Information Technology Reference
In-Depth Information
In the
first step
the matrix
TS
is generated from
X
by the procedure described
in
Section 9.4.3
. This matrix is denoted by
TS
.
Only the set of unipolar leads used for the reconstruction has to be taken into
account. From now on they will be called reconstruction leads.
1
X
is a set of leads:
X X Xi Xm
=
{
(1),
……
,
( ),
,
(
)},
(9.17)
2
2
2
2
where
m
is the number of leads.
For the reconstruction method only a subset of
X
is used, e.g., for four recon-
struction leads denoted as:
{
}
A XiXjXkXl ijkl m
=
( ),
( ),
( ),
( ) ,
,
,
,
∈…
{1,
, }
(9.18)
2
2
2
2
Although we concentrated on four reconstruction leads, their number is arbitrary
but must be less than
m
. The selection procedure for reconstruction leads is
described in
Section 9.4.3.2
.
Lead sets
X
and
A
can alternatively be given in a matrix form:
[ ]
2
A n X nm
=× =×
4 ,
[
],
(9.19)
where
n
is the number of samples. The indices of the reconstruction leads from the
X
leads set form a set of indices:
{ }
I ijkl
=
,,, .
(9.20)
In the
next step
of the algorithm the information contained in
A
, is moved to the
coordinate system defined by PCs. That is accomplished according to Eq. (9.16),
which requires a matrix
TS
(a sorted eigenvector matrix of
X
) obtained from the
2
second MECG. Since
X
would not exist if only the reconstruction leads were used,
we cannot calculate
TS
. However, in our previous work [
27
], we have shown that
the PCs may be considered constant for a person, if nothing drastic, such as heart
surgery happens to the heart. We can formulate this statement in the form:
2
TS
=
TS
2
.
(9.21)
1
Equation (9.16) also expects
X
as the last operand. Only reconstruction leads
A
of set
X
are measured, so we define a new matrix
AE
, with the same size as
X
, but
with all lead vectors equal to 0, except the leads from the set
A
, i.e., the leads that
have indices from the set
I
:
AE j
()
=
X j
()
if j
∈
I
(9.22)
2
( )
AE j
() 0
=
if not
j
∈
I
,
where
()
AE j
and
Xj
are the
j
th lead vector (
j
th columns) of
AE
and
X
2
,
2
()
respectively.
By utilizing Eqs. (9.21) and (9.22), Eq. (9.16) becomes:
)
T
1
( )· ,
−
T
(
AE
¢
=
TS
AE
(9.23)
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