1. Persistent Scatterers in InSAR
Audrey Seybert
December 2, 2015

2. Outline InSAR Large Baseline Problem Formulation
Persistent Scatterer (PS) Identification
Project Summary

3. The Point
Even if the constraints on the temporal or spatial baseline between two SAR images have been violated, InSAR processing can still be applied, albeit to a limited number of pixels that meet certain criteria.
Applications where persistent scatterers are of use:
Overcoming temporal or spatial decorrelation
Active research areas related to persistent scatterers:
Automatic Target Recognition
Reduced latency in scene analysis / disaster response
(areas where PS have already been mapped and characterized)

4. InSAR Problem Formulation
Interferometric Phase change between two observations for a single pixel:
∅ 𝑘 𝐱 = ∅ 𝑟𝑘 𝐱 + ∅ 𝜇𝑘 𝐱 + ∅ 𝑎𝑘 𝐱 + ∅ 𝜎𝑘 𝐱 (4)
∅ 𝑟𝑘 𝐱 Phase due to different satellite observation ranges
∅ 𝜇𝑘 𝐱 Phase change due to target motion in Line of Site (LOS)
∅ 𝑎𝑘 𝐱 Atmospheric phase contributions
∅ 𝜎𝑘 𝐱 Change in scatterer reflectivity phase
[Ferretti00]

5. Baseline Decorrelation
Spatial Correlation and Critical baseline (where 𝜌=0)
𝜌 𝑠𝑝𝑎𝑡𝑖𝑎𝑙 =1− 2|𝐵|∆𝑟 𝑐𝑜𝑠 2 𝜃 λ𝑅 (17) (𝜃 : average look angle between two antennas)
𝐵 𝐶 = λ𝑅 2∆𝑟 𝑐𝑜𝑠 2 𝜃 (18)
Rotational Decorrelation
𝜌 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 =1− 2𝑠𝑖𝑛𝜃|𝑑∅|∆𝑟 λ (21) (∅ : aspect angle)
Temporal Decorrelation
𝜌 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑙 =exp⁡ −0.5 4𝜋 λ 𝜎 𝑦 2 𝑠𝑖𝑛 2 𝜃+ 𝜎 𝑧 2 𝑐𝑜𝑠 2 𝜃 (24)
( 𝜎 𝑦 2 and 𝜎 𝑧 2 are vegetation fluctuations in y and z direction)
[Zebker92]

6. PSInSAR Problem Formulation
𝐇 persistent scatterer candidate (PSC) pixels are identified from 𝐊+𝟏 SAR images.
A [K x H] matrix of interferometric phases is found ( 𝚽 𝑖𝑗 = ∅ 𝑘𝑖𝑗 𝐱 ):
𝚽=𝐚 𝟏 𝑇 + 𝐩 ξ 𝛏 𝑇 + 𝐩 η 𝛈 𝑇 +𝐁 𝐪 𝑇 +𝐓 𝐯 𝑇 +𝐄 (9)
𝐚 : constant phase values [K x 1]
𝐩 ξ 𝛏 𝑇 + 𝐩 η 𝛈 𝑇 : contributions from APS and satellite orbit errors
(𝛏 - azimuth 𝛈 - slant range) [H x 1], 𝐩 [K x 1]
𝐁 : normal baseline values (may be a constant) [K x 1]
𝐪 : elevation of each PS times 4𝜋 λ𝑅𝑠𝑖𝑛(𝛼) [H x 1]
𝐓 : time interval between each image and the master image [K x 1]
𝐯 : slant range PS velocities [H x 1]
𝐄 : atmospheric residues, phase noise due to temp / spatial decorrelation, non uniform pixel motion effects [K x H]
Errors because linear models for APS and pixel velocity are incorrect
Measured or known
[Ferretti00]

7. Choosing PSC
PS that are smaller than a resolution cell show best performance for extending spatial baselines.
PS should ideally have constant velocity over series of SAR images.
PSC selection algorithms work best if starting with relatively short baselines and working up to include larger baseline SAR images.
[Ferretti00]

8. Choosing PSC Option 1: Correlation thresholding
If pixel consistently exhibits coherence above a certain amount, classify as a PSC
Problem: Coherence may be underestimated due to baseline dispersion & reference Digital Elevation Map (DEM) inaccuracy
(remember: the errors on the previous slide haven’t been removed)
Option 2: Time series amplitude analysis of each pixel (absolute value is less sensitive to phase errors on previous slide)
If a pixel has a consistent amplitude in SAR images with large temporal & geometric baselines, classify as a PSC
Dispersion analysis on amplitude
PSC pixel scattering characterized by Rician distribution
[Ferretti00]

9. Interferogram Improvement
After PSC identification, “rephase” the K images so they appear to have been collected from the same geometry as the master SAR image. (Zero Baseline Steering)
Requires
1) estimation of error in satellite orbit ( 𝒑 𝜉 and 𝒑 𝜂 )
2) topography information from DEM (~10 m accuracy) (error in 𝒒)
Estimate Atmospheric Phase Screen (APS) at PSC pixels and interpolate over the scene. Remove calculated APS. ( 𝒑 𝜉 , 𝒑 𝜂 , and 𝐄)
Identify new PSC by including phase stability analysis
Estimate 𝐯 (LOS velocity) and Δ𝐪 (elevation error in DEM) via maximum likelihood estimation where phase coherence is maximized
[Ferretti00]

10. Adding Distributed Scatterers
In non-urban (heavily vegetated) environments, PS that are robust to temporal decorrelation are rare.
Regions of statistically homogenous pixels (SHP) can be identified and processed as a distributed scatterer to achieve a similar effect.
Candidate distributed scatterers include deserts and low vegetation terrain (not including farmland)
Process:
Rephase SAR images to master image
Identify any PS with time amplitude series
Remove effects
Apply adaptive spatial filter over homogeneous regions
[Ferretti11]

11. Project Plan
Persistent Scatterer Simulation with the goal of replicating results in [Ferretti00] and [Zebker92].
Initial simulation
Small simulation size (10x10 pixels with ~ 5-10 PSC pixels)
Perfectly flat ground
No APS or orbital errors
Constant velocity of PS in scene.
Exceed critical spatial baseline
Exceed critical rotational baseline
Vary SCR, non constant velocity, add APS, add terrain.
Possibly leverage ESA SNAP software – it’s cool check it out.

12. References
A. FERRETTI, C. PRATI AND F. ROCCA, “Permanent Scatterers in SAR Interferometry”, IEEE TGARS 1999, June 2000.
A. FERRETTI et al., “A new algorithm for processing interferometric datastacks: SqueeSAR,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 9, pp. 3460–3470, Sep
ESA SNAP Toolbox:
H. A. ZEBKER AND J. VILLASENOR, “Decorrelation in interferometric radar echoes”, IEEE Trans. Geosci. Remote Sensing, Vol. 30, No. 5, pp , 1992.
InSAR Principles: Guidelines for Interferometry Processing and Interpretation. European Space Agency. TM- 19, Part A Retrieved From:
InSAR Principles: A Practical Approach. European Space Agency. TM- 19, Part B Retrieved From:
InSAR Principles: A Mathematical Approach. European Space Agency. TM- 19, Part C Retrieved From: