Mathematics Colloquia and Seminars

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In this talk, I will discuss the two important issues in image representation; sparsity and statistical independence. Sparsity is important for data compression whereas the statistical independence is also important for reducing redundancy in images and useful for stochastic modeling. Many researchers in neuroscience have suggested these criteria may in fact be used to form the feature detectors in our visual cortex. I will clarify the difference between the sparsity and statistical independence using from simple synthetic examples to more complicated natural scene data, use the best basis algorithm to select the sparsest basis and the least statistically-dependent basis, and compare these two bases. Although the statistical independence is important for certain applications such as building stochastic models, our experiments suggest that the sparsity seems to be a more plausible mechanism for efficient coding of natural scenes.