Information-Theoretic

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Information-Theoretic ImagingJ. A. O’Sullivan. CMU Seminar, 03/13/2002Alternating Minimization Example• Linear family: p 1 + 2 p 2 = 2• Exponential family: q 1 = exp (v),(q 2 = exp (-v)(min min I(pqEpL|| q)p 2, q 25432100 1 2 3 4 5p 2, q 25432100 1 2 3 4 5p 2, q 21.210.80.60.4p 1, q 1p 2, q 21.210.80.60.4p 1, q 10.20.6 0.8 1 1.2 1.4p 1, q 10.20.6 0.8 1 1.2 1.4p 1, q 120
Information-Theoretic ImagingJ. A. O’Sullivan. CMU Seminar, 03/13/2002Information Geometry• I-divergence is nonnegative, convex in pair (p,q)• Generalization of relative entropy,example of f-divergencef• First triangle equality: p in Lp*argminpLI(p || q)I(p || q) I(p ||p*) I(p*|| q)• Second triangle equality: q in Eq*arg minqEI(p || q)I(p || q) I(p || q*) I(q*||q)21
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Information-Theoretic

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