paper report - IV. ESTIMATOR Objective: ML estimator Where...

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IV. ESTIMATOR Objective: ML estimator Where P is positive since the elements of P (compartmental parameters, concentrations, myocardial thicknesses, and endocardial radii) are physically positive, and with assumption of Poisson measurement noise where k is a constant independent of P . 1. Fisher scoring iteration approximation To solve the non-linear problem, Fisher scoring is used: A = if A converges according to the preset criteria in the n -th iteration. Where And the Fisher information matrix J(P) is Where Diag{ Y(P) } is a diagonal matrix with its elements from Y(P) From B where n is equal to 2 x number of nodes, s m , is the m th element of S, and = (A.3) For a pixelated system with response existing, (A.3) can be approximated by
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where e m is the m -th unit vector and I k ( S : l ) = fraction of pixels lie in the k -th region. 2. positivity constraints on P n to have Implemented by log transformation on A, which yields to P n is forced to be positive for any positive initial P 0 3. Marquardt's method: optimally update The update direction is chosen to lie in between the direction given by the
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paper report - IV. ESTIMATOR Objective: ML estimator Where...

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