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

Area of Science:

• Biophysics
• Materials Science
• Medical Imaging

Background:

• Nuclear Magnetic Resonance (NMR) diffusion pore imaging analyzes microstructures in biological tissues and porous materials.
• Classical methods yield only the modulus squared of the Fourier transform, creating an inversion problem for pore image reconstruction.
• Accurate pore imaging requires both magnitude and phase information, but phase measurement is experimentally challenging.

Purpose of the Study:

• To present a novel approach for solving the phase problem in NMR diffusion pore imaging.
• To enable unambiguous reconstruction of pore shapes by recovering phase information from the Fourier modulus.
• To eliminate the need for difficult phase measurements using specialized gradient profiles.

Main Methods:

• Application of a phase retrieval algorithm to recover phase information from the Fourier modulus.
• Utilized a combination of the hybrid input-output (HIO) and error reduction (ER) algorithms with a shrinkwrap extension.
• No prior knowledge of pore shape was assumed, only a finite pore extent.

Main Results:

• The phase retrieval approach successfully reconstructed pore images from simulated NMR diffusion data, even with added noise.
• Validation in phantom experiments with well-defined pores using hyperpolarized xenon gas confirmed the method's efficacy.
• The technique successfully recovered phase information, enabling accurate pore shape imaging.

Conclusions:

• The developed phase retrieval method effectively solves the phase problem in NMR diffusion pore imaging.
• This approach simplifies experimental requirements by omitting challenging phase measurements.
• The technique holds significant potential for advancing the investigation of microstructures in various materials.