Distributed Karhunen-Loève Transform with nested subspaces

A network in which sensors observe a common Gaussian source is analyzed. Using a fixed linear transform, each sensor compresses its high-dimensional observation into a low-dimensional representation. The latter is provided to a central decoder that reconstructs the source according to a mean squared error (MSE) distortion metric. The distributed Karhunen-Loeve Transform (d-KLT) has been shown to provide a (locally) optimal linear solution for compression at each sensor. While the d-KLT achieves the lowest distortion linear reconstruction known, it does not maintain a nested subspace structure. In the case of ideal links to the decoder, this paper presents transforms that maintain nested subspaces, allowing the decoder to approximate a delay-limited source in an online fashion according to a desired sensor schedule. A distortion envelope for one distributed transform with nested subspace properties (d-nested-KLT) is provided. In the case of i.i.d. noise to the decoder, under assumptions of power allocation over subspaces, it is also possible to achieve nested subspaces utilizing correlations between sensors´ observations. Results are applicable for data access over networks, and online information processing in sensor networks.