The blind source extraction (BSE) problem for noisy measurements is addressed using the linear predictor method. Based on a previously proposed method for the noise-free case, we propose a cost function with the effect of noise removed. Two adaptive algorithms are next introduced, one of which is based on minimisation of the normalised mean square prediction error (MSPE), whereas the other minimises the MSPE using prewhitening followed by regularisation of the demixing vector. The successful operation of these algorithms requires the knowledge of the correlation matrix of noise