SNR and Noise Variance Estimation in Polarimetric SAR Data

Thermal noise affects polarimetric measurements; but a first order noise correction can be applied if the noise variance (or power) is known. This letter deals with the estimation of the noise variance and the signal-to-noise ratio (SNR) of the cross-polarized channels in polarimetric synthetic aperture radar (SAR) data. Cramér-Rao lower bounds (CRLB) and maximum likelihood (ML) estimators are derived. The ML noise variance estimator is unbiased and efficient, while the ML SNR estimator is biased, but an unbiased SNR estimator can be derived from the biased one. It is also shown that commonly used noise variance and SNR estimators are biased. The results are finally validated using TerraSAR-X fully polarimetric data.

[1]  Irena Hajnsek,et al.  Polarimetric Decomposition Over Glacier Ice Using Long-Wavelength Airborne PolSAR , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[2]  R. Bamler,et al.  Synthetic aperture radar interferometry , 1998 .

[3]  Masanobu Shimada,et al.  The PALSAR Polarimetric Mode for Sea Oil Slick Observation , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[4]  Irena Hajnsek,et al.  Inversion of surface parameters from polarimetric SAR , 2003, IEEE Trans. Geosci. Remote. Sens..

[5]  Jean-Yves Chouinard,et al.  Eigendecomposition of the multi-channel covariance matrix with applications to SAR-GMTI , 2004, Signal Process..

[6]  S. Quegan,et al.  Understanding Synthetic Aperture Radar Images , 1998 .

[7]  S. E. Ahmed,et al.  Handbook of Statistical Distributions with Applications , 2007, Technometrics.

[8]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[9]  Irena Hajnsek,et al.  Removal of additive noise in polarimetric eigenvalue processing , 2001, IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No.01CH37217).

[10]  Harry Denman.  The Inverse of a Matrix , 1969 .

[11]  Anthony Freeman.  The effects of noise on polarimetric SAR data , 1993, Proceedings of IGARSS '93 - IEEE International Geoscience and Remote Sensing Symposium.

[12]  E. Pottier,et al.  Polarimetric Radar Imaging: From Basics to Applications , 2009 .

[13]  Juan M. Lopez-Sanchez,et al.  Rice Phenology Monitoring by Means of SAR Polarimetry at X-Band , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[14]  J. Silvester.  Determinants of block matrices , 2000, The Mathematical Gazette.