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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 nonlinear 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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View Full Documentwhere 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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 Spring '08
 Wakefield

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