Denoising and Completion of Euclidean Distance Matrix from Multiple Observations

For a point set, Euclidean distance matrix (EDM) is the matrix consisting of squared distances between every pair of points in the set. It frequently appears in wide ranging applications such as sensor networks, acoustic arrays, crystallography, and self localization among others. Often the measured EDM are inaccurate (due to noise) and incomplete (due to limited availability of measurements) requiring denoising and completion algorithms, frequently both. In literature, methods based on rank alternation and semi-definite relaxation (SDR) have been successful but are restricted to processing a single noisy and/or incomplete input EDM. In this paper we propose extensions of these two algorithms which can process multiple noisy and incomplete EDM simultaneously. Simulations show that the proposed joint algorithms (which process multiple EDM) outperform the corresponding individual algorithms (which process individual EDM and combine the results). We focus on the challenging case of multiplicative noise.