Abstract:

Minimum entropy deconvolution (MED) is a technique with the purpose of separating the components of a signal, as the convolution model of a smooth wavelet with a series of impulses. The advantage of this method, as compared with traditional methods, is that it obviates strong hypotheses over the components, which require only the simplicity of the output. The degree of simplicity is measured with the Varimax norm for factor analysis. An iterative algorithm for computation of the filter is derived from this norm, having as an outstanding characteristic its stability in presence of noise. Geometrical analysis of the Varimax norm suggests the definition of a new criterion for simplicity: the D norm. A section of numerical examples is included, where the results of an extensive simulation study with synthetic data are analyzed. The numerical computations show in all cases a remarkable improvement resulting from use of the D norm. The properties of stability in the presence of noise are preserved as shown in the examples.-from Author