Correlated Images and Despeckling

Correlations in the data cause the same problems when despeckling as when segmenting. Despeckling uses a neighbourhood of 3x3 pixels to form the reconstruction, which in the example studied in the previous section (6.5.2) is matched to the correlation between samples, in this case. The result of despeckling image 6.7 would therefore be expected to resemble the original image with the individual speckle blobs well reconstructed.

In Figure 6.6(a) we show a detail from Figure 6.7, together with its despeckled version in Figure 6.6(b). The problem cause by the correlations is apparent: the speckle has been well reconstructed!

Figure 6.6(a) Figure 6.6(b)

Figure 6.6(c) Figure 6.6(d)

Figure 6.6 (a) A detail from the original image shown in Figure 6.7 (b) The image despeckled using despeckle (c) The residual speckle (d) The expected residual speckle

If we take the ratio of the original intensity to the despeckled version, the result should have the properties of random speckle with the expected correlation properties and relative variance. In Figure 6.6(c) we show this residual speckle, derived from Figures 6.6(a) and (b). Figure 6.6(d) comprises a simulated speckle image having approximately the correct correlation properties. It is clear that 6.6(c) fails to show the expected speckle correlation properties, a consequence of the despeckling algorithm tending to reconstruct the individual speckle blobs. This is further borne out by the relative variance of Figure 6.6(c), which is 37.9, compared with the ENL of 4.0.

Resampling to remove speckle correlations

Since the original sampling was at approximately one third of the instrument resolution we would expect following the previous study that speckle correlations could be removed by averaging and shrinking the intensity data by a factor of 3 in each direction. When the averaging and resampling by 3x3 is applied to the original image, the image shown in Figure 6.6.1(a) is obtained, while Figure 6.6.1(b) shows the corresponding despeckled reconstruction. It is obvious that this contains large uniform regions, as one would expect and is in stark contrast to the original version in Figure 6.6(b). There are no speckle blob sized segments in Figure 6.6.1(b), which should be compared with the very large number visible in 6.6(b). Figure 6.6.1(c) shows the ratio of the original intensity to the reconstructed cross-section after resampling. This has the expected scale of correlations in the speckle blobs, similar to those in Figure 6.6(d) and completely different from the ratio image obtained from the original data, shown in Figure 6.6(c) and repeated here for comparison in Figure 6.6.1(d). Finally, the ENL derived from the ratio image is 4.03, consistent with the defined value. This indicates that the despeckling derived in this way can be trusted.

Figure 6.6.1(a) Figure 6.6.1(b)

Figure 6.6.1(c) Figure 6.6.1(d)

Figure 6.6.1 Segmentation of the resampled original image from Figure 6.6. (a) Image resampled by 3x3; (b) segmentation of (a); (c) ratio of (a) to (b); (d) corresponding ratio for original data (from Figure 6.6(c)).

Conclusions

This study has demonstrated the following aspects of applying despeckling to correlated data:

• If despeckling is applied directly to SAR intensity images that have been sampled at spacing less than the speckle correlation width, which is determined by the resolution of the system, the speckle blobs are faithfully reconstructed, rather than averaged out.
• The ratio of the original intensity to the despeckled version does not correspond to the expected speckle both in apparent ENL and the speckle correlation properties. Only weak residual correlations on a scale of one pixel remain
• The effects of correlated speckle can be removed by averaging the intensity over an area consistent with the speckle correlation lengths and then subsampling at this spacing, to remove sampling correlations.
• The correlation lengths can be obtained directly from the quoted instrumental resolution and sample spacing. Alternatively it can be derived from the ACF of either the complex (SLC) or intensity images.
• This technique offers the means to despeckle intensity data with any speckle correlation properties in an optimum fashion; optimising both the retention of information by speckle reduction through averaging the intensity and correlation removal by resampling.