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Independent Component Analysis - Chapter 21: Feature Extraction by ICA

A fundamental approach in signal processing is to design a statistical generative model of the observed signals. The components in the generative model then give a representation of the data. Such a representation can then be used in such tasks as compression, denoising, and pattern recognition. This approach is also useful from a neuroscientific viewpoint, for modeling the properties of neurons in primary sensory areas. In this chapter, we consider a certain class of widely used signals, which we call natural images | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic Part IV APPLICATIONS OFICA Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 21 Feature Extraction by ICA A fundamental approach in signal processing is to design a statistical generative model of the observed signals. The components in the generative model then give a representation of the data. Such a representation can then be used in such tasks as compression denoising and pattern recognition. This approach is also useful from a neuroscientific viewpoint for modeling the properties of neurons in primary sensory areas. In this chapter we consider a certain class of widely used signals which we call natural images. This means images that we encounter in our lives all the time images that depict wild-life scenes human living environments etc. The working hypothesis here is that this class is sufficiently homogeneous so that we can build a statistical model using observations of those signals and then later use this model for processing the signals for example to compress or denoise them. Naturally we shall use independent component analysis ICA as the principal model for natural images. We shall also consider the extensions of ICA introduced in Chapter 20. We will see that ICA does provide a model that is very similar to the most sophisticated low-level image representations used in image processing and vision research. ICA gives a statistical justification for using those methods that have often been more heuristically justified. 391 392 FEATURE EXTRACTION BY ICA 21.1 LINEAR REPRESENTATIONS 21.1.1 Definition Image representations are often based on discrete linear transformations of the observed data. Consider a black-and-white image whose gray-scale value at the pixel indexed by a and is denoted