The pi M algorithm: A method for interferometric image reconstruction in SAR/SAS

• Published in: IEEE transactions on image processing 2002-04, Vol.11 (4), p.408-422
• Main Authors: Dias, Jose M B, Leitao, Jose M N
• Format: Article
• Language: English
• ISSN: 1057-7149

This paper presents an effective algorithm for absolute phase (not simply modulo-2 pi ) estimation from incomplete, noisy and modulo-2 pi observations in interferometric aperture radar and sonar (InSAR /InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2 pi -periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (-step), implemented by network programming techniques and an iterative conditional modes (ICM) step ( pi -step). Accordingly, the algorithm is termed pi M, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2 pi -multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.