Blind estimation of interferometric SAR phase images through fuzzy matching-pursuits

This paper presents an original application of fuzzy logic to restoration of interferometric phase images from IFSAR, which are affected by zero-mean uncorrelated noise, whose variance depends on the underlying coherence, thus resulting in a nonstationary random 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 pursuits, 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, e.g., 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. Besides the fact that neither "a priori" knowledge on the noise variance is required, nor a particular signal model is assumed, a performance comparison on simulated noisy images highlights the advantages of the proposed approach. Results on simulated noisy versions of Lenna show a steady SNR improvement of almost 3 dB over Kuan's LLMMSE filtering, irrespective of noise model and intensity. Applications of the proposed filter to interferometric phase images demonstrate a superior ability of preserving fringes discontinuities, together with an effective smoothing performance, irrespective of local coherence characteristics.