Ali Khazaal - igarss2011.pdf
Transcript of Ali Khazaal - igarss2011.pdf
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
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 antennas2) Retrieve the radiometric temperature distribution3) Retrieve Soil Moisture and Sea Surface Salinity
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
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
Band Limited Regularization (BLR)
Image Reconstruction
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
dkl
Ak Al
Band Limited Regularization (BLR)
Image Reconstruction
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
ukl
Band Limited Regularization (BLR)
Image Reconstruction
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Image Reconstruction
Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Image Reconstruction
Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Image Reconstruction
Band Limited Regularization (BLR)
Star shaped frequency coverage HMIRAS is a band limited instrument inside H
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Image Reconstruction
Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Redundancy: nv > nf (number of spatial frequencies)
Image Reconstruction
Band Limited Regularization (BLR)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Band Limited Regularization (BLR)
• idea: reconstruct in Fourier domain• minimize a constrained optimization problem
Image Reconstruction
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
2 kinds of sub-system failures:1) correlator: 1 missing visibilities2) receiver: na -1= 68 missing visibilities
Correlator / Receiver Failures
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
correlator
1 visibility
68 visibilitiesreceiver
Correlator Failure
nv correlator & nf frequency: nf < nv (redundancy)
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Objective: retrieve T with 1 missing visibilities
Correlator Failure
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Condition number of J vs redundancy
Row of J associated to the missing visibilities is suppressed
cond(Jnom) ≈ 10
Correlator Failure
Band Limited Regularization:
• Redundant correlator:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
Band Limited Regularization:
• Redundant correlator:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Matrix J is well conditioned
Correlator Failure
Band Limited Regularization:
• Non redundant correlator: 1st approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Missing data associated to a non redundant frequency Information associated to this frequency is lost : hole
Correlator Failure
Band Limited Regularization:
• Non redundant correlator: 1st approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Matrix J is ill conditioned Pseudo-inversion of J performs a spectral interpolation of each hole
Correlator Failure
Band Limited Regularization:
• Non redundant correlator: 2nd approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
Band Limited Regularization:
• Non redundant correlator: 2nd approach:
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
0
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Matrix J is well conditioned
Band Limited Regularization:
• Non redundant correlator: 2nd approach:
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
Correlator Failure
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Results: • BLR reconstruction with 1 missing measurement: Tr
’
• ΔTr = Tr’ - Tr
Correlator Failure
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
Results: • BLR reconstruction with 1 missing measurement: Tr
’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
Results: • BLR reconstruction with 1 missing measurement: Tr
’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Correlator Failure
Results: • BLR reconstruction with 1 missing measurement: Tr
’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Objective: retrieve T with 68 missing visibilities• Up to 22 non redundant frequencies might be missing
• Matrix J is almost always ill conditioned
Receiver Failure
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Receiver Failure
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
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
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
Receiver Failure
0
0
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
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
Receiver Failure
Results: • BLR reconstruction with 68 missing measurement: Tr
’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Receiver Failure
Results: • BLR reconstruction with 68 missing measurement: Tr
’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Receiver Failure
Results: • BLR reconstruction with 68 missing measurement: Tr
’
• ΔTr = Tr’ - Tr
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Close to Hub
Close to edge
Receiver Failure
Results: • BLR reconstruction with 68 missing measurement: Tr
’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
Receiver Failure
Results: • BLR reconstruction with 68 missing measurement: Tr
’
Ali Khazâal – IGARSS 2011 – Vancouver, Canada July 29, 2011
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
Thank you very much
Ali Khazâal