Contributions to ICA of natural images

In this paper we analyze the results provided by the popular algorithm FastICA when it is applied to natural images, using the kurtosis as non-linearity. In this case show that the so-called ICA filters can be expressed in terms of the eigenvectors associated to the smallest eigenvalues of the data correlation matrix, meaning that these filters are all high-pass. From this property emerges the sparse distribution of the independent components. On the other hand, the use of the kurtosis as contrast function causes the appearance of “spikes” in the independent components that make that the ICA bases are very similar to patches of the images analyzed. Some experiments are included to illustrate the results.