Compressive Sensing and Generalized Likelihood Ratio Test in SAR Tomography

Transcription

1 Comressive Sensing and Generalized Likelihood Ratio Test in SAR Tomograhy G. Fornaro,, A. Pauciullo, D. Reale, M. Weiss 3, A. Budillon, G. Schirinzi - Institute for Electromagnetic Sensing of the Environment (IREA) National Research Council (CNR), Nales, Italy - University of Naoli Parthenoe Deartment of Engineering, Nales, Italy 3- Fraunhofer FR Wachtberg, Germany. CS and GLRT in SAR Tomograhy

2 Outline Synthetic Aerture Radar (SAR) Tomograhy and motivation for suer-resolution Comressive Sensing in Tomo-SAR Scattererdetection roblem Tomo-SAR. Generalized Likelihood Ratio Test (GLRT) schemes: the GLRT with cancellation (GLRT-C) and the suort based GLRT (su-glrt) aroaches Alication to real data: CS, GLRT-C vs su-glrt and su-glr vs CS Conclusions and future works CS and GLRT in SAR Tomograhy

3 SAR Tomograhy for full 3D Imaging SAR Interferometry and Differential SAR Interferometry has imortant alications in Digital Elevation Model(DEM) reconstruction and monitoring of deformation. SAR Tomograhy etends interferometric aroaches for alication to comle scenarios. By synthesizing an antenna also in the slant height direction(orthogonal to the line of sight) it is ossible to analyze the vertical structure of the scattering thus etending SAR imaging form D(azimuth-slant range) to 3D(azimuth-slant range-slant height). CS and GLRT in SAR Tomograhy 3

4 3D SAR Imaging N acquisitions with satial(orthogonal) baseline distribution b...b N n s s ma γ jπξns ( s) e ds ( r ) n N ma backscattering distribution along the slant height ξ n b n,... λ signal to the n-th antenna r RAYLEIG RESOLUTION ( B) sλr B b ma b min s FOURIER INVERSION FROM IRREGULAR SAMPLES: BeamForming(BF) Regularized inversion(svd) Adative Beamforming(Caon) Comressivesensing(CS),. A. Budillon, A. Evangelista, G. Schirinzi. Three-Dimensional SAR Focusing From Multiass Signals Using Comressive Samling. IEEE Trans. Geosci. Remote Sens., 49 (): , 0. X. X. Zhu, and R. Bamler. Tomograhic SAR Inversion by L-Norm Regularization The Comressive Sensing Aroach. IEEE Trans. Geosci. Remote Sens., 48(0): , 00. CS and GLRT in SAR Tomograhy 4

5 n T N [... N ] INVERSION γˆ A ˆ γ Beamforming Matched filter [ j πξ s] γ( s)e n ( s ) a m m ds N measurements DISCRETIZATION s { s,..., s l,.., s L } γ N jπζ Ns jπζnsl e e a [ a ] L (bins): L N tyically L>>N A... a L sensing matri T l jπξ l [... e ] Ns N Aγ steering vector: resonseor firm of a scatterer at a given height CS and GLRT in SAR Tomograhy 5

6 4D SAR Imaging (Differential SAR Tomograhy) N acquisitions with satial baseline distribution b...b N and temoral distribution t...t N Deformation term s n s s ma ma γ ( s) e jπξ s n e 4π j d λ Signal to the n-th antenna ( s, tn) ds e 4π j d λ ( s, t ) n v v ma a ma η t n ( s, v) n λ e jπη v n dv r n s s ma ma v v ma a ma γ ( s, v) η t λ ξ b n n n e jπξ n s jπη v n n ( λr) dvds CS and GLRT in SAR Tomograhy 6

7 Comressive Sensing Aγ [ a... a ]γ [ ] T jπζnsl L al... e N Result: if γis a sarse signal (can be well reresented as few non zero contributions) then, under the condition that a sufficient number of samles are acquired, the unknown can be well reconstructed via the comressive sensing technique. L>> N i.e. few measurements (N) and many unknown (L) K yothesis: the number Kof non-zero entries of γ( ) 0 is sufficiently smaller than L,N (K<<N<<L) γˆ argminγ γ 0 γ subjectto Aγ NP Comlete roblem, i.e. requires the check of all L!/K!/(L-K)! combinations <ε γ Aγ γ Under some mild hyothesis the solution above is equal to that of one of the following (equivalent) conve roblems: γˆ argminγ γ subjectto Aγ <ε { Aγ +δ γ } CS and GLRT in SAR Tomograhy 7 γˆ arg min γ Basis Pursuit De-Noising (BPDN)

8 ScattererDetection Problem Key elements: the False Alarm Probability (FAP) and the Detection Probability (DP). 0: w γ ;γ : aγ + w : aγ + a γ + w are the scatterers reflectivities w is the additive noise Generalized Likelihood Ratio Test (GLRT) is required. Letting to collect the unknown arameters (height, height/velocity, ) for a Gaussian model the discrimination between the first two hyotheses is achieved as: maa P min P a ( ) maa ( ) ma a( ) a ( ) ma < > T 0 ( ) P I aa a a I aa The maimization at the numerator selects the highest eak of the beamforming and normalizes to the data vector norm. A. De Maio, G. Fornaro, A. Pauciullo, Detection of Single Scatterers in Multidimensional SAR Imaging, IEEE Trans. Geosci. Remote Sens.,Vol. 47, No. 7, , Jul. 009 CS and GLRT in SAR Tomograhy 8

9 CS and GLRT in SAR Tomograhy 9 Sequential GLRT with cancellation (GLRT-C) min ) ( ma ) ( ma ) ( P a a a L Estimation from the data of the direction of the first scattererand evaluation of the coherence L () Projection of the data in the comlement orthogonal to the subsace sanned by the estimated direction Estimation from the rojected data of the direction of the second scattererand evaluation of the coherence L () ) (ˆ ˆ ˆ ˆ ˆ a a a a I P c c c c ) ( ) ( ma ) ( a a L Advantages: requires only one dimensional maimizations (comutational time) Disadvantages: no suer-resolution c c ˆ ˆ a P a P A. Pauciullo, D. Reale, A. De Maio, G. Fornaro, Detection of Double Scatterers in SAR Tomograhy, IEEE Trans. Geosci. Remote Sens., Vol. 50, No. 9, , Set. 0

10 Scheme of the GLRT-C detector maa ( ) ˆ L > False ( ) T L ( ) > T False 0 True True The thresholds T and T are set based on the fied values of PFA, on the first and on the second scatterers CS and GLRT in SAR Tomograhy

11 CS and GLRT in SAR Tomograhy su-glrt: an advance over the GLRT-C, ) ( min ), ( min P P g ML estimation Advantages: allows suer-resolution (i.e. detection of targets below the Rayleigh resolution) Disadvantages: comutationally demanding P, ), ( min g 0 g 0 T < > g T < >,, ), ( arg ma ), ( arg min P P w a a w a w : : : γ γ γ 0 ) ( arg ma ) ( arg min P P su-glrt T g > A. Budillon, G. Schirinzi, GLRT Based on Suort Estimation for Multile Scatterers Detection in SAR Tomograhy, IEEE Journ. Select. Toic. Al. Earth Observ. Remote Sens., Vol. 9, No. 3, , March 06

12 The TERRASAR-X dataset over Las Vegas 5 TerraSAR-X Sotlightacquisitionsover the city of Las Vegas USA (from to ) Imaging Mode: S (igh Resolution Sotlight) Orbit Direction: Ascending Beam Identification: sot_04 Orbit Number: 35 Incidence Angle: 35.8 Look Direction: Right Azimuth resolution:. meters Slant Range resolution: 0.6 meters Polarisation Mode: Single Polarisation: VV CS and GLRT in SAR Tomograhy

13 Acquisition distribution of the Las Vegas dataset Rayleigh resolution: 40m (slant height) 7m (vertical) CS and GLRT in SAR Tomograhy 3

14 CS and GLRT in SAR Tomograhy

15 Alication to high resolution data (The Mirage otel) CS and GLRT in SAR Tomograhy 5

16 CS Detected Single Scatterers CS and GLRT in SAR Tomograhy 6

17 CS Detected Double Scatterers(lower) CS and GLRT in SAR Tomograhy 7

18 CS Detected Double Scatterers(higher) CS and GLRT in SAR Tomograhy 8

19 CS Detected Double Scatterers: height difference CS and GLRT in SAR Tomograhy 9

20 su-glrt Detected Single Scatterers CS and GLRT in SAR Tomograhy 0

21 GLRT-C Detected Single Scatterers CS and GLRT in SAR Tomograhy

22 su-glrt Detected Double Scatterers (lower) CS and GLRT in SAR Tomograhy

23 GLRT-C Detected Double Scatterers (lower) CS and GLRT in SAR Tomograhy 3

24 Su-GLRT Detected Double Scatterers (higher) CS and GLRT in SAR Tomograhy 4

25 GLRT-C Detected Double Scatterers (higher) CS and GLRT in SAR Tomograhy 5

26 su-glrt Detected Double Scatterers: height difference CS and GLRT in SAR Tomograhy 6

27 GLRT-C Detected Double Scatterers: height difference CS and GLRT in SAR Tomograhy 7

28 Toograhic Difference Between CS and su-glrt istogram of the difference between the height of double scatterersestimated by CS and su-glrt (mask of oints detected by su-glrt) CS and GLRT in SAR Tomograhy 8

29 Deformation Mean Velocity Difference between CS and su-glrt istogram of the difference between the deformation mean velocity of double scatterersestimated by CS and su-glrt (mask of oints detected by su-glrt) CS and GLRT in SAR Tomograhy 9

30 CS Post Detection Single Scatterers CS and GLRT in SAR Tomograhy 30

31 Su-GLRT Single Scatterers CS and GLRT in SAR Tomograhy 3

32 CS Post Detected Double Scatterers (lower) CS and GLRT in SAR Tomograhy 3

33 Su-GLRT Double Scatterers(lower) CS and GLRT in SAR Tomograhy 33

34 CS Post Detected Double Scatterers (higher) CS and GLRT in SAR Tomograhy 34

35 Su-GLRT Double Scatterers(higher) CS and GLRT in SAR Tomograhy 35

36 Conclusions and future works SAR Tomograhy allows imlementing a radar scannerfrom the sace to reconstruct 3D oint clouds and monitor deformations. Net generation VR sensors (COSMO-SkyMEDII Generation, RWS) will allow further imroving this technology for alication to urban area and critical infrastructure monitoring. Suer-resolution in SAR tomograhyallows achieving imrovements in the generation of 3D oint clouds. An oen issue is the couling between the reliability of the reconstruction and the comutational erformances. To this end a key oint seems to be associated with the assimilation of roer detection schemes within comutationally efficient L methods. TANK YOU DANKE CS and GLRT in SAR Tomograhy 36