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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