## 3 RFI Detection and Mitigation Algorithm in Synthetic Aperture Microwave Radiometry Imagery
### Quantitative Algorithm Performance  
In order to properly quantify the performance of the RFI detection algorithm, the probability of detection and the probability of false alarms must be evaluated. Since it is difficult to ascertain from a real SMOS image whether or not there is RFI, the performance of the mitigation algorithm will be evaluated in the calculation of the induced RMS error between the cleaned and the RFI-contaminated synthetic brightness temperature images. To make the tests more reliable and repetitive, Figure 21 shows the performance of the algorithm with a \(10^{5}\) K RFI source over the sea (simulated as a constant at 100 K), and in the land-sea border.  
These images show the performance of the previously described algorithm over land, sea and the coastline. Recall that over the sea there is no interpolation algorithm applied, but there is over land, which is why only confidence level maps are generated over land. Note also that over land, the side lobes of the impulse response are not detected (unless the threshold is made much smaller). This is because of the higher BT value and--in principle--because the background is unknown and must be estimated, as opposed to the sea where it is known.  
Figure 20: RFI in SMOS: Scenario 8. SMOS image over the Caribbean sea acquired on September 3, 2010 ascending pass: **(a)** Original \(\mathrm{T_{XX}}\) image; **(b)** RFI-cleaned \(\mathrm{T_{XX}}\) image.  
Figure 21: RFI in SMOS: Scenario 9. Synthetic image with a 10\({}^{5}\) K RFI source at: **(a)** (\(-\)0.5, 0) over a 100 K sea; **(b)** (0, 0) over the synthetic coastline; and **(c)** (\(+\)0.5, 0) over a 270 K land. From left to right: original BT image, RFI-cleaned BT image, RFI BT subtracted, and confidence level map.  
A series of 100 Monte Carlo simulations have been performed for intensities of the point RFI sources with equivalent noise temperature from 100 K to 10\({}^{6}\) K. In each of the simulations, the location of the source is randomly selected within the full hexagon to mimic the expected location of the RFI sources in SMOS. On one hand, the fraction of the pixels detected as contaminated by RFI has been computed as a function of the RFI source intensity, and the results averaged for all 100 simulations. Results are plotted in Figure 22. As can be appreciated, the stronger the RFI source, the larger the fraction of pixels contaminated by RFI due to the \"tails\" of the impulse response, reaching \(\sim\)20% of the total number of pixels for a single RFI source of 1,000,000 K intensity.  
The concepts of probability of detection and false alarm should in this case be applied to the single RFI source. However, in a real scenario, the exact number of RFI sources is not known, and the tails of the impulse response were identified as weak RFIs, increasing noticeably the probability of false alarm. Figure 23 shows the average RMS error in the BT maps with a single RFI source of varying amplitude (red) before and (blue) after the RFI mitigation algorithm. As can be appreciated, between 700 and 800 K the two plots cross, that corresponds to the RFI intensity for which the detection and *mitigation* algorithms start performing (\(P_{\text{det}}\sim 1\)). Below it, the intensity of the RFI source is too weak to be detected (only 0.1 % of the points--on average--seem to be contaminated). As can also be noticed, the error plots above 2000 and 3000 K run nearly parallel to one another, suggesting that the algorithm mitigation part is always operational.  
Above 10\({}^{3}\) K it can be concluded that the probability of detection is nearly 1 (100 over 100 RFI Monte Carlo simulation snap-shots), and the probability of false alarm is so low that it cannot be evaluated from simulations (Equation 2).  
Figure 21: Cont.