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
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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.
Regularization, synthetic aperture radar, graph-cut, optimization
Mots clés
Régularisation, radar à synthèse d’ouverture, coupure minimale de graphe, optimisation.
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