## 3 RFI Detection and Mitigation Algorithm in Synthetic Aperture Microwave Radiometry Imagery
### Full-Polarimetric Mode Algorithm
This approach throws away half of the data (time intervals \(\tau\)-2-\(\tau\) and 3-\(\tau\)-4-\(\tau\)) and would not make any use of the polarimetric information contained in Re[T\({}_{\rm XY}\)] and Im[T\({}_{\rm XY}\)], which can be very helpful in detecting the presence of RFI. 2. to define a set of new different masks to detect the presence of RFI in the BT image at XX- or YY-polarization images in the full-polarimetric mode using all the available information. This process is described below:  
Figure 16: Mean maps of (**a**) \(\rm T_{XX}(\xi,\ \eta)\); (**b**) \(\rm T_{YY}(\xi,\ \eta)\); (**c**) \(\rm Re[T_{XY}(\xi,\ \eta)]\); and (**d**) Im[T\({}_{\rm XY}(\xi,\ \eta)\)] computed over the ocean from all clean snap-shots from August 3 to 18, 2010. Note that in the alias-free and extended alias-free FOV regions Re[T\({}_{\rm XY}(\xi,\ \eta)\)], and (**d**) Im[T\({}_{\rm XY}(\xi,\ \eta)\)] are close to zero, but in the alias regions they significantly increase. * BT pixels (XX- or YY- polarizations) larger than a given threshold (threshold 1, e.g., 350 K1) are flagged as corrupted (Figure 17a). This is equivalent to step #2 in the dual-polarization algorithm. * A background image computed from the original BT image low-pass filtered with a disk of 6 pixels radius is subtracted from the original image. The pixels whose value is larger than another threshold (threshold 2, e.g., 350 K1, as well) and that correspond to the land part only of the BT image are flagged as corrupted (Figure 17b). * A third mask is computed from those pixels in \(|\mathrm{Re}[\mathrm{T}_{\mathrm{XY}}(\vec{\xi},\,\eta)]|\) that differ from the mean \(|\mathrm{Re}[\mathrm{T}_{\mathrm{XY}}(\vec{\xi},\,\eta)]|\) image (Figure 16c) more than a given threshold (threshold 3, e.g., 250 K, larger than the maximum expected \(|\mathrm{Re}[\mathrm{T}_{\mathrm{XY}}(\vec{\xi},\,\eta)]|\) values). These pixels are flagged as corrupted (Figure 17c). * A fourth mask is computed from those pixels in \(|\mathrm{Im}[\mathrm{T}_{\mathrm{XY}}(\vec{\xi},\,\eta)]|\) that differ from the mean \(|\mathrm{Im}[\mathrm{T}_{\mathrm{XY}}(\vec{\xi},\,\eta)]|\) image (Figure 16d) more than a given threshold (threshold 4, e.g., 50 K). These pixels are flagged as corrupted (Figure 17d). * Finally, a fifth mask is computed for the ocean pixels only for which \(\mathrm{T}_{\mathrm{XX}}(\vec{\xi},\,\eta)\) or \(\mathrm{T}_{\mathrm{YY}}(\vec{\xi},\,\eta)\) differ from the mean \(\mathrm{T}_{\mathrm{XX}}(\vec{\xi},\,\eta)\) or \(\mathrm{T}_{\mathrm{YY}}(\vec{\xi},\,\eta)\) images (Figures 16a or 16b) more than \(N\): \(\Delta\mathrm{T}(\vec{\xi},\,\eta)\) are flagged as corrupted (Figure 17e). In the algorithm described \(N\) is set to 3, and \(\Delta\mathrm{T}(\vec{\xi},\,\eta)\) is the radiometric sensitivity in the \((\vec{\xi},\,\eta)\) direction, as explained in Section 3.1. The global mask used for RFI detection is actually the \"or\" of the five previous masks, that is, a pixel is flagged, if RFI is detected in any of the tests. Land and ocean pixels are differentiated to take into account their different angular signature, as shown in Figure 17f with light blue the ocean (and sky) pixels, and in maroon, the land pixels that are susceptible to being contaminated by RFI. Now, for the RFI mitigation, ocean and land pixels have to be treated in a differentiated manner, that is, a land-sea mask is needed. For the ocean pixels, the corrupted pixels are replaced by their corresponding mean ones (Figure 16a or 16b). For the land pixels an interpolation method based on an object removal and exemplar-based region filling is used, which combines the best texture synthesis with inpainting algorithms [15]. In addition, this technique produces a confidence map to indicate the reliability of the interpolated values: from 0 (not reliable at all) to 1 (totally reliable).