAR is comparable to the accuracy achieved with non-whitened speckle. NL-InSAR runs with a search area of 31 \(\times\) 31, 3 \(\times\) 3 pixel patterns, nine looks (i.e., the nine surrounding pixels with the largest weights are weighted and averaged), and four iterations. The computational cost is significantly greater than that of the baseline 3 \(\times\) 3 box filtering used in the previous simulations. Nonetheless, NL-InSAR, including its polarimetric version [48] is \"de facto\" recognized as a standard for the coherent processing of SAR data [49], despite its computational requirements, which can be adjusted parametrically. The goal of interferometric processing, however, is not the smoothing of interferograms but to achieve accurate measurements of coherence, as well as spatial regularity and cleanness in the phase map. In fact, a high coherence value, usually above 0.6, indicates that the phase is reliable and can be unwrapped to reveal the topography of the scene. The coherence maps calculated by NL-InSAR from the original and whitened SLC pairs are shown in Figure 9. What immediately stands out is that the map calculated from the whitened data exhibits values 10% lower, on average, than those calculated from the non-whitened data. Interestingly, the difference is concentrated in the vegetated area and is negligible in the built-up area, as shown in Figure 10. The reason for this is the non-local processing of the interferogram. NL-InSAR finds pixels with similar surrounding patterns and averages them. In homogeneous agricultural land cover, such pixels are found close to one another and thus neighboring pixels are averaged, similar to box filtering. In spatially heterogeneous areas, statistically similar pixels are sparse and thus speckles are uncorrelated with each other. In the error map, the difference between the coherence maps calculated from whitened and non-whitened data reflects the heterogeneity of the scene: in homogeneous areas, the estimated coherence is always biased upward if the data are not whitened. In heterogeneous areas, the estimation is accurate in both cases, and the error vanishes.