We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by l{1}-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as Eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

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Abstract-Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

Abstract-When data are transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network, both observation and control packets may be lost or delayed. This process can be modeled by assigning probabilities to successfully receive packets. Determining the impact of this uncertainty on the feedback-loop requires a generalization of classical control theory. This paper presents the foundations of such new theory.Motivations and overview of the efforts of different research groups are described first. Then, novel contributions of the authors are presented. These include showing threshold behaviors which are governed by the uncertainty parameters of the communication network: for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g. TCP-like protocols), there exists critical probabilities for the successful delivery of packets, below which the optimal controller fails to stabilize the system. Furthermore, for these protocols, the separation principle holds and the optimal LQG control is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear.

Abstract-Motivated by our experience in building sensor networks for navigation as part of the Networked Embedded Systems Technology (NEST) project at Berkeley, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multi-hop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded error occurs.