本文旨在提出一些不同於傳統方式的訊號取樣法應用於擴散頻譜攝影（diffusion spectrum imaging, DSI）。使用這些取樣法，理論上將能縮減60%的取樣時間。
為了減少擴散頻譜攝影的訊號擷取時間，本文首先將提出均勻分佈的體心堆積(body-center-cubic, BCC)取樣晶格（sampling lattice）取樣法。對於頻譜是圓球型有限（spherical band-limited）的訊號，使用體心堆積取樣晶格取樣法將能提供相較於傳統笛卡兒（Cartesian）取樣晶格取樣法高30%的取樣效率。由於擴散頻譜攝影的水分子運動機率密度函數同樣是圓球型有限，故應用體心堆積取樣晶格取樣法於其頻域Q空間，理論上能夠減少30%擴散頻譜攝影的資料量同時意味著縮短30%的訊號擷取時間。
由於水分子擴散的機率密度函數（probability density function, PDF）為正值，所以半傅立葉方法（half-Fourier method）也可以應用在擴散頻譜攝影中，即只要在Q空間中擷取半圓球內的訊號即可。如此一來擴散頻譜攝影的訊號擷取時間得以經由半傅立葉方法再縮短40~50%。然而Q空間訊號可能存在著中心偏移（center-shift）的問題，所以本文提出交錯型半球取樣法（half-and-interlaced-spherical sampling scheme）來實現半傅立葉方法並提供校正中心偏移的能力。
另外本文提出了離散頻譜傅立葉轉換（discrete spectrum Fourier transform, DSFT）重建法使得空間中任意位置的機率密度函數得以不經由內差法而直接求取其值來解決次體積（sub-voxel）重建的問題。
經由實驗可發現，合併使用體心堆積和交錯型半球取樣法以及離散頻譜傅立葉轉換重建法得以減少80%擴散頻譜攝影的資料擷取時間，並提供合理的組織纖維走向圖（tractography）。

This thesis presents some innovative techniques useful for the diffusion spectrum imaging (DSI) in the sense that they can be applied together to significantly reduce the data acquisition time up to 60% theoretically.
In order to shorten the data acquisition time of diffusion spectrum imaging (DSI), homogeneous q-space sampling using body-center-cubic (BCC) lattice is proposed. For spherical band-limited 3D signal, the sampling efficiency of BCC is 30% higher than that of conventional Cartesian scheme. Because probability density function (PDF) of water molecular motion of DSI is spherical band-limited, BCC sampling scheme is applicable and may reduce sampling data up to 30% theoretically, which means 30% reduction of data acquisition time.
Since probability density function of water molecular motion is positive, half-Fourier method can be introduced, i.e. only q-space data within half sphere is sufficient to reconstruct PDF, for additional 40~50% of acquisition time reduction. Because there might be center-shift problem for DSI data, half-and-interlaced-spherical acquisition scheme (HIS) is proposed for correcting this artifacts when half-Fourier method is used.
Discrete spectrum Fourier transform (DSFT) is proposed to reconstruct PDF directly on arbitrarily selected positions without interpolation and therefore solves the encountered sub-voxel-reconstruction problem.
Experiments show that reasonable results of tractography can be achieved with 80% reduction of data acquisition time using BCC and HIS sampling scheme and DSFT reconstruction.

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