We have been active in investigating the link between measured diffusion-encoded signal and diffusion restrictions. These works include:
Figure 1. Diffusion lattice imaging.
Left: Simulation of particles diffusing in a periodic lattice. Middle: Bragg-Peaks created using a single diffusion encoding. Right: A lattice image reconstructed by an additional (simulated) measurement with double diffusion encoding.
 Laun FB, Kuder TA, Semmler W, Stieltjes B.
Determination of the defining boundary in nuclear magnetic resonance diffusion experiments.
Phys Rev Lett. 2011 Jul 22;107(4):048102.
 Laun FB, Kuder TA, Wetscherek A, Stieltjes B, Semmler W.
NMR-based diffusion pore imaging.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 1):021906.
 Kuder TA, Laun FB.
NMR-based diffusion pore imaging by double wave vector measurements.
Magn Reson Med. 2013 Sep;70(3):836-41.
 Laun FB, Kuder TA.
Diffusion pore imaging with generalized temporal gradient profiles.
Magn Reson Imaging. 2013 Sep;31(7):1236-44.
 Kuder TA, Laun FB.
Effects of pore-size and shape distributions on diffusion pore imaging by nuclear magnetic resonance.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Aug;92(2):022706.
 Laun FB, Müller L, Kuder TA.
NMR-based diffusion lattice imaging.
Physical Review E, 2016. 93(3).
 Laun FB, Kuder TA, Zong F, Hertel S, Galvosas P.
Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry.
J Magn Reson. 2015 Oct;259:10-9.
 Laun FB, Demberg K, Nagel AM, Uder M, Kuder TA.
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR.
Frontiers in Physics, 2017. 5.
 Laun FB.
Restricted diffusion in NMR in arbitrary inhomogeneous magnetic fields and an application to circular layers.
J Chem Phys. 2012 Jul 28;137(4):044704.
 Kuder TA, Bachert P, Windschuh J, Laun FB.
Diffusion pore imaging by hyperpolarized xenon-129 nuclear magnetic resonance.
Phys Rev Lett. 2013 Jul 12;111(2):028101.
 Demberg K, Laun FB, Windschuh J, Umathum R, Bachert P, Kuder TA.
Nuclear magnetic resonance diffusion pore imaging: Experimental phase detection by double diffusion encoding.
Phys Rev E. 2017 Feb;95(2-1):022404.
 Demberg K, Laun FB, Bertleff M, Bachert P, Kuder TA.
Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction.
Phys Rev E. 2018 May;97(5-1):052412.