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This paper presents a novel approach on solving the phase problem in nuclearmagnetic resonance (NMR) diffusion pore imaging, a method, which allows imagingthe shape of arbitrary closed pores filled with an NMR-detectable medium forinvestigation of the microstructure of biological tissue and porous materials.Classical q-space imaging composed of two short diffusion-encoding gradientpulses yields, analogously to diffraction experiments, the modulus squared ofthe Fourier transform of the pore image which entails an inversion problem: Anunambiguous reconstruction of the pore image requires both magnitude and phase.Here, the phase information is recovered from the Fourier modulus by applying aphase retrieval algorithm. This allows omitting experimentally challengingphase measurements using specialized temporal gradient profiles. A combinationof the hybrid input-output algorithm and the error reduction algorithm was usedwith dynamically adapting support (shrinkwrap extension). No a priori knowledgeon the pore shape was fed to the algorithm except for a finite pore extent. Thephase retrieval approach proved successful for simulated data with and withoutnoise and was validated in phantom experiments with well-defined pores usinghyperpolarized xenon gas.

Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction