Recovering independent components from shifted data using fast independent component analysis and swarm intelligence

Frequency displacement, or spectral shift, is commonly observed in industrial spectral measurements. It can be caused by many factors such as sensor de-calibration or by external influences, which include changes in temperature. The presence of frequency displacement in spectral measurements can cause difficulties when statistical techniques, such as independent component analysis (ICA), are used to analyze it. Using simulated spectral measurements, this paper initially highlights the effect that frequency displacement has on ICA. A post-processing technique, employing particle swarm optimization (PSO), is then proposed that enables ICA to become robust to frequency displacement in spectral measurements. The capabilities of the proposed approach are illustrated using several simulated examples and using tablet data from a pharmaceutical application.