1. SMOS IMAGE RECONSTRUCTION WITH MISSING DATA:
IMPACT OF CORRELATORS AND RECEIVERS FAILURES
Ali Khazâal(1), Eric Anterrieu(2) & François Cabot(1)
(1)CESBIO - Université de Toulouse, CNRS, CNES & IRD – Toulouse, France
(2)IRAP - Université de Toulouse & CNRS Toulouse, France

2. Introduction
 SMOS: launched at November 2nd, 2009
 Objectives: global maps of Soil Moisture (50 km resolution) and
Sea Surface Salinity (200 km resolution)
 Instrument:
• 2D L-band interferometer (MIRAS)
• Y-shaped array
• 69 equally spaced antennas
 Measurement:
1) Complex visibilities: cross-correlating the signals collected
by each pair of antennas
2) Retrieve the radiometric temperature distribution
3) Retrieve Soil Moisture and Sea Surface Salinity
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

3. Image Reconstruction
 Instrument modeling:
 nv = 4695 measurements
 n2= 1282 pixels
nv < n2 : ill-posed inverse problem Regularization
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

4. Image Reconstruction
 Band Limited Regularization (BLR)
Ak Al
dkl
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

5. Image Reconstruction
 Band Limited Regularization (BLR)
ukl
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

6. Image Reconstruction
 Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

7. Image Reconstruction
 Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

8. Image Reconstruction
 Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

9. Image Reconstruction
 Band Limited Regularization (BLR)
Star shaped frequency coverage H
MIRAS is a band limited instrument inside H
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

10. Image Reconstruction
 Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

11. Image Reconstruction
 Band Limited Regularization (BLR)
Redundancy: nv > nf (number of spatial frequencies)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

12. Image Reconstruction
 Band Limited Regularization (BLR)
• idea: reconstruct in Fourier domain
• minimize a constrained optimization problem
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

13. Correlator / Receiver Failures
 2 kinds of sub-system failures:
1) correlator: 1 missing visibilities
2) receiver: na -1= 68 missing visibilities
receiver 68 visibilities
correlator
1 visibility
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

14. Correlator Failure
 nv correlator & nf frequency: nf < nv (redundancy)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

15. Correlator Failure
 Objective: retrieve T with 1 missing visibilities
 Condition number of J vs redundancy
Row of J associated to the missing visibilities is suppressed
 cond(Jnom) ≈ 10
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

16. Correlator Failure
 Band Limited Regularization:
• Redundant correlator:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

17. Correlator Failure
 Band Limited Regularization:
• Redundant correlator:
 Matrix J is well conditioned
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

18. Correlator Failure
 Band Limited Regularization:
• Non redundant correlator:
 1st approach:
 Missing data associated to a non redundant frequency
 Information associated to this frequency is lost : hole
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

19. Correlator Failure
 Band Limited Regularization:
• Non redundant correlator:
 1st approach:
 Matrix J is ill conditioned
 Pseudo-inversion of J performs a spectral interpolation of each hole
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

20. Correlator Failure
 Band Limited Regularization:
• Non redundant correlator:
 2nd approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

21. Correlator Failure
 Band Limited Regularization:
• Non redundant correlator:
 2nd approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

22. Correlator Failure
 Band Limited Regularization:
• Non redundant correlator:
 2nd approach:
0
 Matrix J is well conditioned
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

23. Correlator Failure
 Results:
• Data: SM_OPER_MIR_SC_F1A_20101201T102808_20101201T112207_346_001_1
• Snapshot Identifier: 56745280
• Location: coast of Argentina
• BLR reconstruction using all available data (nominal solution): Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

24. Correlator Failure
 Results:
• BLR reconstruction with 1 missing measurement: Tr’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

25. Correlator Failure
 Results:
• BLR reconstruction with 1 missing measurement: Tr’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

26. Correlator Failure
 Results:
• BLR reconstruction with 1 missing measurement: Tr’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

27. Correlator Failure
 Results:
• BLR reconstruction with 1 missing measurement: Tr’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

28. Receiver Failure
 Objective: retrieve T with 68 missing visibilities
• Up to 22 non redundant frequencies might be missing
• Matrix J is almost always ill conditioned
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

29. Receiver Failure
 Band Limited Regularization:
• 1st approach: suppression of Rows of J
• 2nd approach:
 suppression of Rows of J
 Columns of J associated to the holes are suppressed
 the missing Fourier components are set to Zeros
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

30. Receiver Failure
 Band Limited Regularization:
• 1st approach: suppression of Rows of J
• 2nd approach:
 suppression of Rows of J
 Columns of J associated to the holes are suppressed
 the missing Fourier components are set to Zeros
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

31. Receiver Failure
 Band Limited Regularization:
• 1st approach: suppression of Rows of J
• 2nd approach:
 suppression of Rows of J
 Columns of J associated to the holes are suppressed
 the missing Fourier components are set to Zeros
0
0
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

32. Receiver Failure
 Results:
• BLR reconstruction with 68 missing measurement: Tr’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

33. Receiver Failure
 Results:
• BLR reconstruction with 68 missing measurement: Tr’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

34. Receiver Failure
 Results:
• BLR reconstruction with 68 missing measurement: Tr’
• ΔTr = Tr’ - Tr
Close to Hub
Close to edge
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

35. Receiver Failure
 Results:
• BLR reconstruction with 68 missing measurement: Tr’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

36. Receiver Failure
 Results:
• BLR reconstruction with 68 missing measurement: Tr’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

37. Conclusions
 This work concern SMOS brightness temperature maps retrieval
 Effect of 2 sub-systems failures on the reconstruction are studied:
• Correlator failure
• Receiver failure
 Correlator failure
• Almost no effects for redundant frequencies
• Major effects for non redundant frequencies and especially for low
frequencies
 Receiver failure:
• Missing data is associated to many non redundant frequencies
• Quality of the retrieval depends on the nature of the lost frequencies
 High frequencies: minor effect
 Low frequencies: major effect
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011

38. Thank you very much
Ali Khazâal