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We employ the simulated annealing method in order to restore signals that may contain peaks we wish to preserve but, otherwise, are smooth and buried in colored noise. The problem is formulated as a global optimization one. We propose a piecewise linear model for the noise-free signal that is appropriate for preserving peaks that are often encountered in biomedical or industrial signals. An iterative algorithm is proposed. The restored signal is used to estimate the model parameters that are subsequently used to improve the signal estimation. The algorithm stops when self-consistency has been achieved, i.e., the estimated values of the noise model parameters agree to within the accuracy of their estimation with the parameters used to restore the signal. Application of the method to simulated data with various levels of noise showed that the underlying signal can be restored sufficiently well. The algorithm is also applied to some evoked-response magneto-encephalographic data, as well as to some signals from an automatic industrial inspection problem. Our results are compared with those obtained by using the iterative conditional modes algorithm and shown to be better in terms of preserving the peaks in the signals.