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