We propose a new method for noise reduction using a microphone array. The method takes advantage of the spatial diversity inherent to microphone arrays and optimizes certain criteria, namely, the output signal to noise ratio (SNR) or the mean squared error (MSE), subject to the constraint of spatial prediction that relates the noise free signals captured by the microphones. Simulation results demonstrate that resorting to this new method leads to high rate of noise reduction and low signal distortion.