Abstract
An adaptive noise reduction filter composed of cascaded sandglass-type neural networks (CSNNRF) is proposed. A given number of unit sandglass-type neural networks (SNN), each of which has a three-layer structure and consists of a same number of neural units in the input and the output layers and a single neural unit in the hidden layer, are connected in cascade. The number of unit SNNsis adaptively determined so as to be equal to a rank of covariance matrix of an original noise-free signal (signal component). Outputs of hidden layer units in individual unit SNNs, whose variances are equivalent to eigenvalues of the covariance matrix of the observed signal, are statistically compared by use of ANOVA (analysis of variance) to estimate the rank. When a CSNNRF is composed of the number of unit SNNs equal to the rank, the observed signal is filtered without any loss of signal component while noise component is maximally reduced. It was shown by computer experiments that the rank was almost always estimated accurately in an adaptive manner, and that noise reduction from the signal was carried out optimally.
