Ali Khazaal - igarss2011.pdf

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  • 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 SalinityAli 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 RegularizationAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 4. Image Reconstruction  Band Limited Regularization (BLR) Ak Al dklAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 5. Image Reconstruction  Band Limited Regularization (BLR) uklAli 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 HAli 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 problemAli 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 visibilityAli 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) ≈ 10Ali 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 conditionedAli 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 : holeAli 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 holeAli 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 conditionedAli 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): TrAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 24. Correlator Failure  Results: • BLR reconstruction with 1 missing measurement: Tr’ • ΔTr = Tr’ - TrAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 25. Correlator Failure  Results: • BLR reconstruction with 1 missing measurement: Tr’ • ΔTr = Tr’ - TrAli 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 conditionedAli 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 ZerosAli 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 ZerosAli 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 0Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 32. Receiver Failure  Results: • BLR reconstruction with 68 missing measurement: Tr’ • ΔTr = Tr’ - TrAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 33. Receiver Failure  Results: • BLR reconstruction with 68 missing measurement: Tr’ • ΔTr = Tr’ - TrAli 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 edgeAli 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 effectAli Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
  • 38. Thank you very much Ali Khazâal