Filtering of Interferometric SAR Phase Images as a Fuzzy Matching-Pursuit Blind Estimation
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Filtering of Interferometric SAR Phase Images as a Fuzzy Matching-Pursuit Blind Estimation Bruno Aiazzi Institute of Applied Physics “Nello Carrara” (IFAC), National Research Council (CNR), Via Panciatichi 64, 50127 Florence, Italy Email: [email protected]
Stefano Baronti Institute of Applied Physics “Nello Carrara” (IFAC), National Research Council (CNR), Via Panciatichi 64, 50127 Florence, Italy Email: [email protected]
Massimo Bianchini Department of Electronics and Telecommunications (DET), University of Florence, Via di Santa Marta 3, 50139 Florence, Italy Email: [email protected]
Alessandro Mori Department of Electronics and Telecommunications (DET), University of Florence, Via di Santa Marta 3, 50139 Florence, Italy Email: [email protected]
Luciano Alparone Department of Electronics and Telecommunications (DET), University of Florence, Via di Santa Marta 3, 50139 Florence, Italy Email: [email protected] Received 6 August 2004; Revised 6 April 2005 We present an original application of fuzzy logic to restoration of phase images from interferometric synthetic aperture radar (InSAR), which are affected by zero-mean uncorrelated noise, whose variance depends on the underlying coherence, thereby yielding a nonstationary random noise process. Spatial filtering of the phase noise is recommended, either before phase unwrapping is accomplished, or simultaneously with it. In fact, phase unwrapping basically relies on a smoothness constraint of the phase field, which is severely hampered by the noise. Space-varying linear MMSE estimation is stated as a problem of matching pursuit, in which the estimator is obtained as an expansion in series of a finite number of prototype estimators, fitting the spatial features of the different statistical classes encountered, for example, fringes and steep slope areas. Such estimators are calculated in a fuzzy fashion through an automatic training procedure. The space-varying coefficients of the expansion are stated as degrees of fuzzy membership of a pixel to each of the estimators. Neither a priori knowledge on the noise variance is required nor particular signal and noise models are assumed. Filtering performances on simulated phase images show a steady SNR improvement over conventional box filtering. Applications of the proposed filter to interferometric phase images demonstrate a superior ability of restoring fringes yet preserving their discontinuities, together with an effective noise smoothing performance, irrespective of locally varying coherence characteristics. Keywords and phrases: adaptive filtering, blind estimation, coherence, fuzzy logic, interferometric synthetic aperture radar, phase noise filtering.
1. INTRODUCTION Synthetic aperture radar (SAR) enables imaging of the Earth by processing microwave backscattering data collected along the flight path of an airborne or spaceborne platform. This results in high-resolution images of the local complex ground reflectivity. Given two SAR images obtained from slightly different flight paths, if the complex
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