# 敏感度編碼技術

## 核磁共振影像的成像原理

${\displaystyle \omega =\gamma B}$

## 加速影像的基本概念

${\displaystyle ScanTime=NEX\times \#{\mbox{ phase encoding}}\times TR}$

## SENSE的理論基礎

### 數學描述

${\displaystyle I(x,y)=C(x,y)M(x,y)}$

${\displaystyle I_{j}(x,y)=C_{j}(x,y)M(x,y){\mbox{ , subscript j means j-th coil}}}$

${\displaystyle I_{j}(y)=\sum _{n=0}^{N_{A}-1}C_{j}(y+{\frac {nL}{R}})M(y+{\frac {nL}{R}}){\mbox{ , }}N_{A}{\mbox{ is the number of replicates on position y }}}$

${\displaystyle I=CM}$

${\displaystyle I={\begin{bmatrix}I_{0}(y)\\I_{1}(y)\\\vdots \\I_{c-1}(y)\end{bmatrix}}}$

${\displaystyle M={\begin{bmatrix}M(y)\\M(y+{\frac {L}{R}})\\\vdots \\M(y+(N_{A}-1){\frac {L}{R}})\end{bmatrix}}}$

${\displaystyle C={\begin{bmatrix}C_{0}(y)&\cdots &C_{0}(y+(N+{A}-1){\frac {L}{R}})\\\vdots &\ddots &\vdots \\C_{N_{c}-1}(y)&\cdots &C_{N_{c}-1}(y+(N+{A}-1){\frac {L}{R}})\end{bmatrix}}}$

## 資料來源

1. Matt A. Bernstein, Kevin F. King, Xiaohong Joe Zhou. Handbook of MRI Pulse Sequences. USA: Elsevier Academic Press. 2004: 527–531. ISBN 978-0-12-092861-3.
2. 商玉英. 關于MRI成像過程若干技術問題的探討. 中華現代影像學雜志. 2005-11-08. （原始内容存档于2015年4月26日）.

## 參考文獻

1. ^ Pruessmann, Klaas; Weiger, Markus ; Scheideggar, Markus ; Boesiger, Peter. "SENSE: Sensitivity Encoding for Fast MRI". Magnetic Resonance in Medicine. 1999, 42: 952 – 962.