Introduction To Polarimetric SAR Tomography

Introduction toPolarimetricSAR TomographyLaurent Ferro-FamilUniversity of Rennes 1Laurent.Ferro Famil@univ rennes1.fr

Laurent Ferro-FamilLaurent.Ferro Famil@univ rennes1.frSHINEUniversity of Rennes 1IETR SHINE TeamRennes FranceSAR & Hyperspectral multi-modal Imagingand sigNal processing,Electromagnetic modelingSAPHIR

ContentsSAR tomography basicsApplication of PolTomoSARTowards spaceborne SAR tomographic missionsAcknowledgements

SAR Tomography basicsSAR imaging:resolution improvement based on signal diversity2-D imaging limitations over 3-D scenes:SAR interferometry2-D SAR and inSAR imaging limitations overcomplex (really 3-D) scenes:SAR tomography

Radar response modelBorn approximation at order 1:valid for media with weak dielectric contrastConsequence: linear response model(does not account for multiple interactions)

1-D imaging using SPECTRAL diversity1 scatterer located at distance d0- mono-chromatic waveformNo, ill-conditioned estimation- bi-chromatic waveform2 frequencies for 1 scatterer

1-D imaging using SPECTRAL diversitySeveral scatterers- measurements at many spectral locations- wide bandwidth (rich spectrum) waveformLarge BfSmall BfSeveral scatterers many frequencies

1-D imaging using SPATIAL diversitymono-chromatic waveform2-way wavenumber

1-D imaging using SPATIAL diversity1 scatterer located at distance x0: 2 azimuth positionsSeveral scatterers: many azimuth positions

2-D SAR imaging2-D imaging of several scatterers- 1-D range imaging using spectral diversity (wide bandwith waveform) - 1-D imaging in azimuth using spatial diversity (wide azimuth aperture)

2-D SAR imaging

2-D SAR imaging

SAR Tomography basicsSAR imaging:resolution improvement based on signal diversity2-D imaging limitations over 3-D scenes:SAR interferometry2-D SAR and inSAR imaging limitations overcomplex (really 3-D) scenes:SAR tomography

SAR images of 3-D scenesrDEM of Mt Etna, ItalyxLoss of a dimensionSIR-C X SAR intensity

SAR images of 3-D scenes2-D SAR imaging: cylindrical ambiguity

SAR interferometryAdditional spatial diversity1 scatterer 2 positions: SAR interferometry

SAR interferometry¿s(x; ¿ )Acquired signal (x-τ domain)Delay:x0Baseband pulse:x

SAR interferometryRange focused signal (x-d domain)2-D focused signal (x-r domain)drsrc (x; d)x0x0xxsc (x; r)

Relating InSAR phase to heightCoherent informationz BS1S2 µInSAR assumptions (small B)r2Hr1hInSAR phase differencey

Relating InSAR phase to heightFar-field expression (r1 B)Sensitivity to terrain geometryLocal linearization

InSAR topography estimation

SAR Tomography basicsSAR imaging:resolution improvement based on signal diversity2-D imaging limitations over 3-D scenes:SAR interferometry2-D SAR and inSAR imaging limitations overcomplex (really 3-D) scenes:SAR tomography

SAR imaging of 3-D scenesUrban areasMixture of several contributionsin the elevation direction

SAR imaging of 3-D scenesBIOSAR II, Boreal forest, L bandHH intensity [dB] rangeForest height [m]DEM [m]Mixture ofnumerous contributionsin the elevation direction

SAR imaging of 3-D scenesSeveral mixed scatterers many across-track positions

SAR imaging of 3-D scenesSeveral mixed scatterers many across-track positionsProcessing options- Direct 3-D imaging: coherent combination of M SAR acquisitions- M x 2-D focusing & coherent processing of M-InSAR quantities

SAR imaging of 3-D scenesDirect 3-D imaging of an Alpine glacier at L bandTomoSAR IlluminationTomoSAR Image - 25 m below the Ice surfaceTomoSAR Image - Ice surfaceTomoSAR Image - 50 m below the Ice surface

SAR imaging of 3-D scenesM x 2-D imaging of a Boreal forest at L bandTomoSAR: 3D ImagingSAR: 2D Imagingz 5 m above the terrainz 0 m above the terrainz 10 m above the terrainTotal Backscattered power540054005400520052005200500050005000range [m]range [m]range [m]5200range 0440000200400600200400440006002004006000azimuth [m]azimuth [m]200400600azimuth [m]azimuth [m]z 20 m above the terrainz 15 m above the terrainz 25 m above the terrainLidar range [m]range [m]range [m]range 00200400azimuth [m]6000200400600azimuth [m]o Power distribution in height directiono Full-resolution CAPON44000200400azimuth [m]6000200400azimuth [m]600

TomoSAR Focusing

TomoSAR Focusing

TomoSAR Focusing

TomoSAR FocusingMultiple baselines : Illumination from multiple points of viewAperture Synthesis in thecross-range directionTrack nReference Track(Master)Track 1crossrange Cross-range resolutioncapabilitiesπ/2θslantrangeheight rr

TomoSAR Resolution

TomoSAR Resolution

TomoSAR Resolution

TomoSAR Processing

Modeling of a TomoSAR responseSAR pixel Integral of allcontributions within the resolution cellC resolution celloEach elementary scatterer is phaserotated according to its distance fromthe Radar

Modeling of a TomoSAR responseSAR pixel Integral of allcontributions within the resolution cellCn resolution cell foroEach elementary scatterer is phaserotated according to its distance fromthe n-th view pointthe RadarMultiple baselinesoResolution cell is oriented at differentangles for different baselines Range migration: Targets at differentcross-range positions appear at differentrange positions for different baselinesExact TomoSAR focusingrequires 3D Back-Projection

Relaxing the model Hyp 1: range migration is negligiblesmall aperture, small bandwidth, targets are distributed in a small angular sectorC resolution cellOnly phase terms varyw.r.t. baselines

Relaxing the model Hyp 2 : locally-plane wave approximation (across-track scene extent R)bn normal baseline of the n-th view w.r.t. the Masterview

Relaxed modelCommonSolving the integral w.r.t. r’ and x’ one getsterms for allbaselinesFlat earth phase (w.r.t. reference)s(r,x,v) cross-range projection oftarget reflectivity within the SARresolution cell at (r,x)

TomoSAR focusingSAR Tomography as a Fourier imaging process: M-Fwd 2-D imagingFocused SLC SAR imageFourier Transform of s(r,x,v) the scene complex reflectivity(cross-range coord.)In(r,x) : SLC pixel in the n-th images(r,x,v): cross-range projection of target reflectivitywithin the SAR resolution cell at (r,x)bn : normal baseline for the n-th imageλ : carrier wavelength

TomoSAR focusingSAR Tomography as a Fourier imaging process: Backwd 3D imaging The cross-range distribution of the complex reflectivity can be retrieved byFourier transforming SLC data with respect to the normal baselinesˆ( r , x, v ) DFT { I n ( r , x )}DFT Discrete FourierTransform over the bnsIn other words 4π I n ( r , x ) s ( r , x, v ) exp jbn v dvλr 4π ˆs ( r , x, v ) I n ( r , x ) exp jbn v λr nI n ( r, x) observations ( r , x, v ) unknownsˆ( r , x, v ) estimate

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr n

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr n

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr n

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nTerrain extended target It does not project into apeak Cross-range spread

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 3: terrain

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 3: terrainTerrain extended target Cross-range spreaddepends on terrain slope

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 3: terrainTerrain extended target Cross-range spreaddepends on terrain slope

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 3: terrainge,vTerrain extended targetranofSARResolutions(v)crossRaSi dagh r LtineΔrCell reference position Cross-range spreaddepends on terrain slope

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 4: terrain forest

TomoSAR focusing – examples4π sˆ( r , x, v ) I n ( r , x ) exp jbn v λr nCase 4: terrain forest

AmbiguityDFT produces periodic results Ghost targets appearing at knownposition w.r.t. the real oneo Also referred to as ambiguous targets, orreplicaso Same range as the real targeto Displaced in cross-range

Baseline designBaseline design tipso Ambiguity baseline spacingo Resolution baseline aperture Baseline spacing: small enough to ensure thatambiguous targets stay away from the real ones Baseline aperture: large enough to meetresolution requirement How many passes ?N bap b va v

Projection in the vertical directionTomoSAR forward modelIn(r,x) : SLC pixel in the n-th images(r,x,v): cross-range projection of targetreflectivity within the SAR resolutioncell at (r,x)bn : normal baseline for the n-th imageChange of variable from cross range to heightz v sin θkz is usually referred to as verticalwavenumber or phase to heightconversion factor4π bnk z ( n) λr sin θλ : carrier wavelength

3-D SAR imaging

3-D SAR imaging3-D Synthetic Aperture imagingBeamformer-like formulationSLC dataSteering vector3-D Fourier imaging is equivalentto the Beamformer spectral analysis method

Principles of spectral analysisExample: sum of monochromatic signalsDiscrete-time signal 1/ d 1/ L

Principles of spectral analysisDiscrete-time signalTomographic equivalenceIrregular baseline sampling12zLimited bandwidth kz.MSpeckle effect ?νLxry

Principles of spectral analysisStationary signalTomographic equivalenceI

Advanced TomoSARCurrent paradigm for forested areas: retrieve the vertical distribution of backscattered powerbased on the observed InSAR coherencesSLC dataComplex datavector (Nx1)Coherence estimation(spatial multilooking)Coherence matrix (NxN)Why? Improved performance by usingSpectral Analysiso Super-resolution (super finer than the limit from baselineaperture)o Side-lobe rejectiono Rejection of ambiguous targets (using irregular baseline spacing)TomoSARprocessing

Tomographic imaging using specanAcquired signal (single scatterer)Beamformer (Fast) filter maximizing the output SNRSNR maximized at z z0 :Use: computeestimate parameters from the maxUsed approach: linear filtering

Tomographic imaging using specanUniform baseline samplingFast: resolutionSlow: ambiguitySpatial features of a tomogram rapidly varying: resolution band-limited: sidelobes sampled: ambiguitieszambδzM 6

Tomographic imaging using specanM 6M 12

Tomographic imaging using specanM 6Rule of a thumbM 12

Tomographic imaging using specanBeamformer features Excellent statistical accuracy Fourier resolution (depends on k) Cannot handle closely spaced scatterersCapon's solutionCapon's approach Linear filter (fast)Aims to minimize spatialperturbations & sidelobes

Tomographic imaging using specan Capon: significantly improved resolution For regular baselines, BF & Capon are equally affectedby ambiguities

Tomographic imaging using specanIrregular baseline sampling: logscale distribution BF: strongly affected by ambiguities CAPON: unsynchronized ambiguity are considered as perturbations andfiltered. Good resolution performance preserved

Tomographic imaging using specanOver speckle affected environmentsis a Random Variable (1 realization is not representative) Power Spectral Density In practice BF: quite stable w.r.t L Capon may suffer from a poor covariance matrix conditioning Diagonal Loading

Tomographic imaging using specanTropical forest profile at P bandzzBFCapon

Tomographic imaging using specanCovariance matrix model for discrete scatterersSteering matrixCovariance matrix eigen-decomposition (Ns N)

Tomographic imaging using specanCovariance matrix model for discrete scatterersSteering matrixCovariance matrix eigen-decomposition (Ns N)

Tomographic imaging using specanMUSIC principleMUSIC criterionRemarks The noise space dimension has to be estimated MUSIC is well adapted to DISCRETE scatterers, not to continuous reflectivities (i.e.forest canopies) The values reached by the criterion DO NOT correpond to the PSD (profile intensity) CAPON is NOT HR, MUSIC YES

Tomographic imaging using specanCritical configuration (3 images) in an urban environment at L bandBFCAPONMUSICStrictly speaking, Capon's technique is not HR, but is very convenientand can be easily derived in the full-pol case

Case study: BIOSAR 2 data