SAR Speckle Filtering

Transcription

1 SAR Speckle Filtering SAR Training for forest monitoring 014/015 Cédric Lardeux Jean-Paul Rudant Pierre-Louis Frison SAR for Forest Mapping 014/015

2 Coherent magery System Speckle noise Single pixel value no meaning Homogeneous are statistical distribution SAR for Forest Mapping 014/015

3 Pixels numbers Reminder: Histogram Standard deviation: s Digital number mean: m SAR for Forest Mapping 014/015

4 Pixels numbers Histogram over an homogeneous area deal image With no noise> s 0 mage with little noise > s small mage with high noise > s high Digital number SAR for Forest Mapping 014/015

5 mage histogram over an homogeneous area Amplitude: A p ( / s) A exp A A A s s E A s, EA s ntensity: p ( / s) 1 exp s s 4 E s R, E 8s R p(a) p() A Radar reflectivity: R s E()E(i²+q²)s ² R SAR for Forest Mapping 014/015

6 mage histogram over an homogeneous area Amplitude: A p ( / s) A exp A A A s s E A s, EA s ntensity: p ( / s) 1 exp s s E s, E 8 s 4 p(a) p() R s ² R 1 * R R R 1 R A The higher is R, the more data are spread over SAR for Forest Mapping 014/015 R 1

7 Pixels number SAR speckle filtering Goal of radar image filtering: Histogram over an homogeneous area Digital Number deal image With no noise> s 0 mage with little noise> s small mage with High noise > s high Decrease the standard deviation s noise) without modify the mean m ( radar refelctivity) SAR for Forest Mapping 014/015

8 Speckle: multiplicative noise RADARSAT - Mode Fine 1 Variation coefficient: C A C var() A E( A) var( ) 1 E C x v var( ) E A N var() var() x y x y k N N k 1 E( y) E( x) > multilook data C ML C N Look number: N SAR for Forest Mapping 014/015

9 p() L10 multilook data ml 1 L L k k 1 R L3 L1 p( / R) L R 1 L exp L R L1 L R, E R E ml ml C L ml v ml Cv L ml L1 ml SAR for Forest Mapping 014/015

10 MULTLOOK OBTENTON in spatial domain in time domain Sliding window: image * window Date 1 Date Date 3 E() Date 4 9 looks if pixel sare not correlated 4 looks if surface has not changed Example: ERS data - PR products : 3 looks SAR for Forest Mapping 014/015

11 ntensity image (from SLC product) Sète - France: RADARSAT - FNE 1 NCDENCE 38, 4 x9 m SAR for Forest Mapping 014/015

12 SAR for Forest Mapping 014/015

13 Spatial Multilook Processing 3x1 average window 6x average window < 3 Look Due to pixels correlation! < 1 Look Sète - France: RADARSAT FNE 1 NCDENCE 38, 9 x9 m SAR for Forest Mapping 014/015

14 SPATAL MULTLOOK PROCESSNG Sète - France: RADARSAT FNE 1 - NCDENCE 38, 9 x9 m 3x1 average window 6x average window < 3 Look Due to pixels correlation! < 1 Look Photo aérienne ( SAR for Forest Mapping 014/015

15 TEMPORAL MULTLOOK PROCESSNG ERS - PR product SAR for Forest Mapping 014/015 ERS - 3 dates average image

16 ERS - 3 dates average image SAR for Forest Mapping 014/015 ERS - 3 dates composite image

17 Goal: estimate R s Most simple: Box Filtering: E() E Advantages: simple + best estimation (MMSE) over homogeneous area nconvenients: Details lost, fuzzy introduction Other classical filters: (median, Sigma, math. morph..): WORST! > Need to introduce specific filters taken into account speckle statistics Neighbourhood size depends on local scene characteristics > Adaptive filters SAR for Forest Mapping 014/015

18 Weight coefficient SAR speckle filtering R( d) ( d) m( d) with Frost Filter m Kc d ( d) Kce 1 (MMSE criteria) d: distance to central pixel K1 and K set for the whole image Box filtering c c homogeneous area: heterogeneous area: low high Homogeneous area c, Heterogeneous area Distance to central pixel: d SAR for Forest Mapping 014/015

19 Homogeneous area: R. v Speckle Multiplicative Model E(v) 1 > E() R C v 1 L Area with texture: Pixel intensity Scene reflectivity R E(R). t Speckle noise Speckle noise Area with texture > E(R). v. t Texture variations E(t) 1 > E() E(R) v, t stat. independent > C CC t v C t C v SAR for Forest Mapping 014/015

20 C t v CC t C No texture: (Homogeneous area) C C v C v 1 L E() R Number of looks of the image estimated over an homogenous zone of the image E(), c with texture: C C t t C C R R C C v 1C v 1 LC 1L Estimated in the neighbourhood of the considered pixel Estimated over an homogenous zone 1/L Number of looks of the image SAR mage Filtering Goal: Estimation R of R at the central pixel, through E(), C and C v SAR for Forest Mapping 014/015

21 R E a E homogeneous area: t 0 with Kuan and Lee Filters a ct (MMSE criteria) c RE c > heterogeneous area: more weight on central pixel c,e Kuan: Lee: c c c t c c t v c c t c c c v t c c v 1c v v t c c v t Evaluated on homogeneous area Lc 1 L 1 t a c t c c n the local window v L < 3 > Lee < Kuan L 3 > Lee Kuan SAR for Forest Mapping 014/015

22 Maximize Bayesian criteria: Hypothesis on p(r): law MAP (Maximum a posteriori) Filters p ( R/ ) p( / R). p( R) p( ) > R E L1 E L1 4 LE homogeneous area: high > RE K c p(r): law p(/r): law MAP filter Gamma-Gamma filter SAR for Forest Mapping 014/015

23 SAR for Forest Mapping 014/015

24 SAR for Forest Mapping 014/015

25 SAR for Forest Mapping 014/015

26 SAR for Forest Mapping 014/015

27 SAR for Forest Mapping 014/015

28 CONCLUSON Over homegeneous area: All the filters: ˆ RE Quantitative comparison: (bias, radiometric resolution amelioration) All the filters are equivalent Qualitative comparison: scene dependent SAR for Forest Mapping 014/015