Minimum mean square error (MMSE) is a signal processing criterion which attempts to minimize the mean square error of a processing output. The mean square error can be given by MSE = E[(X - X_m)^2] where X_m is the average of X and E[\cdot] is the average operator.

In particular, using the MMSE criterion the processing w(\cdot) can be optimize as

w_o = \min_{w} E{(w(X) - X_m)^2}

where w_o is the optimal processing in the sense of MMSE.

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