ICA applied to natural image data

Natural images can be defined as photographic images taken in our natural surroundings. For example, of the images below, those on the left side would be considered part of the class of natural images, as opposed to the various other kinds of images on the right-hand side.

The statistical structure of natural images is important for two reasons:

1. It is needed for any kind of intelligent image-processing. For example, methods for image compression, image denoising, and image interpolation (zooming) all depend (either explicitly or implicitly) on the statistical structure inherent in images.

2. Any kind of visual system (whether that of a machine or an animal) must inherently rely on the structure of the visual data it is working with. Hence, understanding the statistics of natural images is crucial to understanding the visual cortex of the brain.

A fundamental statistical model for natural image statistics is independent component analysis (ICA), which models images as linear superpositions of basis images, with non-Gaussian, independent weighting coefficients. This model, first applied to images by Olshausen and Field, is illustrated below.

When the basis images are optimized to make the model fit actual image data as well as possible, they become oriented, localized, band-pass features, as shown below.

Such features have been widely used in image processing under the name of wavelets. Furthermore, the found decomposition strongly resembles the representation given by simple-cells in the mammalian primary visual cortex.

In summary, it can be said that the image representation given by ICA has been successful with regards to both image processing and visual cortical modeling: First, it has justified many of the methods based on wavelet decompositions by giving them a statistical interpretation; in some cases it has also suggested improvements to the methods. Second, ICA has provide a framework in which to understand cortical early sensory processing. Our work in this project has concentrated on extending these basic results.