An adaptive noise reduction filter composed of a sandglass-type neural network (SNN) noise reduction filter (RF) is proposed in this paper. SNN was originally devised to work effectively for information compression. It is a hierarchial network and is symmetrically structured. SNN consists of the same number of units in the input and output layers and a smaller number of units in the hidden layer. It is known that SNN has signal processing performance which is equivalent to KarhunenLoeve expansion after learning.
We proved the theoretical suitability of SNN for an adaptive noise reduction filter for discrete signals. The SNNRF behaves optimally when the number of units in the hidden layer is equal to the rank of the covariance matrix of the signal components included in the input signal. Further we show by applying the recursive least squares method to learning of the SNNRF that the filter can process signals for on-line adaptive noise reduction. This is an extremely desirable feature for practical application.
In order to verify the validity of SNNRF, we performed computer experiments examining how the noise reduction ability of SNNRF is affected by altering the properties of the input pattern, learning algorithm, and SNN. The results confirm that the SNNRF acquired appropriate characteristics for noise reduction from the input signals, and markedly improved the SNR of the signals.