Analysis of Compact Polarimetric SAR Imaging Modes

Size: px
Start display at page:

Download "Analysis of Compact Polarimetric SAR Imaging Modes"

Transcription

1 Analysis of Compact Polarimetric AR Imaging Modes T. L. Ainsworth 1, M. Preiss, N. tacy, M. Nord 1,3 & J.-. Lee 1,4 1 Naval Research Lab., Washington, DC 0375 UA Defence cience and Technology Organisation, Edinburgh, A 5111 Australia 3 Applied Physics Lab., Johns Hopkins Univ., Laurel, MD 073 UA 4 Center for pace and Remote ensing Research, Central National Univ., Taiwan

2 Compact Polarimetry Enhancing Dual-Pol Imagery Dual-Pol AR Imagery e.g. π/4 Transmit with (H, V) Receive Polarimetric cattering Model Pseudo Quad-Pol Data 1) tandard Quad-Pol Analysis ) Quad-Pol Decomposition 3) Classification, etc.

3 Compact Polarimetry Enhancing Dual-Pol Imagery Dual-Pol AR Imagery e.g. π/4 Transmit with (H, V) Receive Polarimetric cattering Model Pseudo Quad-Pol Data 1) tandard Quad-Pol Analysis ) Quad-Pol Decomposition 3) Classification, etc. Two Questions: 1) How appropriate is the scattering model? ) What type of dual-pol imagery provides the best input to the scattering model?

4 Compact Polarimetric Modes / Models Dual-Pol Data Collection Modes tandard Linear Modes: Transmit H (or V) with H & V Receive Not Appropriate for Compact Polarimetry π/4 Mode: Linear Transmit with H & V Linear Receive Circular Transmit Modes: Circular Transmit with Left & Right Circular Receive Circular Transmit with H & V Linear Receive Model imple Natural catterers Reflection ymmetry Assumption Random Volume cattering Model Double-Bounce Correction to Random Volume Model

5 Compact Polarimetric Modes Dual-Pol cattering Vectors: r T kh = [ HH HV ] r kπ / 4 = HH + HV VV + r T kdc = [ RR RL] r k = + i i + CTLR [ ] T [ ] HH HV π/4 Mode Covariance Matrix [ C ] = [ k ] [ k ] π / 4 π 4 π 4 + = 1 1 VV HH R HH HH VV ( ) HV HH + VV HV HH VV HV HV VV HV T + HH 1 R HV HV HV + VV HV HV ( ) VV HV HV

6 Reflection ymmetry Assumption Too Many Variables (9), Not Enough Equations (4) Assume Reflection ymmetry HH HV = VV HV = 0 Define a Relationship Between HV and ρ ρ = HH HH VV VV HV + VV ( 1 ρ ) True for a Randomly Oriented Cloud of Dipoles (Volume cattering), but HH = 4

7 DLR E-AR Imagery Quad-Pol Data to imulate Compact Polarimetric Modes Pauli Display Red: HH-VV Green: HV Blue: HH+VV L-band Imagery of Oberpfaffenhafen

8 Test of HV vs. ρ Relationship A catter Plot of vs. HH HV + VV 1 4 ( 1 ρ ) hows a Possible Problem. ( 1 ρ ) 4 (All points should lie on the diagonal line.) HV HH + VV

9 Double-Bounce Correction A Useful Mathematical Inequality: ( ) ( ) ρ + 1 HH VV HH VV Rewriting Yields ( ) + HH HV VV ( 1 ρ ) HH HV VV HH - VV / HV is the Double-Bounce Correction First Estimate the HH - VV / HV Ratio Then Apply this New Relationship

10 Use the Original Compact Polarimetry Model to Estimate the HH - VV / HV Ratio. Model Improvement Use this Estimate to Determine the Ratio of HH HV + VV HH VV To ( 1 ρ ) And olve for the Pseudo Quad-Pol Data ( 1 ρ )( HH + VV )

11 π/4 Mode vs. Quad-Pol

12 π/4 Mode vs. Quad-Pol

13 CTLR Mode vs. Quad-Pol

14 CTLR Mode vs. Quad-Pol

15 Pseudo Quad-Pol Comparison Original Quad-Pol Imagery Red: HH-VV Green: HV Blue: HH+VV π/4 Mode Compact Polarimetric Imagery Dual-Circ Compact Polarimetric Imagery Circ X-mit / Linear Rec. Compact Polarimetric Imagery

16 Graphic Dual-Pol Analysis Dual-Pol Receives Two Orthogonal Polarizations Can ynthesize Any Receive Polarization, in Principle Ellipticity and Orientation Fully Characterize the Polarization of the Received ignal Dual-Pol Decompositions Entropy is Entropy, but Alpha Angle No Longer Just a cattering Mechanism b a tan χ = b a

17 Linear Dual-Pol ignatures Linear Horizontal Transmit Polarization Dihedral Response urface Response

18 π/4 Dual-Pol ignatures Linear π/4 Transmit Polarization Dihedral Response urface Response

19 Dual-Pol Circular ignatures Right-hand Circular Transmit Polarization Dihedral Response urface Response

20 Dual-Pol Vegetation ignatures H Transmit Looks like the Dihedral and urface Plots! π/4 Transmit Looks like the urface Plot.

21 Dual-Pol Vegetation ignatures H Transmit Looks like the Dihedral and urface Plots! Right-hand π/4 Transmit Circular Looks This like one the is urface Different. Plot.

22 Circular-Transmit, Dual-Pol Conclusions Circular Dual-Pol eparates catterers Dihedrals, Rough urfaces, Dipoles, Vegetation ignature Plots Differ for These catterers Circular Does Not Detect Target Orientation Except for ingle Dipole catterers Extracting Terrain lopes May be Difficult Without an Orientation Angle Response

23 Example of Dual-Pol Imagery PIAR X-band Imagery, Tsukuba, Japan Quad-Pol Imagery Pauli Basis Display Dual-Pol Display

24 Example of Dual-Pol Imagery PIAR X-band Imagery, Tsukuba, Japan Quad-Pol Imagery Pauli Basis Display Dual-Pol Display

25 Ingara Quad-Pol X-Band Dataset Quad-Pol tandard Display: Hue: α-angle at.: Entropy Value: pan

26 (HH, HV) Dual-Pol Imagery Dual-Pol Display: Red: HH Green: HV Blue: HH HV

27 Rotated Dihedral catterer Linear Horizontal Transmit Polarization Unrotated Dihedral 30º Rotated Dihedral

28 Rotated Dipole catterer Linear Horizontal Transmit Polarization Unrotated Rotated 30º

29 Rotated urface catterer Linear Horizontal Transmit Polarization Unrotated urface 30º Rotated urface

30 H Transmit, Dual-Pol Information Linear Dual-Pol Can Distinguish Between Rotated Dihedrals (or Dipoles) Rough urfaces (Trihedrals) Randomly Oriented Dipole Distributions Typical Vegetation Models Linear Dual-Pol Cannot Distinguish Between Dihedrals and Dipoles, Either Rotated or Not Unrotated Dihedrals (or Dipoles) and Any Rough urface

31 Linear Dual-Pol Decomposition Eigen Decomposition of the x Covariance Matrix C C HH, HH HV, HH C C HH, HV HV, HV cosα1 = sinα1 e α λ1 Define Angle and Entropy as α = λ α + ιϕ = cosα sinα e ιϕ cosα1 λ cosα ( π ) 1 1 λα λ1α 1 λ α1 + sinα e 1 sinα e ιϕ ιϕ ( λ lnλ + λ ln ) ln Entropy = 1 1 λ with ( ) λ i = λ i λ 1 + λ

32 H Transmit, Dual-Pol Entropy-Alpha Plot Allowed Dual-Pol α / Entropy Region Blue: urface cattering Green: Vegetation Random Dipole Distribution Cyan: Vegetation urface Mix Red: ingle Dipoles or Double Bounce Magenta: Dihedral urface Mix Yellow: Dihedral Vegetation Mix White: High Entropy Low Polarimetric Content Orange: Rotated Dihedral / Dipole Mix, HV > HH with HH HV ~ 0

33 Linear Dual-Pol Decomposition (HH, HV) Dual-Pol Imagery Hue: α-angle at.: Entropy Value: pan

34 ummary Compact Polarimetry Results Depend Upon: The Reflection ymmetry Assumption An Appropriate cattering Model Matched to the Transmitted Polarization The Double-Bounce Correction Appears to Give Fairly Good, Robust Results Dual-Pol ignature Plots: Complete Polarimetric Description of Dual-Pol Imagery Provides a imple, Visual Analysis Technique Dual-Pol Decompositions: Alpha Angle Not Just the cattering Mechanism Any More Interpretation of Dual-Pol Alpha-Entropy Plots Depends Upon the Transmitted Polarization

35

36 Dual-Circular Mode vs. Quad-Pol

37 Dual-Circular Mode vs. Quad-Pol

38 Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.

39 Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.

40 Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.

41 Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.

42 Quad-Pol Entropy / Alpha pace Low Medium High MULTIPLE CATTERING VOLUME CATTERING URFACE CATTERING

43 Linear Dual-Pol Decomposition (VV, VH) Dual-Pol Imagery Hue: α-angle at.: Entropy Value: pan

44 Linear Dual-Pol Decomposition (VV, VH) Dual-Pol Imagery Hue: VV VH at.: Entropy Value: pan

45 Linear Dual-Pol Decomposition (HH, HV) Dual-Pol Imagery Hue: HH HV at.: Entropy Value: pan

Making a case for full-polarimetric radar remote sensing

Making a case for full-polarimetric radar remote sensing Making a case for full-polarimetric radar remote sensing Jeremy Nicoll Alaska Satellite Facility, University of Alaska Fairbanks 1 Polarization States of a Coherent Plane Wave electric field vector vertically

More information

SAN FRANCISCO BAY. L-band 1988 AIRSAR. DC8 P, L, C-Band (Quad) Microwaves and Radar Institute, Wolfgang Keydel

SAN FRANCISCO BAY. L-band 1988 AIRSAR. DC8 P, L, C-Band (Quad) Microwaves and Radar Institute, Wolfgang Keydel SAN FRANCISCO BAY L-band 1988 AIRSAR DC8 P, L, C-Band (Quad) TARGET GENERATORS HH+VV T11=2A0 HV T33=B0-B HH-VV T22=B0+B TARGET GENERATORS Sinclair Color Coding HH HV VV Pauli Color Coding HH+VV T11=2A0

More information

Polarimetric Calibration of the Ingara Bistatic SAR

Polarimetric Calibration of the Ingara Bistatic SAR Polarimetric Calibration of the Ingara Bistatic SAR Alvin Goh, 1,2 Mark Preiss, 1 Nick Stacy, 1 Doug Gray 2 1. Imaging Radar Systems Group Defence Science and Technology Organisation 2. School of Electrical

More information

Evaluation and Bias Removal of Multi-Look Effect on Entropy/Alpha /Anisotropy (H/

Evaluation and Bias Removal of Multi-Look Effect on Entropy/Alpha /Anisotropy (H/ POLINSAR 2009 WORKSHOP 26-29 January 2009 ESA-ESRIN, Frascati (ROME), Italy Evaluation and Bias Removal of Multi-Look Effect on Entropy/Alpha /Anisotropy (H/ (H/α/A) Jong-Sen Lee*, Thomas Ainsworth Naval

More information

EE/Ge 157 b. Week 2. Polarimetric Synthetic Aperture Radar (2)

EE/Ge 157 b. Week 2. Polarimetric Synthetic Aperture Radar (2) EE/Ge 157 b Week 2 Polarimetric Synthetic Aperture Radar (2) COORDINATE SYSTEMS All matrices and vectors shown in this package are measured using the backscatter alignment coordinate system. This system

More information

ABSTRACT. Index terms compact polarimetry, Faraday rotation, bare soil surfaces, soil moisture.

ABSTRACT. Index terms compact polarimetry, Faraday rotation, bare soil surfaces, soil moisture. COPARION BETWEEN THE CONFORITY COEFFICIENT AND PREVIOU CLAIFICATION TECHNIQUE FOR BARE URFACE DICRIINATION AND APPLICATION TO COPACT POLARIETRY ODE y-linh Truong-Loï 13, A. Freeman, P. Dubois-Fernandez

More information

Advanced SAR 2 Polarimetry

Advanced SAR 2 Polarimetry Advanced SAR Polarimetry Eric POTTIER Monday 3 September, Lecture D1Lb5-3/9/7 Lecture D1Lb5- Advanced SAR - Polarimetry Eric POTTIER 1 $y RADAR POLARIMETRY $x r Ezt (, ) $z Radar Polarimetry (Polar : polarisation

More information

Wave Propagation Model for Coherent Scattering from a Randomly Distributed Target

Wave Propagation Model for Coherent Scattering from a Randomly Distributed Target Wave Propagation Model for Coherent Scattering from a Randomly Distributed Target Don Atwood,Ben Matthiss, Liza Jenkins, Shimon Wdowinski, Sang Hoon Hong, and Batuhan Osmanoglu Outline Requirements for

More information

ADVANCED CONCEPTS POLSARPRO V3.0 LECTURE NOTES. Eric POTTIER (1), Jong-Sen LEE (2), Laurent FERRO-FAMIL (1)

ADVANCED CONCEPTS POLSARPRO V3.0 LECTURE NOTES. Eric POTTIER (1), Jong-Sen LEE (2), Laurent FERRO-FAMIL (1) ADVANCED CONCEPTS Eric POTTIER (), Jong-Sen LEE (), Laurent FERRO-FAMIL () () I.E.T.R UMR CNRS 664 University of Rennes Image and Remote Sensing Department, SAPHIR Team Campus de Beaulieu, Bat D, 63 Av

More information

General Four-Component Scattering Power Decomposition with Unitary Transformation of Coherency Matrix

General Four-Component Scattering Power Decomposition with Unitary Transformation of Coherency Matrix 1 General Four-Component Scattering Power Decomposition with Unitary Transformation of Coherency Matrix Gulab Singh, Member, IEEE, Yoshio Yamaguchi, Fellow, IEEE and Sang-Eun Park, Member, IEEE Abstract

More information

Features for Landcover Classification of Fully Polarimetric SAR Data

Features for Landcover Classification of Fully Polarimetric SAR Data Features for Landcover Classification of Fully Polarimetric SAR Data Jorge V. Geaga ABSTRACT We have previously shown that Stokes eigenvectors can be numerically extracted from the Kennaugh(Stokes matrices

More information

Analysis of the Temporal Behavior of Coherent Scatterers (CSs) in ALOS PalSAR Data

Analysis of the Temporal Behavior of Coherent Scatterers (CSs) in ALOS PalSAR Data Analysis of the Temporal Behavior of Coherent Scatterers (CSs) in ALOS PalSAR Data L. Marotti, R. Zandona-Schneider & K.P. Papathanassiou German Aerospace Center (DLR) Microwaves and Radar Institute0 PO.BOX

More information

STUDIES OF OCEAN S SCATTERING PROPERTIES BASED ON AIRSAR DATA

STUDIES OF OCEAN S SCATTERING PROPERTIES BASED ON AIRSAR DATA STUDIES OF OCEAN S SCATTERING PROPERTIES BASED ON AIRSAR DATA Wang Wenguang *, Sun Jinping, Wang Jun, Hu Rui School of EIE, Beihang University, Beijing 00083, China- wwenguang@ee.buaa.edu.cn KEY WORDS:

More information

Detecting an area affected by forest fires using ALOS PALSAR

Detecting an area affected by forest fires using ALOS PALSAR Detecting an area affected by forest fires using ALOS PALSAR Keiko Ishii (1), Masanobu Shimada (2), Osamu Isoguchi (2), Kazuo Isono (1) (1)Remote Sensing Technology Center of Japan (2)Japan Aerospace Exploration

More information

A New Model-Based Scattering Power Decomposition for Polarimetric SAR and Its Application in Analyzing Post-Tsunami Effects

A New Model-Based Scattering Power Decomposition for Polarimetric SAR and Its Application in Analyzing Post-Tsunami Effects A New Model-Based Scattering Power Decomposition for Polarimetric SAR and Its Application in Analyzing Post-Tsunami Effects Yi Cui, Yoshio Yamaguchi Niigata University, Japan Background (1/5) POLSAR data

More information

EVALUATION OF CLASSIFICATION METHODS WITH POLARIMETRIC ALOS/PALSAR DATA

EVALUATION OF CLASSIFICATION METHODS WITH POLARIMETRIC ALOS/PALSAR DATA EVALUATION OF CLASSIFICATION METHODS WITH POLARIMETRIC ALOS/PALSAR DATA Anne LÖNNQVIST a, Yrjö RAUSTE a, Heikki AHOLA a, Matthieu MOLINIER a, and Tuomas HÄME a a VTT Technical Research Centre of Finland,

More information

Archimer

Archimer Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive publisher-authenticated version is available on the publisher Web site Ieee

More information

POLARIMETRIC MODELING OF LUNAR SURFACE FOR SCATTERING INFORMATION RETRIEVAL USING MINI-SAR DATA OF CHANDRAYAAN-1

POLARIMETRIC MODELING OF LUNAR SURFACE FOR SCATTERING INFORMATION RETRIEVAL USING MINI-SAR DATA OF CHANDRAYAAN-1 POLARIMETRIC MODELING OF LUNAR SURFACE FOR SCATTERING INFORMATION RETRIEVAL USING MINI-SAR DATA OF CHANDRAYAAN-1 KAUSIKA BALA BHAVYA March, 2013 SUPERVISORS: Mr. Shashi Kumar Dr. V.A. Tolpekin POLARIMETRIC

More information

POLARIMETRY-BASED LAND COVER CLASSIFICATION WITH SENTINEL-1 DATA

POLARIMETRY-BASED LAND COVER CLASSIFICATION WITH SENTINEL-1 DATA POLARIMETRY-BASED LAND COVER CLASSIFICATION WITH SENTINEL-1 DATA Xavier Banqué (1), Juan M Lopez-Sanchez (2), Daniel Monells (1), David Ballester (2), Javier Duro (1), Fifame Koudogbo (1) (1) Altamira

More information

Study and Applications of POLSAR Data Time-Frequency Correlation Properties

Study and Applications of POLSAR Data Time-Frequency Correlation Properties Study and Applications of POLSAR Data Time-Frequency Correlation Properties L. Ferro-Famil 1, A. Reigber 2 and E. Pottier 1 1 University of Rennes 1, Institute of Electronics and Telecommunications of

More information

POLARIMETRIC SPECKLE FILTERING

POLARIMETRIC SPECKLE FILTERING $y $x r Ezt (, ) $z POLARIMETRIC SPECKLE FILTERING E. Pottier, L. Ferro-Famil (/) SPECKLE FILTERING SPECKLE PHENOMENON E. Pottier, L. Ferro-Famil (/) SPECKLE FILTERING OBSERVATION POINT SURFACE ROUGHNESS

More information

New Simple Decomposition Technique for Polarimetric SAR Images

New Simple Decomposition Technique for Polarimetric SAR Images Korean Journal of Remote Sensing, Vol.26, No.1, 2010, pp.1~7 New Simple Decomposition Technique for Polarimetric SAR Images Kyung-Yup Lee and Yisok Oh Department of Electronic Information and Communication

More information

THE PYLA 2001 EXPERIMENT : EVALUATION OF POLARIMETRIC RADAR CAPABILITIES OVER A FORESTED AREA

THE PYLA 2001 EXPERIMENT : EVALUATION OF POLARIMETRIC RADAR CAPABILITIES OVER A FORESTED AREA THE PYLA 2001 EXPERIMENT : EVALUATION OF POLARIMETRIC RADAR CAPABILITIES OVER A FORESTED AREA M. Dechambre 1, S. Le Hégarat 1, S. Cavelier 1, P. Dreuillet 2, I. Champion 3 1 CETP IPSL (CNRS / Université

More information

CLASSIFICATION, decomposition, and modeling of polarimetric

CLASSIFICATION, decomposition, and modeling of polarimetric IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 3, MAY 1998 963 A Three-Component Scattering Model for Polarimetric SAR Data Anthony Freeman, Senior Member, IEEE, Stephen L. Durden Abstract

More information

Target Detection Studies Using Fully Polarimetric Data Collected by the Lincoln Laboratory MMW SAR. L.M. Novak MIT Lincoln Laboratory

Target Detection Studies Using Fully Polarimetric Data Collected by the Lincoln Laboratory MMW SAR. L.M. Novak MIT Lincoln Laboratory Target Detection Studies Using Fully Polarimetric Data Collected by the Lincoln Laboratory MMW SAR Abstract L.M. Novak MIT Lincoln Laboratory Under DARPA sponsorship, MIT Lincoln Laboratory is investigating

More information

Shashi Kumar. Indian Institute of Remote Sensing. (Indian Space Research Organisation)

Shashi Kumar. Indian Institute of Remote Sensing. (Indian Space Research Organisation) Practical-1 SAR Image Interpretation Shashi Kumar Indian Institute of Remote Sensing (Indian Space Research Organisation) Department of Space, Government of India 04 Kalidas Road, Dehradun - 248 001, U.K.

More information

Model based forest height estimation with ALOS/PalSAR: A first study.

Model based forest height estimation with ALOS/PalSAR: A first study. Model based forest height estimation with ALOS/PalSAR: A first study. K.P. Papathanassiou*, I. Hajnsek*, T.Mette*, S.R. Cloude** and A. Moreira* * (DLR) (DLR-HR) Oberpfaffenhofen, Germany ** AEL Consultants

More information

A Multi-component Decomposition Method for Polarimetric SAR Data

A Multi-component Decomposition Method for Polarimetric SAR Data Chinese Journal of Electronics Vol.26, No.1, Jan. 2017 A Multi-component Decomposition Method for Polarimetric SAR Data WEI Jujie 1, ZHAO Zheng 1, YU Xiaoping 2 and LU Lijun 1 (1. Chinese Academy of Surveying

More information

Shipborne polarimetric weather radar: Impact of ship movement on polarimetric variables

Shipborne polarimetric weather radar: Impact of ship movement on polarimetric variables Shipborne polarimetric weather radar: Impact of ship movement on polarimetric variables M. Thurai 1, P. T. May and A. Protat 1 Colorado State Univ., Fort Collins, CO Center for Australian Weather and Climate

More information

On the use of Matrix Information Geometry for Polarimetric SAR Image Classification

On the use of Matrix Information Geometry for Polarimetric SAR Image Classification On the use of Matrix Information Geometry for Polarimetric SAR Image Classification Pierre Formont 1,2,Jean-PhilippeOvarlez 1,andFrédéric Pascal 2 1 French Aerospace Lab, ONERA DEMR/TSI, France 2 E3S-SONDRA,

More information

Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell

Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell 1. Scattering Introduction - Consider a localized object that contains charges

More information

DUAL-POLARIZED COSMO SKYMED SAR DATA TO OBSERVE METALLIC TARGETS AT SEA

DUAL-POLARIZED COSMO SKYMED SAR DATA TO OBSERVE METALLIC TARGETS AT SEA DUAL-POLARIZED COSMO SKYMED SAR DATA TO OBSERVE METALLIC TARGETS AT SEA F. Nunziata, M. Montuori and M. Migliaccio Università degli Studi di Napoli Parthenope Dipartimento per le Tecnologie Centro Direzionale,

More information

Spectral Clustering of Polarimetric SAR Data With Wishart-Derived Distance Measures

Spectral Clustering of Polarimetric SAR Data With Wishart-Derived Distance Measures Spectral Clustering of Polarimetric SAR Data With Wishart-Derived Distance Measures STIAN NORMANN ANFINSEN ROBERT JENSSEN TORBJØRN ELTOFT COMPUTATIONAL EARTH OBSERVATION AND MACHINE LEARNING LABORATORY

More information

PUBLICATIONS. Radio Science. Impact of cross-polarization isolation on polarimetric target decomposition and target detection

PUBLICATIONS. Radio Science. Impact of cross-polarization isolation on polarimetric target decomposition and target detection PUBLICATIONS RESEARCH ARTICLE Key Points: Prior studies are on calibration; we evaluate its impact from users perspective Impact on polarimetric target decomposition is analyzed, and 25 db is concluded

More information

MARINE AND MARITIME SAR APPLICATIONS: COSMO-SKYMED FROM 1 ST TO 2 ND GENERATION

MARINE AND MARITIME SAR APPLICATIONS: COSMO-SKYMED FROM 1 ST TO 2 ND GENERATION MARINE AND MARITIME SAR APPLICATIONS: COSMO-SKYMED FROM 1 ST TO 2 ND GENERATION Maurizio Migliaccio, Ferdinando Nunziata, Andrea Buono Dipartimento di Ingegneria, Università degli Studi di Napoli Parthenope

More information

THE OBJECTIVE of the incoherent target decomposition

THE OBJECTIVE of the incoherent target decomposition IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 1, JANUARY 2007 73 Target Scattering Decomposition in Terms of Roll-Invariant Target Parameters Ridha Touzi, Member, IEEE Abstract The Kennaugh

More information

Unsupervised Wishart Classifications of Sea-Ice using Entropy, Alpha and Anisotropy decompositions

Unsupervised Wishart Classifications of Sea-Ice using Entropy, Alpha and Anisotropy decompositions Unsupervised Wishart Classifications of Sea-Ice using Entropy, Alpha and Anisotropy decompositions A. Rodrigues (1), D. Corr (1), K. Partington (2), E. Pottier (3), L. Ferro-Famil (3) (1) QinetiQ Ltd,

More information

Airborne Holographic SAR Tomography at L- and P-band

Airborne Holographic SAR Tomography at L- and P-band Airborne Holographic SAR Tomography at L- and P-band O. Ponce, A. Reigber and A. Moreira. Microwaves and Radar Institute (HR), German Aerospace Center (DLR). 1 Outline Introduction to 3-D SAR Holographic

More information

The Importance of Microwave Remote Sensing for Operational Sea Ice Services And Challenges

The Importance of Microwave Remote Sensing for Operational Sea Ice Services And Challenges The Importance of Microwave Remote Sensing for Operational Sea Ice Services And Challenges Wolfgang Dierking January 2015 (1) Why is microwave remote sensing important (=useful) for sea ice mapping? Problems

More information

Polarimetry-based land cover classification with Sentinel-1 data

Polarimetry-based land cover classification with Sentinel-1 data Polarimetry-based land cover classification with Sentinel-1 data Banqué, Xavier (1); Lopez-Sanchez, Juan M (2); Monells, Daniel (1); Ballester, David (2); Duro, Javier (1); Koudogbo, Fifame (1) 1. Altamira-Information

More information

Multitemporal Spaceborne Polarimetric SAR Data for Urban Land Cover Mapping

Multitemporal Spaceborne Polarimetric SAR Data for Urban Land Cover Mapping Multitemporal Spaceborne Polarimetric SAR Data for Urban Land Cover Mapping Xin Niu Feburary 2011 TRITA SoM 2011-05 ISSN 1653-6126 ISRN KTH/SoM/11-05/SE ISBN 978-91-7415-909-7 Xin Niu TRITA SoM 2011-05

More information

LAND COVER CLASSIFICATION OF PALSAR IMAGES BY KNOWLEDGE BASED DECISION TREE CLASSI- FIER AND SUPERVISED CLASSIFIERS BASED ON SAR OBSERVABLES

LAND COVER CLASSIFICATION OF PALSAR IMAGES BY KNOWLEDGE BASED DECISION TREE CLASSI- FIER AND SUPERVISED CLASSIFIERS BASED ON SAR OBSERVABLES Progress In Electromagnetics Research B, Vol. 30, 47 70, 2011 LAND COVER CLASSIFICATION OF PALSAR IMAGES BY KNOWLEDGE BASED DECISION TREE CLASSI- FIER AND SUPERVISED CLASSIFIERS BASED ON SAR OBSERVABLES

More information

Determining the Points of Change in Time Series of Polarimetric SAR Data

Determining the Points of Change in Time Series of Polarimetric SAR Data Downloaded from orbit.dtu.dk on: Jul 4, 28 Determining the Points of Change in Time Series of Polarimetric SAR Data Conradsen, Knut; Nielsen, Allan Aasbjerg; Skriver, Henning Published in: IEEE Transactions

More information

RADAR REMOTE SENSING OF PLANETARY SURFACES

RADAR REMOTE SENSING OF PLANETARY SURFACES RADAR REMOTE SENSING OF PLANETARY SURFACES BRUCE A. CAMPBELL Smithsonian Institution CAMBRIDGE UNIVERSITY PRESS Contents Acknowledgments page ix 1 Introduction 1 1.1 Radar remote sensing 1 1.2 Historical

More information

ASSESSMENT OF L-BAND SAR DATA AT DIFFERENT POLARIZATION COMBINATIONS FOR CROP AND OTHER LANDUSE CLASSIFICATION

ASSESSMENT OF L-BAND SAR DATA AT DIFFERENT POLARIZATION COMBINATIONS FOR CROP AND OTHER LANDUSE CLASSIFICATION Progress In Electromagnetics Research B, Vol. 36, 303 321, 2012 ASSESSMENT OF L-BAND SAR DATA AT DIFFERENT POLARIZATION COMBINATIONS FOR CROP AND OTHER LANDUSE CLASSIFICATION D. Haldar 1, *, A. Das 1,

More information

DUAL FREQUENCY POLARIMETRIC SAR DATA CLASSIFICATION AND ANALYSIS

DUAL FREQUENCY POLARIMETRIC SAR DATA CLASSIFICATION AND ANALYSIS Progress In Electromagnetics Research, PIER 31, 247 272, 2001 DUAL FREQUENCY POLARIMETRIC SAR DATA CLASSIFICATION AND ANALYSIS L. Ferro-Famil Ecole Polytechnique de l Université de Nantes IRESTE, Laboratoire

More information

IEEE Copyright notice.

IEEE Copyright notice. This is a pre print version of the paper. Please cite the final version of the paper: G. Di Martino, A. Iodice, A. Natale and D. Riccio, Polarimetric Two Scale Two omponent Model for the Retrieval of Soil

More information

Decomposition of polarimetric synthetic aperture radar backscatter from upland and ooded forests

Decomposition of polarimetric synthetic aperture radar backscatter from upland and ooded forests int. j. remote sensing, 1997, vol. 18, no. 6, 1319± 1332 Decomposition of polarimetric synthetic aperture radar backscatter from upland and ooded forests Y. WANG Department of Geography, East Carolina

More information

Rice Monitoring using Simulated Compact SAR. Kun Li, Yun Shao Institute of Remote Sensing and Digital Earth

Rice Monitoring using Simulated Compact SAR. Kun Li, Yun Shao Institute of Remote Sensing and Digital Earth Rice Monitoring using Simulated Compact SAR Kun Li, Yun Shao Institute of Remote Sensing and Digital Earth Outlines Introduction Test site and data Results Rice type discrimination Rice phenology retrieval

More information

Fitting a two-component scattering model to polarimetric SAR data from forests

Fitting a two-component scattering model to polarimetric SAR data from forests Fitting a two-component scattering model to polarimetric SAR data from forests A. Freeman, Fellow, IEEE Jet Propulsion Laboratory, California Institute of Technology 4800 Oak Grove Drive, Pasadena, CA

More information

Polarimetric synthetic aperture radar study of the Tsaoling landslide generated by the 1999 Chi-Chi earthquake, Taiwan

Polarimetric synthetic aperture radar study of the Tsaoling landslide generated by the 1999 Chi-Chi earthquake, Taiwan JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. F1, 6006, doi:10.1029/2003jf000037, 2003 Polarimetric synthetic aperture radar study of the Tsaoling landslide generated by the 1999 Chi-Chi earthquake, Taiwan

More information

2986 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 51, NO. 5, MAY 2013

2986 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 51, NO. 5, MAY 2013 986 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 51, NO. 5, MAY 013 A New Polarimetric Change Detector in Radar Imagery Armando Marino, Member, IEEE, Shane R. Cloude, Fellow, IEEE, and Juan

More information

TEXTURE ANALSYS OF SAR IMAGERY IN THE SPACE-SCALE-POLARIZATION DOMAIN BY WAVELET FRAMES

TEXTURE ANALSYS OF SAR IMAGERY IN THE SPACE-SCALE-POLARIZATION DOMAIN BY WAVELET FRAMES TEXTURE ANALSYS OF SAR IMAGERY IN THE SPACE-SCALE-POLARIZATION DOMAIN BY WAVELET FRAMES G. De Grandi 1, J. Kropacek 1, A. Gambardella 2, R.M. Lucas 3, M. Migliaccio 2 Joint Research Centre 21027, Ispra

More information

Soil moisture retrieval over periodic surfaces using PolSAR data

Soil moisture retrieval over periodic surfaces using PolSAR data Soil moisture retrieval over periodic surfaces using PolSAR data Sandrine DANIEL Sophie ALLAIN Laurent FERRO-FAMIL Eric POTTIER IETR Laboratory, UMR CNRS 6164, University of Rennes1, France Contents Soil

More information

MULTI-POLARISATION MEASUREMENTS OF SNOW SIGNATURES WITH AIR- AND SATELLITEBORNE SAR

MULTI-POLARISATION MEASUREMENTS OF SNOW SIGNATURES WITH AIR- AND SATELLITEBORNE SAR EARSeL eproceedings 5, 1/2006 111 MULTI-POLARISATION MEASUREMENTS OF SNOW SIGNATURES WITH AIR- AND SATELLITEBORNE SAR Eirik Malnes 1, Rune Storvold 1, Inge Lauknes 1 and Simone Pettinato 2 1. Norut IT,

More information

A Family of Distribution-Entropy MAP Speckle Filters for Polarimetric SAR Data, and for Single or Multi-Channel Detected and Complex SAR Images

A Family of Distribution-Entropy MAP Speckle Filters for Polarimetric SAR Data, and for Single or Multi-Channel Detected and Complex SAR Images A Family of Distribution-Entropy MAP Specle Filters for Polarimetric SAR Data, and for Single or Multi-Channel Detected and Complex SAR Images Edmond NEZRY and Francis YAKAM-SIMEN PRIVATEERS N.V., Private

More information

Snow property extraction based on polarimetry and differential SAR interferometry

Snow property extraction based on polarimetry and differential SAR interferometry Snow property extraction based on polarimetry and differential SAR interferometry S. Leinß, I. Hajnsek Earth Observation and Remote Sensing, Institute of Enviromental Science, ETH Zürich TerraSAR X and

More information

Snow Microphysical Retrieval Based on Ground Radar Measurements

Snow Microphysical Retrieval Based on Ground Radar Measurements Snow Microphysical Retrieval Based on Ground Radar Measurements V. Chandrasekar Colorado State University June 27, 2007 1 Outline Role of inter comparing ground and space borne radar Class of measurements

More information

Physics 215 Quantum Mechanics 1 Assignment 1

Physics 215 Quantum Mechanics 1 Assignment 1 Physics 5 Quantum Mechanics Assignment Logan A. Morrison January 9, 06 Problem Prove via the dual correspondence definition that the hermitian conjugate of α β is β α. By definition, the hermitian conjugate

More information

Application of Bootstrap Techniques for the Estimation of Target Decomposition Parameters in RADAR Polarimetry

Application of Bootstrap Techniques for the Estimation of Target Decomposition Parameters in RADAR Polarimetry Application of Bootstrap Techniques for the Estimation of Target Decomposition Parameters in RADAR Polarimetry Samuel Foucher Research & Development Dept Computer Research Institute of Montreal Montreal,

More information

A Test Statistic in the Complex Wishart Distribution and Its Application to Change Detection in Polarimetric SAR Data

A Test Statistic in the Complex Wishart Distribution and Its Application to Change Detection in Polarimetric SAR Data 4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 1, JANUARY 2003 A Test Statistic in the Complex Wishart Distribution and Its Application to Change Detection in Polarimetric SAR Data

More information

Investigating Coastal Polynya Thin Sea Ice State in the Laptev Sea Using TerraSAR-X Dual-Pol Stripmap Data

Investigating Coastal Polynya Thin Sea Ice State in the Laptev Sea Using TerraSAR-X Dual-Pol Stripmap Data Investigating Coastal Polynya Thin Sea Ice State in the Laptev Sea Using TerraSAR-X Dual-Pol Stripmap Data Thomas Busche (1), Irena Hajnsek (1), Thomas Krumpen (2), Lasse Rabenstein (2), Jens Hoelemann

More information

RADAR TARGETS IN THE CONTEXT OF EARTH OBSERVATION. Dr. A. Bhattacharya

RADAR TARGETS IN THE CONTEXT OF EARTH OBSERVATION. Dr. A. Bhattacharya RADAR TARGETS IN THE CONTEXT OF EARTH OBSERVATION Dr. A. Bhattacharya 1 THE RADAR EQUATION The interaction of the incident radiation with the Earth s surface determines the variations in brightness in

More information

Comparison between Multitemporal and Polarimetric SAR Data for Land Cover Classification

Comparison between Multitemporal and Polarimetric SAR Data for Land Cover Classification Downloaded from orbit.dtu.dk on: Sep 19, 2018 Comparison between Multitemporal and Polarimetric SAR Data for Land Cover Classification Skriver, Henning Published in: Geoscience and Remote Sensing Symposium,

More information

Evaluation of the Sacttering Matrix of Flat Dipoles Embedded in Multilayer Structures

Evaluation of the Sacttering Matrix of Flat Dipoles Embedded in Multilayer Structures PIERS ONLINE, VOL. 4, NO. 5, 2008 536 Evaluation of the Sacttering Matrix of Flat Dipoles Embedded in Multilayer Structures S. J. S. Sant Anna 1, 2, J. C. da S. Lacava 2, and D. Fernandes 2 1 Instituto

More information

Studies of Target Detection Algorithms That Use Polarimetric Radar Data

Studies of Target Detection Algorithms That Use Polarimetric Radar Data ESD-TR-88-180 Project Report TT-71 Studies of Target Detection Algorithms That Use Polarimetric Radar Data L.M. Novak M.B. Sechtin M.J. Cardullo 12 October 1988 Lincoln Laboratory MASSACHUSETTS INSTITUTE

More information

17. Jones Matrices & Mueller Matrices

17. Jones Matrices & Mueller Matrices 7. Jones Matrices & Mueller Matrices Jones Matrices Rotation of coordinates - the rotation matrix Stokes Parameters and unpolarized light Mueller Matrices R. Clark Jones (96-24) Sir George G. Stokes (89-93)

More information

Robust covariance matrices estimation and applications in signal processing

Robust covariance matrices estimation and applications in signal processing Robust covariance matrices estimation and applications in signal processing F. Pascal SONDRA/Supelec GDR ISIS Journée Estimation et traitement statistique en grande dimension May 16 th, 2013 FP (SONDRA/Supelec)

More information

Unitary representations of the icosahedral graded Hecke algebra

Unitary representations of the icosahedral graded Hecke algebra Unitary representations of the icosahedral graded Hecke algebra AMS Southeastern Section Meeting, LA - March 9, 008 Cathy Kriloff Idaho State University krilcath@isu.edu Joint work in progress with Yu

More information

Modeling Surface and Subsurface Scattering from Saline Soils

Modeling Surface and Subsurface Scattering from Saline Soils Modeling Surface and Subsurface Scattering from Saline Soils PolInSAR 2007 Tony Freeman, Jet Propulsion Laboratory Tom Farr, Jet Propulsion Laboratory Philippe Paillou, Astronomical Observatory of Bordeaux

More information

1. Regarding the availability of two co-polarized (HH and VV) channels.

1. Regarding the availability of two co-polarized (HH and VV) channels. Dear Anonymous Referee #2, Thank you for your insightful and stimulating review comments. Modifications based on these comments will significantly improve the quality of this research paper. General Comments:

More information

CHARACTERISTICS OF SNOW AND ICE MORPHOLOGICAL FEATURES DERIVED FROM MULTI-POLARIZATION TERRASAR-X DATA

CHARACTERISTICS OF SNOW AND ICE MORPHOLOGICAL FEATURES DERIVED FROM MULTI-POLARIZATION TERRASAR-X DATA CHARACTERISTICS OF SNOW AND ICE MORPHOLOGICAL FEATURES DERIVED FROM MULTI-POLARIZATION TERRASAR-X DATA Dana Floricioiu 1, Helmut Rott 2, Thomas Nagler 2, Markus Heidinger 2 and Michael Eineder 1 1 DLR,

More information

ATTI. XIX Riunione Nazionale di Elettromagnetismo (RiNEm) DELLA «FONDAZIONE GIORGIO RONCHI» Numero Speciale 8 - Serie di Elettromagnetismo su

ATTI. XIX Riunione Nazionale di Elettromagnetismo (RiNEm) DELLA «FONDAZIONE GIORGIO RONCHI» Numero Speciale 8 - Serie di Elettromagnetismo su ANNO LXVIII LUGLIO-AGOSTO 013 N. 4 ATTI DELLA «FONDAZIONE GIORGIO RONCHI» Numero Speciale 8 - Serie di Elettromagnetismo su XIX Riunione Nazionale di Elettromagnetismo (RiNEm) Roma, 10-14 settembre 01

More information

Screening of Earthen Levees using TerraSAR-X Radar Imagery

Screening of Earthen Levees using TerraSAR-X Radar Imagery Screening of Earthen Levees using TerraSAR-X Radar Imagery James Aanstoos (1), Khaled Hasan (1), Majid Mahrooghy (1), Lalitha Dabbiru (1), Rodrigo Nobrega (1), Saurabh Prasad (1) (1) Geosystems Research

More information

Chapter 2 Canonical Correlation Analysis

Chapter 2 Canonical Correlation Analysis Chapter 2 Canonical Correlation Analysis Canonical correlation analysis CCA, which is a multivariate analysis method, tries to quantify the amount of linear relationships etween two sets of random variales,

More information

Multivariate Statistical Analysis

Multivariate Statistical Analysis Multivariate Statistical Analysis Fall 2011 C. L. Williams, Ph.D. Lecture 4 for Applied Multivariate Analysis Outline 1 Eigen values and eigen vectors Characteristic equation Some properties of eigendecompositions

More information

12.2 Dimensionality Reduction

12.2 Dimensionality Reduction 510 Chapter 12 of this dimensionality problem, regularization techniques such as SVD are almost always needed to perform the covariance matrix inversion. Because it appears to be a fundamental property

More information

2: Distributions of Several Variables, Error Propagation

2: Distributions of Several Variables, Error Propagation : Distributions of Several Variables, Error Propagation Distribution of several variables. variables The joint probabilit distribution function of two variables and can be genericall written f(, with the

More information

Correcting Polarization Distortion in a Compact Range Feed

Correcting Polarization Distortion in a Compact Range Feed Correcting Polarization Distortion in a Compact Range Feed Brett T. alkenhorst, David Tammen NSI-MI Technologies Suwanee, GA 324 bwalkenhorst@nsi-mi.com dtammen@nsi-mi.com Abstract A high quality antenna

More information

Regularized Discriminant Analysis and Reduced-Rank LDA

Regularized Discriminant Analysis and Reduced-Rank LDA Regularized Discriminant Analysis and Reduced-Rank LDA Department of Statistics The Pennsylvania State University Email: jiali@stat.psu.edu Regularized Discriminant Analysis A compromise between LDA and

More information

Principal Component Analysis (PCA)

Principal Component Analysis (PCA) Principal Component Analysis (PCA) Salvador Dalí, Galatea of the Spheres CSC411/2515: Machine Learning and Data Mining, Winter 2018 Michael Guerzhoy and Lisa Zhang Some slides from Derek Hoiem and Alysha

More information

Improved sea-ice monitoring for the Baltic Sea Project summary

Improved sea-ice monitoring for the Baltic Sea Project summary Improved sea-ice monitoring for the Baltic Sea Project summary Leif E.B. Eriksson (1), Karin Borenäs (2), Wolfgang Dierking (3), Anders Berg (1) and Per Pemberton (2) (1) Chalmers University of Technology,

More information

Target Detection using Weather Radars and Electromagnetic Vector Sensors

Target Detection using Weather Radars and Electromagnetic Vector Sensors Target Detection using Weather Radars and Electromagnetic Vector Sensors Prateek Gundannavar and Arye Nehorai Email: nehorai@ese.wustl.edu Preston M. Green Department of Electrical & Systems Engineering

More information

EITN90 Radar and Remote Sensing Lecture 5: Target Reflectivity

EITN90 Radar and Remote Sensing Lecture 5: Target Reflectivity EITN90 Radar and Remote Sensing Lecture 5: Target Reflectivity Daniel Sjöberg Department of Electrical and Information Technology Spring 2018 Outline 1 Basic reflection physics 2 Radar cross section definition

More information

Expectation Maximization

Expectation Maximization Expectation Maximization Machine Learning CSE546 Carlos Guestrin University of Washington November 13, 2014 1 E.M.: The General Case E.M. widely used beyond mixtures of Gaussians The recipe is the same

More information

Utilization of Dual-pol data

Utilization of Dual-pol data WMO/ASEAN Training Workshop on Weather Radar Data Quality and Standardization Utilization of Dual-pol data 8 February 2018 Hiroshi Yamauchi Observation Department Japan Meteorological Agency Japan Meteorological

More information

Complete Polarization Control in Multimode Fibers with Polarization and Mode Coupling: Supplementary Information PER

Complete Polarization Control in Multimode Fibers with Polarization and Mode Coupling: Supplementary Information PER Complete Polarization Control in Multimode Fibers with Polarization and Mode Coupling: Supplementary Information Wen Xiong, Chia Wei Hsu, Yaron Bromberg, 2 Jose Enrique Antonio-Lopez, 3 Rodrigo Amezcua

More information

Evaluation of raindrop size distribution. retrievals based on the Doppler spectra. using three beams. Christine Unal

Evaluation of raindrop size distribution. retrievals based on the Doppler spectra. using three beams. Christine Unal Evaluation of raindrop size distribution retrievals based on the Doppler spectra using three beams Christine Unal Remote-sensing of the environment (RE) In this talk: Differential reflectivity Z dr cannot

More information

BUILDING HEIGHT ESTIMATION USING MULTIBASELINE L-BAND SAR DATA AND POLARIMETRIC WEIGHTED SUBSPACE FITTING METHODS

BUILDING HEIGHT ESTIMATION USING MULTIBASELINE L-BAND SAR DATA AND POLARIMETRIC WEIGHTED SUBSPACE FITTING METHODS BUILDING HEIGHT ESTIMATION USING MULTIBASELINE L-BAND SAR DATA AND POLARIMETRIC WEIGHTED SUBSPACE FITTING METHODS Yue Huang, Laurent Ferro-Famil University of Rennes 1, Institute of Telecommunication and

More information

Lecture notes on Quantum Computing. Chapter 1 Mathematical Background

Lecture notes on Quantum Computing. Chapter 1 Mathematical Background Lecture notes on Quantum Computing Chapter 1 Mathematical Background Vector states of a quantum system with n physical states are represented by unique vectors in C n, the set of n 1 column vectors 1 For

More information

A Note on Cohomology of a Riemannian Manifold

A Note on Cohomology of a Riemannian Manifold Int. J. Contemp. ath. Sciences, Vol. 9, 2014, no. 2, 51-56 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2014.311131 A Note on Cohomology of a Riemannian anifold Tahsin Ghazal King Saud

More information

Chapter 4: Polarization of light

Chapter 4: Polarization of light Chapter 4: Polarization of light 1 Preliminaries and definitions B E Plane-wave approximation: E(r,t) ) and B(r,t) are uniform in the plane ^ k We will say that light polarization vector is along E(r,t)

More information

I HH. I data, and the PWF are compared with the

I HH. I data, and the PWF are compared with the Optimal Speckle Reduction in Polarimetric SAR Imagery* Leslie M. Novak Michael C. Burl ABSTRACT Speckle is a major cause of degradation in synthetic aperture radar (SAR) imagery. With the availability

More information

1 if X v I v (X) = 0 if X < v. e sx p(x)dx

1 if X v I v (X) = 0 if X < v. e sx p(x)dx Homework 3 Solution Problem Chernoff Bound: The indicator function I v (X) for a real random variable X i defined a, { if X v I v (X) 0 if X < v For 0 (i) if X < v (ii) if X v E{e X } e v P rx v I v (X)

More information

POLARIMETRIC SAR MODEL FOR SOIL MOISTURE ESTIMATION OVER VINEYARDS AT C-BAND

POLARIMETRIC SAR MODEL FOR SOIL MOISTURE ESTIMATION OVER VINEYARDS AT C-BAND Progress In Electromagnetics Research, Vol. 142, 639 665, 213 POLARIMETRIC SAR MODEL FOR SOIL MOISTURE ESTIMATION OVER VINEYARDS AT C-BAND J. David Ballester-Berman *, Fernando Vicente-Guijalba, and Juan

More information

Bayesian Decision Theory

Bayesian Decision Theory Bayesian Decision Theory Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Fall 2017 CS 551, Fall 2017 c 2017, Selim Aksoy (Bilkent University) 1 / 46 Bayesian

More information

Supporting Information: Nonlinear generation of vector beams from. AlGaAs nanoantennas

Supporting Information: Nonlinear generation of vector beams from. AlGaAs nanoantennas Supporting Information: Nonlinear generation of vector beams from AlGaAs nanoantennas Rocio Camacho-Morales, Mohsen Rahmani, Sergey Kruk, Lei Wang, Lei Xu,, Daria A. Smirnova, Alexander S. Solntsev, Andrey

More information

Linear Algebra in Computer Vision. Lecture2: Basic Linear Algebra & Probability. Vector. Vector Operations

Linear Algebra in Computer Vision. Lecture2: Basic Linear Algebra & Probability. Vector. Vector Operations Linear Algebra in Computer Vision CSED441:Introduction to Computer Vision (2017F Lecture2: Basic Linear Algebra & Probability Bohyung Han CSE, POSTECH bhhan@postech.ac.kr Mathematics in vector space Linear

More information

1.6: 16, 20, 24, 27, 28

1.6: 16, 20, 24, 27, 28 .6: 6, 2, 24, 27, 28 6) If A is positive definite, then A is positive definite. The proof of the above statement can easily be shown for the following 2 2 matrix, a b A = b c If that matrix is positive

More information

Factor Analysis Continued. Psy 524 Ainsworth

Factor Analysis Continued. Psy 524 Ainsworth Factor Analysis Continued Psy 524 Ainsworth Equations Extraction Principal Axis Factoring Variables Skiers Cost Lift Depth Powder S1 32 64 65 67 S2 61 37 62 65 S3 59 40 45 43 S4 36 62 34 35 S5 62 46 43

More information