标题： 扩散MRI中球面采样的调和分析 显示英文标题

标题： Harmonic analysis of spherical sampling in diffusion MRI

摘要： 在过去十年中，扩散MRI已成为一种强大的工具，用于非侵入性地研究大脑白质的完整性。 最近，许多研究小组将注意力集中在多壳球面采集上，旨在通过较少的q空间样本有效映射扩散信号，从而显著减少采集时间。 在此背景下，一个常被研究的量是所谓的方向分布函数（ODF）。 在这一框架下，球面谐波（SH）变换因其能够高效且准确地执行卷积操作而广受欢迎，例如用于从q空间数据计算ODF所需的Funk-Radon变换。 然而，如果在任何探测的b值处，q空间信号的角分辨率不合适，则不可避免地会产生混叠（或插值）伪影。 到目前为止，这一方面仅通过经验方法处理，据我们所知，尚无研究以定量方法解决这一问题。 本文的目的在于更理论地研究多壳球面采样的效率，以便更好地理解HYDI类方法，可能为进一步的优化策略铺平道路。 显示英文摘要

摘要： In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of effectively mapping the diffusion signal with a lower number of q-space samples, hence enabling a crucial reduction of acquisition time. One of the quantities commonly studied in this context is the so-called orientation distribution function (ODF). In this setting, the spherical harmonic (SH) transform has gained a great deal of popularity thanks to its ability to perform convolution operations efficiently and accurately, such as the Funk-Radon transform notably required for ODF computation from q-space data. However, if the q-space signal is described with an unsuitable angular resolution at any b-value probed, aliasing (or interpolation) artifacts are unavoidably created. So far this aspect has been tackled empirically and, to our knowledge, no study has addressed this problem in a quantitative approach. The aim of the present work is to study more theoretically the efficiency of multi-shell spherical sampling in diffusion MRI, in order to gain understanding in HYDI-like approaches, possibly paving the way to further optimization strategies.