Extracting post-nonlinear signals based on Gaussianizing transformation

The problem of extracting the desired source as the first output from the post-nonlinear (PNL) mixture is addressed in this paper. The proposed solution is a two-stage process that consists of a Gaussianizing transformation and extracting the desired source with specific kurtosis range. First, the nonlinear distortions in the PNL mixture are compensated by the Gaussianizing transformation. Then, the prior knowledge about the desired source, such as their normalized kurtosis range, is treated as constraints and incorporated into the contrast function to form a constrained optimization problem. Finally, the desired source is extracted by minimizing this constrained optimization problem with standard gradient descent method. The validity and performance of the proposed solution are confirmed through extensive computer simulations and experiments on real-world ECG data.