Higher-Order Statistical Properties Arising from the Non-Stationarity of Natural Signals

The first is that a variety of natural signals can be related through a common modelof spherically invariant random processes, which have the attractive property that the joint densities can be constructed from the one dimensional marginal. The second is that in some cases thenon-stationarity assumption and only second order methods can be explicitly exploited to find a linear basis that is equivalent to independent components obtained with higher-order methods. This is demonstrated on spectro-temporal components of speech. 1 Introduction Recently, considerable attention has been paid to understanding and modeling the non-Gaussian or "higher-order" properties of natural signals, particularly images. Several non-Gaussian properties have been identified and studied. For example, marginal densities of features have been shown to have high kurtosis or "heavy tails", indicating a non-Gaussian, sparse representation. Another example is the "bowtie" shape of conditional distributions of neighboring features, indicating dependence ofvariances [11]. These non-Gaussian properties have motivated a number of image and signal processing algorithms that attempt to exploit higher-order s tatistics of the signals, e.g., for blind source separation. In this paper we show that these previously observed higher-order phenomena are ubiquitous and can be accounted for by a model which simply varies the scale of an otherwise stationary Gaussianprocess. This enables us to relate a variety of natural signals to one another and to spherically invariant random processes, which are well-known in the signal processing literature [6, 3].