Noise power reduction through comparison with another statistically dependent noise

Consider a signal s(t) in presence of an additive noise n(t) and suppose that another noise v(t), statistically dependent on n(t), is available. This paper discusses the problem of the above mentioned statistical dependence in order to reduce the power of the noise n(t). No hypotheses on the signal nature are being made. The use of linear networks is examined in detail and we show how the noise power can be reduced to a lower limit which depends on the cross-correlation function of n(t) and v(t).