= Derek Jones
{disambiguate=magnetic resonance researcher}
{c}
= Derek K. Jones
{c}
{synonym}
\b[Derek Jones] is a physicist at Cardiff University whose research develops quantitative <magnetic resonance imaging>, especially <diffusion tensor imaging>. He trained in <physics> at Nottingham, <medical physics> at Leeds and completed a Leicester doctorate on <diffusion tensor imaging>. His work asks how acquisition design changes what can be inferred from a measured <signal>.<Derek Jones profile at Cardiff University>[Overview, Research and Biography: research focus and1993/1995/1998 education]{ref}
\Image[https://profiles-cardiff.imgix.net/attachments/4543?auto=format&crop=faces&fit=crop&h=200&w=200]
{title=Derek Jones, from his labeled Cardiff University staff-profile portrait}
{height=200}
Jones investigated how <diffusion MRI gradient sampling> affects the <measurement uncertainty> of inferred <diffusion tensors>. In 2004, Jones used <Monte Carlo simulations> to compare sampling schemes at a <diffusion weighting b-value> of $1000\,\mathrm{s/mm^2}$, tracking tensor orientation, <trace> and <fractional anisotropy>. It showed why a minimal set of directions need not give robust estimates; its numerical findings belong to the tested models and noise conditions.<The effect of gradient sampling schemes on measures derived from diffusion tensor MRI: A Monte Carlo study by Derek K. Jones>[Original abstract: controlled b-value, tensor-derived outcomes and comparison of angular sampling schemes]{ref}
An earlier conference report made the comparison with a fixed observation budget: one baseline and 60 diffusion-weighted observations. Six unique orientations repeated 10 times and 30 orientations repeated twice therefore used the same number of diffusion-weighted observations. Varying angular coverage while controlling that budget separates a direction-design question from simply acquiring more data.<The Effect of Gradient Sampling Scheme on Estimates of Fiber Orientation: Implications for Fiber Tractography by D. K. Jones>[Methods and Table1:61 total rows, unique orientations and repetition counts]{ref}
A noise-free calculation illustrates <diffusion tensor identifiability>. With separately known baseline $S_0$, fixed $b>0$ and a unit direction $\mathbf g$, the Gaussian <diffusion tensor> model gives
$$
y_{\mathbf g}=-\frac{\log(S_{\mathbf g}/S_0)}{b}
=\mathbf g^T\mathbf D\mathbf g.
$$
The <symmetric matrix> $\mathbf D$ has six independent coefficients. Its <quadratic form> produces a row $(g_x^2,g_y^2,g_z^2,2g_xg_y,2g_xg_z,2g_yg_z)$ in a <linear least squares> design. Directions $\pm\mathbf e_x,\pm\mathbf e_y,\pm\mathbf e_z$ give six observations but only <matrix rank> three: opposite directions repeat a row and the off-diagonal coefficients remain undetermined.
Adding the normalized mixed directions $(\mathbf e_x+\mathbf e_y)/\sqrt2$, $(\mathbf e_x+\mathbf e_z)/\sqrt2$ and $(\mathbf e_y+\mathbf e_z)/\sqrt2$ to the three positive coordinate axes instead gives <matrix rank> six. For example,
$$
\boxed{D_{xy}=y_{(\mathbf e_x+\mathbf e_y)/\sqrt2}-\frac{D_{xx}+D_{yy}}2.}
$$
This establishes uniqueness in the stated noise-free model. It does not establish small <measurement uncertainty> or an optimal experimental design.
\Image[/diffusion-tensor-gradient-design.png]
{title=Original noise-free diffusion-tensor design matrices: six antipodal directions give rank three, while axes plus three mixed directions give rank six}
Jones also interviewed <John E. Tanner> about the physical origins of <pulsed field gradient NMR>. The interview preserved concrete details of the apparatus, including Tanner's carefully spaced mica stack and the practical difficulties of rapidly switching <magnetic field gradients>.<John Tanner, the return to Germelshausen, and the work that nearly never happened by Derek Jones>[pp.6–7: restricted-diffusion apparatus and switching problems]{ref}
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