4 December 2000 Sparsity vs. statistical independence from a best-basis viewpoint
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We examine the similarity and difference between sparsity and statistical independence in image representations in a very concrete setting: use the best basis algorithm to select the sparsest basis and the least statistically- dependent basis from basis dictionaries for a given dataset. In order to understand their relationship, we use synthetic stochastic processes as well as the image patches of natural scene. Our experiments and analysis so far suggest the following: 1) Both sparsity and statistical independence criteria selected similar bases for most of our examples with minor differences; 2) Sparsity is more computationally and conceptually feasible as a basis selection criterion than the statistical independence, particularly for dat compression; 3) The sparsity criterion can and should be adapted to individual realization rather than for the whole collection of the realizations to achieve the maximum performance; 4) The importance of orientation selectivity of the local Fourier and brushlet dictionaries was not clearly demonstrated due to the boundary effect caused by the folding and local periodization.
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Naoki Saito, Naoki Saito, Brons M. Larson, Brons M. Larson, Bertrand Benichou, Bertrand Benichou, } "Sparsity vs. statistical independence from a best-basis viewpoint", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408635; https://doi.org/10.1117/12.408635

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