Robust adaptive detection of buried pipes using GPR

Transcription

1 Robust adaptive detection of buried pipes using GPR Q. Hoarau, G. Ginolhac, A. M. Atto, J.-P. Ovarlez, J.-M. Nicolas Université Savoie Mont Blanc - Centrale Supelec - Télécom ParisTech 12 th July 2016 Q. Hoarau Adaptive detection of pipes 12 th July

2 Me Quentin Hoarau Formations : CPGE PCSI puis PSI, Toulouse Ecole d Ingénieur ENSEEIHT, Toulouse Spécialité Electronique et traitement du signal, otpion Traitement Signal et Images. Stage recherche au Signal Processing Lab, Háskóli Íslands Travail sur la visualisation des images hyperspectrales. Enseignements : à l IUT d Annecy Traitement d images (Cours-TP-TD, 2e Année) Théorie des graphes (TD, 1e année) Q. Hoarau Adaptive detection of pipes 12 th July

3 Contents Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

4 Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

5 Buried objects detection Figure: GPR operating principle. Q. Hoarau Adaptive detection of pipes 12 th July

6 Buried objects detection Figure: GPR operating principle. Q. Hoarau Adaptive detection of pipes 12 th July

7 Buried objects detection Figure: GPR operating principle. Q. Hoarau Adaptive detection of pipes 12 th July

8 Buried objects detection Figure: GPR operating principle. Q. Hoarau Adaptive detection of pipes 12 th July

9 GPR image example Figure: example of a GPR image, also called B-Scan or radargram. Q. Hoarau Adaptive detection of pipes 12 th July

10 Usual GPR processing Figure: usual GPR processing : migration of the objects hyperbolas. Q. Hoarau Adaptive detection of pipes 12 th July

11 Usual GPR processing Figure: pre-processed migration to remove layer signatures. Q. Hoarau Adaptive detection of pipes 12 th July

12 Issues Presence of layers and noise: noise power not constant, high influence on PFA levels when using common GPR detection methods; Wave speed unknown: relative permittivity not directly measurable on the image; Depth of the pipes: strong signal attenuation. Q. Hoarau Adaptive detection of pipes 12 th July

13 Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

14 GPR signal model Received signal model The scene contains P scatterers of reflection coefficient a p located in (y p, z p ). the received signal at position u m is: r m (t) = P a p e (t τ m (y p, z p, ɛ )) p=1 τ m (y p, z p, ɛ ) is the time delay of the echoed signals. For a simple ground configuration: τ m (y p, z p, ɛ ) = 2 ɛ z 2 + (y u n ) 2 c 0 (1) Q. Hoarau Adaptive detection of pipes 12 th July

15 GPR signal model Digital system: B-scan: M positions (u m ) N T time samples (t i ), Reconstructed scene: N y N z pixels with a p as value. We create: vector a = [a 1... a p... a NyN z ] T, matrices H m R N T N yn z, [H m ] ip = e(t i τ m (y p, z p, ɛ )) Signal at position u m : r m = H m a B-scan formation Using H = [ ] H1 T... HM T T, we obtain the complete B-scan image: r = Ha (2) Q. Hoarau Adaptive detection of pipes 12 th July

16 Detection problem Figure: Sampling process of vector x ɛ,y,z R N. Q. Hoarau Adaptive detection of pipes 12 th July

17 Detection problem Matrix form of the sampling process The Sampling of vector x ɛ,y,z can be put in matrix form using a sampling matrix T ɛ,y,z R N MN T. x ɛ,y,z = T ɛ,y,zr (3) T is constructed as follows: { 1 if one wants [xɛ [T ɛ,y,z] ij =,y,z] i = [r] j 0 else Q. Hoarau Adaptive detection of pipes 12 th July

18 Detection problem Trying to detect buried objects in a B-scan image is equivalent to detecting a reflection hyperbola around the sampled position. Detection problem We look for a theoretical hyperbola p in the vector x ɛ,y,z following two hypotheses: { H0 : x ɛ,y,z = n H 1 : x ɛ,y,z = a ɛ,y,zp + n Q. Hoarau Adaptive detection of pipes 12 th July

19 Noise model Two models are proposed for the additive noise n: Noise model for n Gaussian noise: n follows a Gaussian law N (0, R). SIRV : n = κg, where g N (0, R), and κ a deterministic positive variable. Q. Hoarau Adaptive detection of pipes 12 th July

20 Noise model Figure: Sampling of a signal free secondary dataset {x k } 1,K, x k = n k. Q. Hoarau Adaptive detection of pipes 12 th July

21 Noise model n k follows a model similar to n Noise model for n k Gaussian noise: n k follows a Gaussian law N (0, σr). SIRV : n k = κ k g k, where g k N (0, R), and κ k a deterministic positive variable. Q. Hoarau Adaptive detection of pipes 12 th July

22 Global detection problem Detection problem We look for a theoretical hyperbola p R N in the vector x ɛ,y,z R N following two hypotheses: { H0 : x ɛ,y,z = n, x k = n k k 1; K (4) H 1 : x ɛ,y,z = a ɛ,y,zp + n, x k = n k k 1; K with n, n k L(0, R) and K N. Q. Hoarau Adaptive detection of pipes 12 th July

23 Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

24 Adaptive detector To solve the detection problem, we resort to the Generalised Likelihood Ratio Test (GLRT ). Λ = max L(x H 1 ) κ R + ou σ R +,R R N N a R,ɛ R + max L(x H 0 ) κ R + ou σ R +,R R N N Supposing R known, Normalised Matched Filter (NMF): H 1 H 0 η NMF p T R 1 x 2 H 1 Λ = max ɛ R + (p T R 1 p)(x T R 1 η x) H 0 Q. Hoarau Adaptive detection of pipes 12 th July

25 Adaptive detector In practice, R is unknown. To solve this issue, we plug an estimated value in the NMF, creating the Adaptive NMF (ANMF): ANMF p ˆΛ T = max ˆR 1 x 2 H 1 ɛ R + (p T ˆR 1 p)(x T ˆR η (5) 1 x) H 0 Estimation: Depends on the selected noise model, Done using the secondary dataset {x k }, Need K = 2N vectors for a good estimation. Not enough secondary data available in the images: regularised estimators are used. Q. Hoarau Adaptive detection of pipes 12 th July

26 Gaussian Case Maximum likelihood estimators Regularised SCM [Ledoit 2004]: ˆR = β 1 K K x k x T k + αi N (6) k=1 Optimal ˆα 0 and ˆβ 0 value are given in [Du 2010]. SIRV Case Regularised Tyler estimator [Ollila 2014]: ˆR = (1 α) N K α [max ( 0, 1 K N ), 1]. K k=1 x k x T k x T k ˆR 1 x k + αi N (7) Optimal α 0 values are given in [Chen 2011] and [Ollila 2014]. Q. Hoarau Adaptive detection of pipes 12 th July

27 M-estimators An alternative to the FPE: Huber estimator, compromise between the FPE and the SCM. ˆR = 1 K K u(x T ˆR k 1 x k )x k x T k, k=1 In regularised form [Ollila 2014]: Regularised Huber estimator α 0. ˆR = 1 K { 1, for t c 2 u(t) = c 2 /t, for t > c 2 K u(x T ˆR k 1 x k )x k x T k + αi N, (8) k=1 To our knowledge, no optimal α value exists in the literature. Q. Hoarau Adaptive detection of pipes 12 th July

28 Simulations - Context Analytic laws P F A = f(η) for the ANMF with regularised estimators are unknown. Two solutions: Random matrix theory: asymptotic (approximate) laws, Simulations: empirical laws. Effect of α on Huber s estimator is also unknown: Find the best value to ensure a CFAR behaviour. Simulations PFA-Texture PFA-Threshold Q. Hoarau Adaptive detection of pipes 12 th July

29 Simulations - Parameters Size of x: N = 153, Number of secondary data: K = 40, Noise n,n k generated following a SIRV process: g N (0, R) with R Toeplitz [R]ij = ρ i j, ρ = 0.9 κ Γ(ν, 1/ν) value of a computed from the SNR: a = SNR T r(r) Number of Monte-Carlo runs: N MC = Q. Hoarau Adaptive detection of pipes 12 th July

30 Simulations - Results (Huber) Figure: PFA-Texture curve for the Huber estimator under varying α values. N = 153, K = 40. Q. Hoarau Adaptive detection of pipes 12 th July

31 Simulations - Results (All estimators) (a) (b) Figure: PFA-Threshold curves for all estimators. (a) ν = 2, (b) ν = 0.1. N = 153, K = 40. Q. Hoarau Adaptive detection of pipes 12 th July

32 Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

33 Real data (B-scan 0028.RAD) Figure: 0028.RAD - Raw B-Scan image Q. Hoarau Adaptive detection of pipes 12 th July

34 Real data (B-scan 0028.RAD) Q. Hoarau Adaptive detection of pipes 12 th July

35 Real data (B-scan 0028.RAD) Q. Hoarau Adaptive detection of pipes 12 th July

36 Introduction Buried objects detection Adaptive detection Application on real data Conclusion and perspectives Q. Hoarau Adaptive detection of pipes 12 th July

37 Conclusion GPR buried objects detection viewed as a statistical detection problem: The proposed ANMF detector achieves better results than the usual GPR processing techniques Detection of pipes with low response levels is enhanced, Detectors are close to CFAR, Gaussian and SIRV models returns similar results on the data. Q. Hoarau Adaptive detection of pipes 12 th July

38 Perspectives Prospects Theoretical work on the regularised estimators to provide good optimal parameter values for the under-sampled case, Validation of practical performance (CFAR behaviour) on other types of ground fills, Improvement of the signal model used in the steering vector. Q. Hoarau Adaptive detection of pipes 12 th July

39 Publications Publication in Signal Processing : special issue on GPR To be published in october 2016 Presentation at EUSIPCO Conference, Budapest, 29 Aug. - 2 Sept "Special Session: Advanced signal processing techniques." Q. Hoarau Adaptive detection of pipes 12 th July

40 Thank you for your time! Any questions? Q. Hoarau Adaptive detection of pipes 12 th July