Joint Filtering of SAR Amplitude And Interferometric Phase with Graph-Cuts. Filtrage Conjoint de la Phase Interférométrique et de L’Amplitude en Imagerie Radar par Champs de Markov et Coupes Minimales

Joint Filtering of SAR Amplitude And Interferometric Phase with Graph-Cuts

Filtrage Conjoint de la Phase Interférométrique et de L’Amplitude en Imagerie Radar par Champs de Markov et Coupes Minimales

Loïc Denis Florence Tupin  Jérôme Darbon  Marc Sigelle 

École Supérieure de Chimie Physique Électronique de Lyon et Laboratoire Hubert Curien, CNRS UMR 5516, St-Étienne

Télécom ParisTech, CNRS UMR 5141, Paris, France

Department of Mathematics of UCLA, Los Angeles, USA

Page: 
127-144
|
Received: 
4 January 2008
|
Accepted: 
N/A
|
Published: 
30 April 2009
| Citation

OPEN ACCESS

Abstract: 

Like other coherent imaging modalities, synthetic aperture radar (SAR) images suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms.

Numerous approaches have been proposed to filter speckle noise. Markov Random Field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges.

Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving non-convex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the α-expansion) is too heavy specially when considering joint regularization of several images.

We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.

Résumé

L’imagerie radar à ouverture synthétique (SAR), comme d’autres modalités d’imagerie cohérente, souffre de la présence du chatoiement (speckle). Cette perturbation rend difficile l’interprétation automatique des images et le filtrage est souvent une étape nécessaire à l’utilisation d’algorithmes de traitement d’images classiques. De nombreuses approches ont été proposées pour filtrer les images corrompues par un bruit de chatoiement. La modélisation par champs de Markov (CdM) fournit un cadre adapté pour exprimer à la fois les contraintes sur l’attache aux données et les propriétés désirées sur l’image filtrée. Dans ce contexte la minimisation de la variation totale a été abondamment utilisée afin de limiter les oscillations dans l’image régularisée tout en préservant les bords.

Le bruit de chatoiement suit une distribution de probabilité à queue lourde et la formulation par CdM conduit à un problème de minimisation mettant en jeu des attaches aux données non-convexes. Une telle minimisation peut être obtenue par une approche d’optimisation combinatoire en calculant des coupures minimales de graphes. Bien que cette optimisation puisse être menée en théorie, ce type d’approche ne peut être appliqué en pratique sur les images de grande taille rencontrées dans les applications de télédétection à cause de leur grande consommation de mémoire. Le temps de calcul des algorithmes de minimisation approchée (en particulier α-extension) est généralement trop élevé quand la régularisation jointe de plusieurs images est considérée.

Nous montrons qu’une solution satisfaisante peut être obtenue, en quelques itérations, en menant une exploration de l’espace de recherche avec de grands pas. Cette dernière est réalisée en utilisant des techniques de coupures minimales. Cet algorithme est appliqué pour régulariser de manière jointe à la fois l’amplitude et la phase interférométrique d’images SAR en milieu urbain.

Keywords: 

Regularization, synthetic aperture radar, graph-cut, optimization

Mots clés

Régularisation, radar à synthèse d’ouverture, coupure minimale de graphe, optimisation.

1. Introduction
2. Modèle Markovien
3. Algorithme Proposé
4. Résultats
5. Conclusion
  References

[1] F. ARGENTI and L. ALPARONE. Speckle removal from SAR images in the undecimated wavelet domain. IEEE Transactions on Geoscience and Remote Sensing, 40(11) :2363–2374, 2002.

[2] G. AUBERT and J.F. AUJOL. A Variational Approach to Removing Multiplicative Noise. SIAM Journal on Applied Mathematics, 68:925, 2008.

[3] M. BELGE, M.E. KILMER, and E.L. MILLER. Efficient determination of multiple regularization parameters in a generalized L-curve framework. Inverse Problems, 18(4) :1161–1183, 2002.

[4] J. BESAG. On the statistical analysis of dirty pictures. J. R. Statist. Soc. B, 48(3) :259–302, 1986.

[5] J. M. BIOUCAS-DIAS and G. VALADAO. Phase unwrapping via graph cuts. IEEE Transactions on Image Processing, 16(3) :698–709, 2007.

[6] A. BLAKE and A. ZISSERMAN. Visual Reconstruction. MIT Press, 1987.

[7] Y. BOYKOV and V. KOLMOGOROV. An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(9) :1124–1137, 2004.

[8] Y. BOYKOV, O. VEKSLER, and R. ZABIH. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(2) :147–159, 2001.

[9] J.L. CASTELLANOS, S. GÓMEZ, and V. GUERRA. The triangle method for finding the corner of the L-curve. Applied Numerical Mathematics, 43(4) :359–373, 2002.

[10] A. CHAMBOLLE. Total variation minimization and a class of binary mrf models. In Energy Minimization Methods in Computer Vision and Pattern Recognition, volume LNCS 3757, pages 136–152, St. Augustine, Florida, USA, 2005.

[11] P. CHARBONNIER. Reconstruction d’image : régularisation avec prise en compte des discontinuités. PhD thesis, Université de Nice Sophia Antipolis, 1994.

[12] P.L. COMBETTES and J.C. PESQUET. Image restoration subject to a total variation constraint. IEEE Transactions on Image Processing, 13(9) :1213–1222, 2004.

[13] J. DARBON. Composants logiciels et algorithmes de minimisation exacte d’énergies dédiées au traitement des images. PhD thesis, École Nationale Supérieure des Télécommunications (ENST E050), 2005.

[14] J. DARBON and S. PEYRONNET. A vectorial self-dual morphological filter based on total variation minimization. In Proceedings of the First International Conference on Visual Computing, volume 3804 of Lecture Notes in Computer Science Series, pages 388–395, Lake Tahoe, Nevada, USA, December 2005. Springer-Verlag.

[15] J. DARBON and M. SIGELLE. Image restoration with discrete constrained Total Variation part I : Fast and exact optimization. Journal of Mathematical Imaging and Vision, 26(3) :261–276, December 2006.

[16] J. DARBON and M. SIGELLE. Image restoration with discrete constrained Total Variation part II : Levelable functions, convex priors and non-convex cases. Journal of Mathematical Imaging and Vision, 26(3) :277–291, December 2006.

[17] J. DARBON, M. SIGELLE and F. TUPIN. The use of levelable regularization functions for MRF restoration of SAR images while preserving reflectivity. In SPIE, editor, IS&T/SPIE 19th Annual Symposium Electronic Imaging, volume E 112, 2007.

[18] S. FOUCHER, G. BERTIN BÉNIÉ and J.-M. BOUCHER. Multiscale MAP filtering of SAR images. IEEE Transactions on Image Processing, 10(1) :49–60, 2001.

[19] V. S. FROST, J. ABBOTT STILES, K. S. SHANMUGAN and J. C. HOLTZMAN. A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4(2) :157–166, March 1982.

[20] N.P. GALATSANOS and A.K. KATSAGGELOS. Methods for choosing the regularization parameter and estimatingthe noise variance in image restoration and their relation. IEEE Transactions on Image Processing, 1(3) :322–336, 1992.

[21] D. GEMAN and G. REYNOLDS. Constrained restoration and the recovery of discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-14(3) :367–383, 1992.

[22] S. GEMAN and D. GEMAN. Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6) :721–741, November 1984.

[23] J.W GOODMAN. Statistical properties of laser speckle patterns. In Laser Speckle and Related Phenomena, volume 9, pages 9–75. J.C Dainty (Springer Verlag, Heidelberg, 1975), 1975.

[24] D. M. GREIG, B. T. PORTEOUS, and A. H. SEHEULT. Exact maximum a posteriori estimation for binary images. J. R. Statist. Soc. B, 51(2) :271–279, 1989.

[25] P.C. HANSEN, T.K. JENSEN, and G. RODRIGUEZ. An adaptive pruning algorithm for the discrete L-curve criterion. Journal of Computational and Applied Mathematics, 198(2) :483–492, 2007.

[26] P.C. HANSEN and D.P. O’LEARY. The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems. SIAM Journal on Scientific Computing, 14 :1487, 1993.

[27] H. ISHIKAWA. Exact optimization for Markov random fields with convex priors. IEEE Trans. on Pattern Analysis and Machine Intelligence, 25(10) :1333–1336, October 2003.

[28] E. JAKEMAN. On the statistics of K-distributed noise. J. Phys. A : Math. Gen., 13 :31–48, 1980.

[29] A. JALOBEANU, L. BLANC-FERAUD, and J. ZERUBIA. Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method. Pattern Recognition, 35(2): 341–352, 2002.

[30] J. K. JAO. Amplitude distribution of composite terrain radar clutter and the K-distribution. IEEE Transactions on Antennas and Propagation, AP-32(10) :1049–1062, October 1984.

[31] V. KOLMOGOROV. Primal-dual algorithm for convex markov random fields. Technical report, Microsoft Research, 2005.

[32] V. KOLMOGOROV and R. ZABIH. What energy functions can be minimized via graph-cuts ? IEEE Trans. on Pattern Analysis and Machine Intelligence, 26(2), 2004.

[33] KUAN, SAWCHUK, STRAND, and CHAVEL. Adaptive restauration of images with speckle. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-35(3) :373–383, 1987.

[34] D. T. KUAN, A. A. SAWCHUK, T. C. STRAND, and P. CHAVEL. Adaptive noise smoothing filter for images with signal dependant noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-7(2) :165–177, March 1985.

[35] J-S LEE. Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-2(2) :165–168, March 1980.

[36] J.-S. LEE. Speckle analysis and smoothing of synthetic aperture radar images. Computer Graphics and Image Processing, 17 :24–32, 1981.

[37] J. S. LEE, K. W. HOPPEL, S. A. MANGO and A. R. MILLER. Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery. IEEE Transactions on Geoscience and Remote Sensing, 32(5) :1017–1028, 1994.

[38] J. S. LEE, I. JURKEVICH, P. DEWAELE, P. WAMBACK and A. OOSTERLINCK. Speckle filtering of synthetic aperture radar images : A review. Remote Sensing Reviews, 8 :313–340, 1994.

[39] F. LOMBARDINI, F. BORDONI and F. GINI. Feasibility study of along-track sar interferometry with the cosmo-skymed satellite system. In IGARSS04, volume 5, pages 337–3340, 2004.

[40] A. LOPES, E. NEZRY, R. TOUZI and H. LAUR. Structure detection, and statistical adaptive filtering in SAR images. Int. J. Remote Sensing, 14(9) :1735–1758, 1993.

[41] Y. MEYER. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, 2001.

[42] J.M. NICOLAS. A Fisher-MAP filter for SAR image processing. In IGARSS03, volume 3, Toulouse, France, jul 2003.

[43] J.M. NICOLAS, F. TUPIN and H. MAÎTRE. Smoothing speckle SAR images by using maximum homogeneous region filters : an improved approach. In IGARSS01, volume 3, pages 1503–1505, Sydney, Australie, jul 2001.

[44] M. NIKOLOVA. A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 20:99–120, 2004.

[45] S. OSHER, M. BURGER, D. GOLDFARB, J. XU and W. YIN. An Iterative Regularization Method for Total Variation Based Image Restoration. SIAM journal on Multiscale modeling and Application, 4 :460–489, 2005.

[46] J.P. PICARD and H.D. RATLIF. Minimum cuts and related problem. Networks, 5 :357–370, 1975.

[47] R. ROMEISER and H. RUNGE. Theoretical evaluation of several possible along-track InSAR modes of TerraSAR-X for ocean current measurements. IEEE Transactions on Geoscience and Remote Sensing, 45 :21–35, 2007.

[48] L. RUDIN, S. OSHER and E. FATEMI. Nonlinear total variation based noise removal algorithms. Physica D., 60 :259–268, 1992.

[49] J. SHI and S. OSHER. A nonlinear inverse scale space method for a convex multiplicative noise model. Technical Report 07-10, UCLA, 2007.

[50] D. STRONG and T. CHAN. Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems, 19(6), 2003.

[51] R. TOUZI. A review of speckle filtering in the context of estimation theory. IEEE Transactions on Geoscience and Remote Sensing, 40(11) :2392–2404, 2002.

[52] G. VASILE, E. TROUVÉ, J.S. LEE and V. BUZULOIU. Intensitydriven adaptive neighborhood technique for polarimetric and interferometric SAR parameters estimation. IEEE Transactions on Geoscience and Remote Sensing, 44(6) :1609–1621, 2003.

[53] M. WALESSA and M. DATCU. Model-based despeckling and information extraction of SAR images. IEEE Transactions on Geoscience and Remote Sensing, 38(5), 2000.

[54] Y. WU and H. MAÎTRE. Smoothing speckled synthetic aperture radar images by using maximum homogeneous region filters. Optical Engineering, 31(8) :1785–1792, 1992.

[55] Z. ZHOU, R.N. LEAHY and J. QI. Approximate maximum likelihood hyperparameter estimation for Gibbs priors. IEEE Transactions on Image Processing, 6(6) :844–861, 1997.