Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields

Thumbnail Image
Full text at PDC
Publication Date
Villa Hernández, José de Jesús
Rodríguez-Vera, Ramón
Rosa Vargas, José Ismael de la
González Ramírez, Efrén
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Sci. Ltd.
Google Scholar
Research Projects
Organizational Units
Journal Issue
In our recently reported work [1] (Villa et al., 2009) we derived a regularized quadratic-cost function, which includes fringe orientation information, for denosing fringe pattern images. In this work we adopt such idea for denoising wrapped phase-maps. We use a regularized cost-function that uses complex-valued Markov random fields (CMRFs) with orientation information of the filtering direction along isophase lines. The advantage of using an anisotropic filter along isophase lines is that phase and noise can be properly separated while 2 pi phase jumps are preserved even in high frequency zones. Apart from its robustness, the outstanding advantage of our method is its minimal computational effort. We present some results processing simulated and real phase-maps.
© 2010 Elsevier Ltd. We acknowledge the partial support for the realization of this work to the Secretaría de Educación Pública of México through the project PIFI-2007, and the Ministerio de Ciencia y Tecnología of Spain trough the project DPI2005-03891.
[1] Villa J, Antonio Quiroga J, de la Rosa I. Regularized quadratic cost function for oriented fringe-pattern filtering.Opt Lett 2009; 34 (11): 1741–3. [2] Ghiglia D G, Pritt M D. Two-dimensional phase-unwrapping. NewYork, N.Y. : John Wiley & Sons; 1998. [3] Aebischer H A ,Waldner S. A simple and effective method for filtering speckle- interferometric phase fringe patterns. Opt Commun 1999; 162: 205–10. [4] Palacios F, Goncalves E, Ricardo J, Valin J L. Adaptive filter to improve the performance of phase-unwrapping in digital holography. Opt Commun 2004; 238:245–51. [5] Takeda M, Ina H, Kobayashi S. Fourier transform method of fringe pattern analysis for computer based topography and interferometry. J Opt Soc Am 1982; 72: 156–60. [6] Ferraiuolo G, Poggi G. A Bayesian filtering technique for SAR interferometric phase fields. IEEE Trans Image Process 2004; 13 (10): 1368–78. [7] Yu Q, Yang X, Fu S, Liu X, Sun X. An adaptive contoured window filter for interferometric synthetic aperture radar. IEEE Geosci Remote Sensing Lett 2007; 4 (1): 23–6. [8] Kemao Q, Nam L T H, Feng L, Soon S H. Comparative analysis on some filters for wrapped phase maps. Appl Opt 2007; 46 (30): 7412–8. [9] Tang C, Wang W, Yan H, Gu X. Tangent least-squares fitting filtering method for electrical speckle pattern interferometry phase fringe patterns. ApplOpt 2007; 46 (15): 2907–13. [10] Tang C, Han L, Ren H, Gao T, Wang Z, Tang K. The oriented-couple partial differential equations for filtering in wrapped phase patterns. Opt Express 2009; 17 (7): 5606–17. [11] Besag J E. Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc Ser B 1974; B-36: 192–236. [12] Geman S, Geman D. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Trans Pattern Anal Machine Intell 1984; PAMI-6: 721–41. [13] Rivera M, Marroquín J L. Efficient half-quadratic regularization with granularity control. Image Vision Comput 2003; 21: 345–57. [14] Derin H, Elliot H, Cristi R, Geman D. Bayes smoothing algorithms for segmentation. IEEE Trans Pattern Anal Mach Intell 1984; PAMI-6: 707–20. [15] Bouman C, Sauer K. A generalized gaussian image model for edge-preserving MAP estimation. IEEE Trans Nucl Sci 1992; 99 (4): 1144–52. [16] Golub G H, Van Loan C F. Matrix computations. Baltimore, Maryland: Johns Hopkins University Press ; 1990. [17] Yang X, Yu Q, Fu S. An algorithm for estimating both fringe orientation and fringe density. Opt Commun 2007; 274: 286–92. [18] Kemao Q. Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations. Opt Lasers Eng 2007; 45: 304–17. [19] Fienup J R. Invariant error metrics for image reconstruction. Appl Opt 1997; 36: 8352–7. [20] Goldstein R M, Werner C L. Radar interferogram filtering for geophysical applications. Geophys Res Lett 1998; 25 (21): 4035–8.