Multi-exponential Inversion of the Relaxometry Data of Low-field Nuclear Magnetic Resonance for Cement-based Materials

Low-field Nuclear Magnetic Resonance (LF-NMR) technique has been attracting increasing concern in nondestructively characterising cement-based materials (CBMs), whose nanoscale pore structure are sensitive to water removal. In order to achieve the multi-exponential inversion of relaxometry data preferred by the interpretation on local pore structure of CBMs, an algorithm incorporating L1 regularisation with capability of yielding sparse solution is developed with the aids of Interior-Point method and various principles for optimising the regularisation parameter. Numerical analyses on representative cases show that, the proposed algorithm equipped with the Morozov discrepancy principle is capable of resolving all artificially designed exponential components of various intensities with satisfactory accuracy and precision, even at relatively low signal-to-noise ratio. When applying to resolve the relaxometry data obtained on a cement paste, the algorithm is good at characterising its pore structure with clear significance and capturing its detailed evolution during curing under hot water with good precision.