The nonparametric decentralized detection problem is investigated, in which the joint distribution of the environmental event and the sensors' observations are not known and only a set of training samples are available. The system features rate constraints, i.e., integer bit constraints on sensors' transmissions, different qualities of observations, additional observations to the fusion center, and multi-level tree-structured network. Our study adopts the kernel-based nonparametric approach proposed by Nguyen, Wainwright, and Jordan with the following generalization. A weighted count kernel is introduced so that the corresponding reproducing kernel Hilbert space (RKHS) (over which the fusion center's decision rule is optimized) allows the fusion center's decision rule to count information from sensors and its own observations differently. In order to find the optimal decision rules, our optimization is solved by alternatively and recursively conducting three optimization steps: finding the optimal weight parameters in the weighted count kernel for selecting the best associated RKHS, finding the best optimal decision rule for the fusion center over the identified RKHS, and finding the local decision rules for sensors. Generalization to multilevel tree-structured networks is also discussed. Finally numerical results are provided to demonstrate the performance based on the proposed weighted count kernel.

In this paper, we propose a simple interactive way for a novel type of image synthesis called image rearrangement whose goal is to construct a new image based on some objects cropped from source images. The synthesis results are obtained by copying patches from the source images in a globally consistent way. The patch copying problem is formulated with the Markov random field model, and belief propagation is used as the optimization tool. To speed up our algorithm, a two-step belief propagation and a multi-scale patch copying scheme are taken. Experimental results indicate that our algorithm obtains satisfactory results in both performance and efficiency.