## 3 RFI Detection and Mitigation Algorithm in Synthetic Aperture Microwave Radiometry Imagery
### Dual-Polarization Mode Algorithm  
As can be appreciated in Figures 7 to 10, most RFI sources appear as point sources to instrument's angular resolution. Therefore, they look like the MIRAS instrument impulse response, even though in many cases their amplitude is not strong enough so that the tails of the impulse response (see Figures 15b and 21) appear clearly differentiated from the BT background. Figure 12: Detail of switching sequence from time 0 to 2t. (**a**) Step 1 of MIRAS polarimetric mode: all receivers switched to Y-polarization and corresponding visibility map (all baselines are YY). All other baselines XX, XY and YX can be obtained from this switching scheme; (**b**) Step 2: left arm in Y-polarization, others in X-polarization; (**c**) Step 3: right arm in Y-polarization, others in X; (**d**) Step 4: central arm in Y-polarization, other in X. Adapted from Figures 8 and 10 in [12]. Figure 11: MIRAS polarimetric mode switching sequences with interlacing and alternating polarization for equi-sensitivity. Adapted from Figure 7 in [12]. The proposed algorithm takes advantage of previous techniques developed in the frame of the SMOS mission, such as the successful Sun cancellation algorithm [13] and the extended CLEAN [14]. The steps of the algorithm are summarized below:  
Very strong RFI sources:  
1. If the BT of a large fraction (user-selectable) of pixels is larger than a given threshold--The 350 K threshold is selected to be above the maximum brightness temperature of a blackbody at the maximum temperature registered on the Earth (\(\sim\)58 \({}^{\circ}\)C = 331 K). Sun glint is not an issue, because it always happens on Earth's pixels outside the extended alias-free field of view--(e.g., 350 K), the whole snap-shot is flagged as totally contaminated (see Figure 8c). Strong RFI sources: if the snap-shot is not flagged as totally contaminated then:  
2. BT pixels larger than a given threshold (e.g., 350 K) are flagged as potentially corrupted. 3. Following the same concept of the Sun cancellation algorithm derived in [13], but applied recursively as in the CLEAN algorithm [14] to all the BT pixels found in step #2, the strongest RFI sources are located and recursively cancelled. In this way, not only the main lobe of the impulse response is attenuated (eventually cancelled), but the side lobes as well. In this case the main problems are that: * As opposed to the Sun, the exact location of the RFI sources is not _a priori_ known, and the accuracy of the estimation is limited by the step of the (\(\xi\), \(\eta\)) grid. In the SMOS data processing ground segment the grid size is \(128\times 128\) pixels. In the proposed algorithm an optimum interpolation based on hexagonal Fourier transforms [11] and zero-padding is performed to try to determine more precisely the position of the sources (up to 4 times thinner grid). * Due to the (usually) lower values of the equivalent BT values of the RFI sources, as compared to the Sun (between \(10^{5}\) and \(10^{6}\) K), the background BT estimation becomes more critical (Equations 11-16 in [13]), * Background BT estimation is even more difficult, since most RFI sources tend to be in coastal regions where population concentrates. This means that about half of the surrounding pixels are land pixels, and about half are sea pixels. And * Since RFI sources tend to be very time-dependent, it is not possible to average a number of consecutive snap-shots to improve the RFI amplitude estimations. Moderate RFI sources: in the remaining BT image, once strong sources have been cancelled or attenuated (mitigated, but not totally cancelled),  
4. A background image is subtracted. This background BT image is computed from the BT image resulting from step #3, but low-pass filtered with a disk of 6 pixels radius. 5. In the differential image (step #4: cleaned BT image minus background image), pixels with values larger than \(N\Delta\)T(\(\xi\), \(\eta\)) are flagged as RFI and not as noise spikes.