Independent components of natural images under variable compression rate

A generalized ICA model allowing overcomplete bases and additive noises in the observables is applied to natural image data. It is well known that such a model produces independent components that resemble simple cells in primary visual cortex or Gabor functions. We adopt a variable-sparsity density on each independent component, given by the mixture of a delta function and a standard Gaussian density. In the experiment, we observe that the aspect ratios of the optimal bases increase with the noise level and the degree of sparsity. The meaning of this phenomenon is discussed.