Filtering of Interferometric SAR Phase Images as a Fuzzy Matching-Pursuit Blind Estimation

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.