Information-Theoretic

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Information-Theoretic ImagingJ. A. O’Sullivan. CMU Seminar, 03/13/2002Alternating Minimization Algorithms• Define problem as min q (q) (q)• Derive Variational Representation: (q) (q) = min p J(p,q)• J is an auxiliary function p is in auxiliary set P• Result: double minimization min q min p J(p,q)• Alternating minimization algorithmpq( l1)( l1)argminpPargminqQJ ( p,qJ ( p( l)( l1)), q)Comments: Guaranteed Monotonicity; J selected carefully18
Information-Theoretic ImagingJ. A. O’Sullivan. CMU Seminar, 03/13/2002Alternating Minimization Algorithms:I-Divergence, Linear, Exponential Families• Special Case of Interest: J is I-divergenceI• Families of Interest:Linear Family L(A,b) = {p: Ap = b}Exponential Family E(,B) = {q: q i = i exp[ j b ij j ]}pq( l1)( l1)argminpLargminqEI(p || qI(p( l1)( l))|| q)Csiszár and Tusnádydy; Dempster, , Laird, Rubin; Blahut;Richardson; Lucy; Vardi, Shepp, , and Kaufman; Cover;Miller and Snyder; O'Sullivan19
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