Speckle & coherence
Speckle is multiplicative noise that arises when the reflected waves of dozens to hundreds of scatterers inside one SAR pixel (resolution cell) interfere with each other, making even uniform ground look like a salt-and-pepper texture of bright and dark points. Coherence measures, on a 0–1 scale, how well two SAR images preserved the same scattering characteristics; it cannot be computed from a single pixel due to insufficient statistics, so it is estimated over a surrounding window (e.g. 5×5), which is why it is called 'Coherence Estimation'. Multilooking (e.g. 3×1 to 9×3) adds more pixels to stabilize and raise coherence, but it trades off against resolution, so it is not free. The SNAP coherence map is not a displacement map but a reliability map, so when SBAS or SNAPHU results look wrong, the coherence map is the very first thing to check.
Speckle — SAR's intrinsic multiplicative noise
- SAR is an active sensor that emits radio waves and receives their echoes, so the reflected waves of dozens to hundreds of scatterers (rock, soil, leaves, grass) inside one resolution cell are vector-summed into a single pixel value.
- When phases align they constructively interfere and appear bright, when opposite they destructively interfere and appear dark, so even uniform reflectivity can show up in the SLC as speckle.
- Unlike additive noise it is multiplicative, scaling with signal strength, so it is reduced with multilooking or a Goldstein filter.
- In InSAR it is hard to tell whether a Master/Slave pixel-value difference is real change or speckle, so when an interferogram looks noisy it is usually speckle.
Coherence — similarity of two images (0–1) and estimation
- Coherence expresses how well two acquisitions (Master/Slave) preserved the same scattering characteristics for a region: identical is 1.0, slightly different is 0.5, completely different is 0.0.
- In the defining formula the numerator captures how similar the two images are and the denominator handles normalization, so the value falls between 0 and 1.
- The key point is that a single pixel lacks the statistics to compute coherence, so it is averaged over a surrounding window (e.g. 5×5 = 25 pixels) to be estimated — hence 'Coherence Estimation'.
- coherence value (0–1)
- complex pixel values of the Master and Slave SLC
- average over the window (the statistics needed)
Why multilooking raises coherence
- Because the estimate depends on the number of pixels in the window, gathering more pixels via multilooking stabilizes the estimate and raises coherence.
- For forest coherence as an example, 3×1 has few pixels so the estimate is unstable at ~0.2, while 9×3 has many pixels so the estimate is stable at ~0.45.
- This is the first principle behind backing off 3×1 to 9×3 in r6 10m to recover unwrapping, but it trades off against resolution and so is not free.
| 3×1 | 9×3 | |
|---|---|---|
| pixel count | few | many |
| estimate | unstable | stable |
| forest coherence example | ~0.2 | ~0.45 |
Reading the coherence map — reliability, not displacement
- The map seen daily in SNAP is not a displacement map but a reliability map: white (0.8–1.0) is trustworthy, gray (0.4–0.7) is ambiguous, black (0–0.3) is almost untrustworthy.
- In practice a coh > 0.3 or > 0.4 mask is typically used.
- The processing order Interferogram → Coherence → Goldstein → SNAPHU exists because SNAPHU uses coherence to decide which phases to trust and which to discard, so when SBAS results look wrong you should check the input coherence map first, not SNAPHU.
Do not mistake the coherence map for a displacement map — white means 'high reliability', not 'large displacement'. Also, higher multilook raises coherence but lowers resolution, so it is not free; when urban high resolution is needed, switching tools from multilooking to PSI is the right answer. Meanwhile, since coherence itself arises from the correlation of speckle between the two images, speckle is two-sided: it is noise yet also the source of the signal.