  We propose a low complexity, graph based linear minimum mean square error
(LMMSE) filter in which the non-white characteristics of a random process are
taken into account. Our method corresponds to block LMMSE filtering, and has
the advantage of complexity linearly increasing with the block length and the
ease of incorporating the a priori information of the input signals whenever
possible. The proposed method can be used with any random process with a known
autocorrelation function with the help of an approximation to an autoregressive
(AR) process. We show through extensive simulations that our method performs
very close to the optimal block LMMSE filtering for Gaussian input signals.
