### Table 2. Compensation ability of our adaptive median filter in the 1st stage and the im- age quality enhancement system in the 2nd stage with respect to Lena.

"... In PAGE 13: ... 937 Fig. 9 and Table2 show the indispensability of the noise removal stage to remove the noise well and the image quality enhancement stage to compensate the blur and jaggy edge. Because we take the advantages of noise-exclusive scheme and the median filter with adaptive-size well, the proposed first-stage processing is so powerful in removing the impulse noise.... ..."

### Table 1. Results of the comparison between the GPS time series and two pro les of the SAR interferogram, (i) based on synoptic (syn) wind observations and (ii) based on a best- t (b.f.) analysis. The observed synoptic wind speed, vw, and wind direction, w, are listed for comparison. RMS values between the interpolated GPS measurements and the two SAR pro les, and the total range of atmospheric delay variation are shown to compare signal and noise magnitudes.

"... In PAGE 4: ... Results The results of the tropospheric delays estimated by GPS and InSAR are shown in Fig. 1 and Table1 . The Fig.... In PAGE 4: ...5 m/s it was assumed that no signi cant delay changes were present and so this synoptic data was not used in the averaging. Table1 lists, for every interferogram, the correlation coe cient between the pro les and the interferometric data. Based on the amount of rotation and stretching of the GPS pro le, wind speed and wind direction can be derived.... In PAGE 4: ... tween the GPS and the SAR data. Table1 shows that the best- t correlations between GPS and InSAR for the ve analyzed interferograms are 0.8 or better, while the estimated wind directions are accurate to within 30 and wind speeds di er maximally 4.... ..."

### Table 1. Exponentially-weighted Histories Filter Median Relative Instability

"... In PAGE 6: ... We added a per-link EWMA to our simulator with the goal that it would capture changes in network conditions and dampen the outliers we had seen. Table1 shows the median value of the distribution of median relative error and stabil- Table 1. Exponentially-weighted Histories Filter Median Relative Instability... ..."

### Table 1. Summary of noise reduction results using adaptive filtering.

"... In PAGE 4: ... In this particular case, the noise is reduced by about 30%. Table1 is a summary of the noise reduction results for different combinations. The noise reduction in the latitude component (LTr) ranges from 11% to 62%; in the longitude component (LNr) 14% to 59%; in the height component (HTr) 8% to 42%; in the average of the three components (Ar) 12% to 54%; and in the average of the horizontal components (Hr) 13% to 60%.... ..."

### Table 2. Summary of noise reduction results using adaptive filtering.

1999

"... In PAGE 4: ... In this particular case, the noise is reduced by about 30%. Table2 is a summary of noise reduction results from different combinations. To address the problem of correlation between measurements, a zero-baseline test using two Leica CRS1000 GPS receivers, sampling at 10Hz, was carried out on 2 November 1999 for a 2 hour period at UNSW.... ..."

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### Table 2 MAE results for median filtering

"... In PAGE 7: ... Salt-and-pepper noise is commonly cleaned in image pro- cessing by median filtering and we have compared this tra- ditional technique to the proposed approach. Table2 shows the MAE results for two increasing size median filters. Com- paring these results with those presented in Table 1 indicates seemed performances using at least 1 image to select the win- dow and 1 image to train the W-operator for the case of Fig- ure 8.... In PAGE 7: ...1.7% (from 0.00046 to 0.00036). Figures 12(c) and 12(d) illustrate the results obtained by applying median with feed- backing to the Figures 10(e) and 10(f) respectively. Finally, Table 4 shows the results for the resulting images with MAE given by Table2 taken as input to the median operation. The application of the feedback operation more than once does not change significantly the results.... ..."

### Table 5: Noise reduction (in dB) achieved by the location-invariant multichannel L- lters for the bivariate contaminated Gaussian noise model (Filter length N = 9). Filter NR LMS location-invariant multichannel L- lter -11.853 LMSN location-invariant multichannel L- lter -11.998 non-adaptive location-invariant multichannel L- lter -10.997 marginal median -9.8209

"... In PAGE 18: ... We see that LMSN exhibits a faster convergence rate. Moreover, its steady state MSE is lower than the LMS, as can be deduced from Table5 , where the NR achieved by both adaptive algorithms is tabulated, and Figure 2. The NR achieved by the nonadaptive design [14] is included in Table 5 for comparison purposes.... In PAGE 18: ...b, respectively. We see that LMSN exhibits a faster convergence rate. Moreover, its steady state MSE is lower than the LMS, as can be deduced from Table 5, where the NR achieved by both adaptive algorithms is tabulated, and Figure 2. The NR achieved by the nonadaptive design [14] is included in Table5 for comparison purposes. The NR achieved by the marginal me- dian is included for the same purposes as well.... ..."

### Table 7: Noise reduction (in dB) achieved in (NTSC) RGB color space by several lters in the restoration of the 50th color frame of \Trevor White quot; corrupted by mixed additive white trivariate contaminated Gaussian plus impulsive noise (Filter window 3 3). Filter NR Ranking marginal median -11.748 [7]

"... In PAGE 22: ... Note that the best RE estimator corresponds to index J = 2 [16]. By examining Table7 we conclude: 1. Nonlinear lters are ranked as the four best lters, namely, the multichannel DWMTM lter, the MC LMSN adaptive multichannel L- lter, the MC NLMS multichannel L- lter and the MC LMSN location-invariant multichannel L- lter.... ..."

### Table 8: Noise reduction (in dB) achieved in U V W color space by several lters in the restoration of the 50th color frame of \Trevor White quot; corrupted by mixed additive white trivariate contami- nated Gaussian plus impulsive noise (Filter window 3 3). Filter NR Ranking marginal median -11.270 [12]

"... In PAGE 23: ... As before, the adaptation step-size parameter that yields the best result in terms of the visual quality of the ltered image has been used in NLMS algorithms. It can be found in the corresponding entry of Table8 . For LMSN algorithms, one may use the parameters = 0:01 and = 0:001 and either the xed step size = 5 10?4 or a variable step-size (k) given by (k) = 0 ~ XT (k) ^ R?1 p (k) ~ X(k) as in algorithm II [26].... In PAGE 23: ... For LMSN algorithms, one may use the parameters = 0:01 and = 0:001 and either the xed step size = 5 10?4 or a variable step-size (k) given by (k) = 0 ~ XT (k) ^ R?1 p (k) ~ X(k) as in algorithm II [26]. In the latter case, the parameter 0 used is given in the corresponding entry of Table8 . The inspection of Table 8 reveals that:... ..."

### Table 1. Denoising using median filtering: SNR comparison

"... In PAGE 7: ... The SV median filter removes all germ-grain noise while preserving the edges and the geometry of the original image. Table1 displays the signal-to-noise ratio (SNR) of the filtered images. (a) (b) (c) (d) (e) (f) Figure 2.... ..."