Multichannel Phase Unwrapping: Problem Topology and Dual-Level Parallel Computational Model

In the theoretical purview of the discrete Calculus, a rigorous gradient-based formulation of the multichannel phase unwrapping (MCh-PhU) problem is systematically established in terms of discrete differential operators, which are defined by the topology of the intrinsically discrete spaces upon which they act, thus capturing the essential topological character of the problem within a suitable matrix formalism and providing interesting implications. Within this methodological framework, the extended minimum cost flow (EMCF) algorithm, which provides an effective strategy aimed at solving the MCh-PhU problem, is revised, and its computational structure is analyzed. A parallel formulation of the computational-intensive EMCF algorithm is then presented. Emphasis is placed on the methodological and practical aspects leading to a novel dual-level parallel computational model in which the parallelism is hierarchically implemented at two different levels. Performance evaluation relevant to the implemented prototype solution is also carried out, thus quantifying the benefit of parallelism at different levels. The significant experimentally achieved speedup demonstrates the validity of our approach. As a result, the attained parallel prototype enables the large-scale solution of the MCh-PhU problem in a reasonable time frame, with a great impact on systematic exploitation of the available SAR archives.