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.

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 (∼58 °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).

The performance of this algorithm is qualitative shown with real SMOS data in Figures 13 and 14, corresponding to Figures 9 and 10. It works reasonably well for most quasi-point sources, even if they are in the alias regions. On some occasions it tends to over-compensate the RFI sources, while on others it fails to compensate them completely due to errors in the location of the sources and/or estimation of the background. One of the drawbacks is that it cannot handle extended targets as the ones in Figure 13c, even though they are not too extended. The algorithm explained in Section 3.2 shows how to handle such cases.

At the end of the SMOS commissioning phase it was decided that the instrument should operate in full-polarimetric mode only. In this mode of operation the four Stokes parameters images (T_XX, T_YY, Real{T_XY} and Im{T_XY} are obtained after four switching intervals, as sketched in Figure 11. In many cases, pulsed RFI sources happen in one or several of the intervals, but not in all with the same amplitude, which distorts the side lobes and tails of the impulse response, preventing the use of the Sun cancellation algorithm described in Section 3.1. Also, since they affect only a subset of the whole visibility samples, fictitious third and fourth Stokes parameters may appear.

In order to better understand the differences of the problem in the full-polarimetric case, as compared to the dual-polarization one (section 3.1), Figure 15 illustrates these effects with an SMOS image acquired on September 3, 2010 over the Aegean Sea (Cyprus island appears in the bottom part of the image).

As can be appreciated in the T_XX image (Figure 15a,b), there is an intense RFI source around (-0.25, +0.35) whose “tails” (impulse response) are not even symmetrical: the tails at +30° and at -90° with respect to the ξ axis are mostly negative (dark blue color), instead of positive, indicating that this RFI source has occurred only during some intervals of the switching sequence. The other RFI sources, being even stronger (e.g., (-0.35, -0.02) and (0.19, -0.35)) appear more “round” and symmetric, indicating that the RFI was most probably present during the four switching periods. Figures 15c and 15d show the T_YY image. Compared to Figure 15a, the strongest sources are now in different positions, new ones can also be seen, while others have nearly disappeared, particularly the one at (-0.25, +0.35). Figures 15e and 15f show the real and imaginary parts of T_XY (Re[T_XY] and Im[T_XY]) in the alias-free FOV, which should be close to zero in the Earth horizontal-vertical reference frame (Re[T_HV] and Im[T_HV]), but actually are not. This reveals the presence of new RFI sources that have passed inadvertently in the T_XX and T_YY images.

The fact that Re[T_XY] and Im[T_XY] should be close to zero is based on two factors:

the low cross-polar antenna pattern in the alias-free FOV, and

Outside the alias-free FOV, the values of Re[T_XY] and Im[T_XY] increase due to the overlapping of regions far away from the antenna boresight, where the co- to cross-polar ratio is much lower. Figures 16a and 16b show the mean values of Re[T_XY] and Im[T_XY] computed over the ocean to minimize the risk of undetected RFI.

Note also that, within the alias-free field of view, the T_XX(ξ, η) and T_YY(ξ, η) images (Figure 16a,b) capture the angular dependence of the brightness temperatures at X- and Y-polarizations in the antenna reference frame, which allows easily distinguishing RFI contaminated pixels. Over land, the problem is more complex due to the large range of BTs that can be encountered.

At this moment, two strategies can be followed:

to use only the YY- and XX-polarization BT images obtained during the time intervals 0-τ and 2·τ-3·τ, respectively (marked as 1 and 1′ in Figure 11), and use the dual-polarization RFI detection and mitigation algorithm (Section 3.1). This approach throws away half of the data (time intervals τ-2·τ and 3·τ-4·τ) and would not make any use of the polarimetric information contained in Re[T_XY] and Im[T_XY], which can be very helpful in detecting the presence of RFI.

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). Actually, this interpolation technique could also be used for the ocean pixels as well, but in many cases (i.e., Figure 18 below) the number of corrupted pixels in the whole image is so large, that the algorithm does not function. Therefore, we have resorted to use the mean values over the corrupted ocean pixels, and then interpolate only the contaminated land pixels.

Figures 18, 19 and 20 show three different examples of the application of the RFI detection and mitigation algorithm described above for the real SMOS data in full-polarimetric case. Figure 18 corresponds to a SMOS image over the Aegean Sea acquired on September 3, 2010 (a few snap-shots earlier than that in Figure 15). Figure 18a shows the original SMOS image at X-polarization (T_XX). Figure 18b shows the RFI-cleaned image. Figure 18c shows the RFI map that was subtracted from Figure 18a to obtain Figure 18b. Finally Figure 18d shows the confidence map. As can be appreciated, the lowest confidence values happen in the central parts of the largest regions detected as contaminated by RFI, while for small RFI sources, the interpolated values have a large confidence value (>0.8–0.9). Figures 19 and 20 show two more examples over the Iberian Peninsula and the Caribbean Sea acquired on the same date.

One of the features of this algorithm is that the coastline appears to be better defined. Actually, the coastline information is added in the interpolation process to separate the ocean and land parts, which are put together afterwards. However, no additional information is included in the image reconstruction process and the instrument's resolution is therefore not improved, and consequently, on the land side, brightness temperature decreases when approaching the coastlines from the land, as in the original RFI-corrupted image, when the coastline mask was not applied.

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 10⁵ 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.

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 10⁶ 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 ∼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_det ∼ 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 10³ 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).