Complex-valued independent component analysis of natural images

Authors:
Valero Laparra;Michael U. Gutmann;Jesús Malo;Aapo Hyvärinen
Affiliations:
Image Processing Laboratory, Universitat de València, Spain;Department of Computer Science, Department of Mathematics and Statistics, Helsinki Institute for Information Technology, University of Helsinki, Finland;Image Processing Laboratory, Universitat de València, Spain;Department of Computer Science, Department of Mathematics and Statistics, Helsinki Institute for Information Technology, University of Helsinki, Finland
Venue:
ICANN'11 Proceedings of the 21st international conference on Artificial neural networks - Volume Part II
Year:
2011

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Abstract

Linear independent component analysis (ICA) learns simple cell receptive fields fromnatural images. Here,we showthat linear complex-valued ICA learns complex cell properties from Fourier-transformed natural images, i.e. two Gabor-like filters with quadrature-phase relationship. Conventional methods for complex-valued ICA assume that the phases of the output signals have uniform distribution. We show here that for natural images the phase distributions are, however, often far from uniform. We thus relax the uniformity assumption and model also the phase of the sources in complex-valued ICA. Compared to the original complex ICA model, the new model provides a better fit to the data, and leads to Gabor filters of qualitatively different shape.