A multi-criteria method for noise reduction

The article presents two multi-criteria methods for noise reduction. The idea of these methods is based on a combination of two criteria. The first criterion is the sum of squares of the finite differences of the first and/or the second order. The second criterion is square difference of input signal and its evaluation. In the work, we prove the convergence and uniqueness of solutions obtained. We discuss influence of method's parameters on the result of noise reduction. On the set of test signals, we show the effectiveness of smoothing and noise reduction.