Pei Xie

Keyou You, Qizhu Chen, Pei Xie et al.

This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements. The network consists of target nodes, each of which has only access position information in a local fixed coordinate frame, and anchor nodes with GPS position information. To localize target nodes, we aim to align their coordinate frames, which leads to a non-convex optimization problem over a rotation group $\text{SO}(3)$. Then, we reformulate it as an optimization problem with a convex objective function over spherical surfaces. We explicitly design both iterative and recursive algorithms for localizing a target node with an anchor node, and extend to the case with multiple target nodes. Finally, the advantages of our algorithms against the literature are validated via simulations.

Keyou You, Roberto Tempo, Pei Xie

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a "global solution" of the scenario problem (SP), we resort to {\it multiple interconnected processors} that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual sub-gradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum_{t=1}^kζ^t))$ where $\{ζ^t\}$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms.

Pei Xie, He-Feng Yin, Xiao-Jun Wu

Face recognition remains a hot topic in computer vision, and it is challenging to tackle the problem that both the training and testing images are corrupted. In this paper, we propose a novel semi-supervised method based on the theory of the low-rank matrix recovery for face recognition, which can simultaneously learn discriminative low-rank and sparse representations for both training and testing images. To this end, a correlation penalty term is introduced into the formulation of our proposed method to learn an incoherent dictionary. Experimental results on several face image databases demonstrate the effectiveness of our method, i.e., the proposed method is robust to the illumination, expression and pose variations, as well as images with noises such as block occlusion or uniform noises.