Homeopathic ICA: A simple approach to expand the use of independent component analysis (ICA)

• A pre-processing method to extend the use of independent image analysis
• Simple examples of the pre-processing technique
• Actual chemical image data of energy dispersive X-ray spectrometry (EDS) of a Cu–Ni diffusion couple and a braze interface

Independent component analysis (ICA) is an increasingly popular method to resolve complex data sets, such as chemical image data, into images and their associated spectra. Unfortunately, the pre-requisite of statistical independence severely limits the application of ICA. In this paper we will show that, for a certain class of data, increasing the sparsity of a data set increases the independence of components, which enables the successful application of ICA. The sparsity can be increased by simply adding zeros to the data set or by applying a Haar-wavelet transform. ICA will be explained using simple numerical examples and actual data sets obtained by energy dispersive X-ray spectrometry (EDS) of a Cu–Ni diffusion couple and a braze interface.