A greedy variational approach for generating sparse T₁-T₂ NMR relaxation time distributions

Area of Science:

• Geophysics
• Physical Chemistry
• Applied Mathematics

Background:

• Nuclear Magnetic Resonance (NMR) is crucial for characterizing materials.
• Analyzing complex NMR relaxation time and diffusion coefficient distributions is challenging.
• Existing inversion methods can be computationally intensive and lack sparsity.

Purpose of the Study:

• To develop a nonlinear inversion method for sparse solutions to Fredholm Integral equations in NMR.
• To approximate distributions of exponential rate constants using a sum of Dirac delta functions.
• To enable efficient real-time processing for mobile NMR applications.

Main Methods:

• A greedy variational nonlinear inversion approach is presented.
• The method approximates distributions with Dirac delta functions, promoting sparsity.
• Iterative least squares misfit reduction refines Dirac delta function parameters.

Main Results:

• The method generates sparse solutions for 2D NMR relaxation time and diffusion coefficient distributions.
• Demonstrated effectiveness with synthetic data and experimental T1-T2 correlations in porous rocks.
• Achieved sparse representations ideal for real-time processing and data transmission.

Conclusions:

• The developed nonlinear inversion method offers efficient and sparse solutions for NMR data.
• Its sparsity is advantageous for real-time processing in remote and mobile NMR applications.
• The technique shows promise for applications like well logging and portable NMR devices.