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)
Search WWH ::




Custom Search