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lines changed Original file line number Diff line number Diff line change @@ -307,13 +307,13 @@ first voxel in the last (slice index = $N-1$) slice to mm space. So:
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.. math ::
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- \left (\begin {smallmatrix}T^N\\ 1 \end {smallmatrix}\right ) = A \left (\begin {smallmatrix}0 \\ 0 \\- 1 + N \\ 1 \end {smallmatrix}\right )
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+ \left (\begin {smallmatrix}T^N\\ 1 \end {smallmatrix}\right ) = A \left (\begin {smallmatrix}0 \\ 0 \\ N - 1 \\ 1 \end {smallmatrix}\right )
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From this it follows that:
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.. math ::
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- \begin {Bmatrix}k_{{1 }} : \frac {T^{1 }_{{1 }} - T^{N }_{{1 }}}{1 - N }, & k_{{2 }} : \frac {T^{1 }_{{2 }} - T^{N }_{{2 }}}{1 - N }, & k_{{3 }} : \frac {T^{1 }_{{3 }} - T^{N }_{{3 }}}{1 - N }\end {Bmatrix}
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+ \begin {Bmatrix}k_{{1 }} : \frac {T^{N }_{{1 }} - T^{1 }_{{1 }}}{N - 1 }, & k_{{2 }} : \frac {T^{N }_{{2 }} - T^{1 }_{{2 }}}{N - 1 }, & k_{{3 }} : \frac {T^{N }_{{3 }} - T^{1 }_{{3 }}}{N - 1 }\end {Bmatrix}
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and therefore:
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@@ -324,7 +324,7 @@ and therefore:
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.. math ::
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- A_{multi} = \left (\begin {smallmatrix}F_{{11 }} \Delta {r} & F_{{12 }} \Delta {c} & \frac {T^{1 }_{{1 }} - T^{N }_{{1 }}}{1 - N } & T^{1 }_{{1 }}\\ F_{{21 }} \Delta {r} & F_{{22 }} \Delta {c} & \frac {T^{1 }_{{2 }} - T^{N }_{{2 }}}{1 - N } & T^{1 }_{{2 }}\\ F_{{31 }} \Delta {r} & F_{{32 }} \Delta {c} & \frac {T^{1 }_{{3 }} - T^{N }_{{3 }}}{1 - N } & T^{1 }_{{3 }}\\ 0 & 0 & 0 & 1 \end {smallmatrix}\right )
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+ A_{multi} = \left (\begin {smallmatrix}F_{{11 }} \Delta {r} & F_{{12 }} \Delta {c} & \frac {T^{N }_{{1 }} - T^{1 }_{{1 }}}{N - 1 } & T^{1 }_{{1 }}\\ F_{{21 }} \Delta {r} & F_{{22 }} \Delta {c} & \frac {T^{N }_{{2 }} - T^{1 }_{{2 }}}{N - 1 } & T^{1 }_{{2 }}\\ F_{{31 }} \Delta {r} & F_{{32 }} \Delta {c} & \frac {T^{N }_{{3 }} - T^{1 }_{{3 }}}{N - 1 } & T^{1 }_{{3 }}\\ 0 & 0 & 0 & 1 \end {smallmatrix}\right )
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A_{single} = \left (\begin {smallmatrix}F_{{11 }} \Delta {r} & F_{{12 }} \Delta {c} & \Delta {s} n_{{1 }} & T^{1 }_{{1 }}\\ F_{{21 }} \Delta {r} & F_{{22 }} \Delta {c} & \Delta {s} n_{{2 }} & T^{1 }_{{2 }}\\ F_{{31 }} \Delta {r} & F_{{32 }} \Delta {c} & \Delta {s} n_{{3 }} & T^{1 }_{{3 }}\\ 0 & 0 & 0 & 1 \end {smallmatrix}\right )
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