On the estimation and compression of distributed correlated signals with incomplete observations

In this paper we study the problem of optimal compression and signal reconstruction based on distributed correlated observations of the signal. In the mean square estimation context this involves finding the optimal signal representation based on multiple incomplete or only partial observations which are correlated. In particular this leads to the study of finding the optimal Karhunen-Loève basis based on the censored observations. We give a precise characterization of the necessary conditions with or without side information. We also provide new insights into the structure of the problem. In particular, we show that a recently proposed scheme provides estimates that satisfy only necessary conditions for optimality and hence can be sub-optimal.