Decentralized reconstruction from compressive random projections driven by principal components

The decentralized reconstruction of data acquired m a sensor network via compressive random projections is considered. Assuming each node acquires a signal while simultaneously reducing its dimensionality, the proposed decentralized reconstruction recovers each signal to its original dimensionality with the reconstruction process being distributed across the network such that each node performs limited computation with limited communication with its neighboring nodes. In contrast to prior decentralized reconstructions driven by sparsity-based compressed-sensing techniques, the proposed approach employs reconstruction based on principal component analysis using an iterative consensus algorithm to calculate the required covariance across the network. Experimental results reveal that the performance of the proposed decentralized reconstruction approaches that of the original centralized algorithm as the number of consensus iterations increases.