IL NUOVO CIMENTO Vol. 24 C, N. 1 Gennaio-Febbraio 2001 Global approaches and local strategies for phase unwrapping ( ∗ )( ∗∗ ) L. Guerriero( 1 ), A. Refice( 1 )( ∗∗∗ ) S. Stramaglia( 1 ), G. Satalino( 2 ) N. Veneziani( 2 ), P. Blonda( 2 ), G. Pasquariello( 2 ) and M. T. Chiaradia( 1 ) ( 1 ) Dipartimento Interateneo di Fisica - Via Amendola 173, 70126 Bari (Italy) ( 2 ) Istituto Elaborazione Segnali ed Immagini, C.N.R. - Via Amendola 166/5, 70126 Bari (Italy) (ricevuto il 12 Novembre 1999; revisionato il 6 Giugno 2000; approvato il 26 Giugno 2000) Summary. — Phase unwrapping, i.e. the retrieval of absolute phases from wrapped, noisy measures, is a tough problem because of the presence of rotational inconsis- tencies (residues), randomly generated by noise and undersampling on the principal phase gradient field. These inconsistencies prevent the recovery of the absolute phase field by direct integration of the wrapped gradients. In this paper we examine the relative merit of known global approaches and then we present evidence that our approach based on “stochastic annealing” can recover the true phase field also in noisy areas with severe undersampling, where other methods fail. Then, some ex- periments with local approaches are presented. A fast neural filter has been trained to eliminate close residue couples by joining them in a way which takes into account the local phase information. Performances are about 60–70% of the residues. Fi- nally, other experiments have been aimed at designing an automated method for the determination of weight matrices to use in conjunction with local phase unwrapping algorithms. The method, tested with the minimum cost flow algorithm, gives good performances over both simulated and real data. PACS 07.05.Pj – Image processing. PACS 07.05.Mh – Neural networks, fuzzy logic, artificial intelligence. PACS 02.60.Pn – Numerical optimization. 1.–Introduction Phase unwrapping is a problem which arises in various realms of signal processing, in particular Synthetic Aperture Radar Interferometry (INSAR) [1]. It consists of retrieving ( ∗ ) Paper presented at the Workshop on Synthetic Aperture Radar (SAR), Florence, 25-26 February, 1998. ( ∗∗ ) The authors of this paper have agreed to not receive the proofs for correction. ( ∗∗∗ ) Support for this work was provided through a post-doc grant by the Istituto Nazionale di Fisica della Materia (INFM). c  Societ` a Italiana di Fisica 205 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Scientific Open-access Literature Archive and Repository