A novel communication efficient scheme for reconstructing a field sensed by spatially scattered sensors is proposed. The field is formed by multiple sources, while a fusion center gathers the sensor measurements. The goal is to reconstruct the field at the fusion center using only the measurements of a small number of sensors. The framework entails learning the correlation structure of the field by determining clusters of correlated sensors observing the same set of sources. Combining moving-average filtering along with principal component analysis applied in the sensor data covariance the number of sources can be determined, while norm-one regularized canonical correlations are utilized to determine the different correlated clusters. A novel iterative interplay of regularized canonical correlations with principal component analysis is designed that determines correctly the correlated clusters as the number of training data goes to infinity. From each cluster only a head sensor transmits data to the fusion center, while the measurements of the remaining sensors are reconstructed using proper linear filters that learn the correlation pattern within a cluster via normalized least mean squares. The novel approach substantially reduces the communication cost. Extensive numerical tests demonstrate the effectiveness of the proposed scheme in field recovery.
- Adaptive filtering
- Communication efficiency
- Field reconstruction
- Norm-one regularized canonical correlation analysis