Improving multi-exponential inversion of low-field NMR relaxation data for porous cement-based materials through Bayesian principles and prior information

Low-field nuclear magnetic resonance technology is increasingly being recognized for its potential in the nondestructive characterization of cement-based materials, whose pore structures are highly sensitive to water removal. To quantitatively detect their nanoscale pore structure, a Maximum a Posteriori algorithm was developed to solve the multi-exponential inversion problem and yield a discrete transverse relaxation time spectrum based on Bayesian theory. This algorithm, which circumvents the challenges of non-uniqueness and inherent high uncertainty of inverse calculation, enables accurate and precise calculation. Numerical analyses of representative artificial cases show that, the L1 regularization method tending to yield sparse solution effectively provides good prior information for the MAP algorithm. Even under the condition of relatively low signal-to-noise ratio, the varying intensities of artificially designed fast-relaxing exponential components can be resolved with satisfactory precision and accuracy. When applied to cement-based materials, the MAP algorithm accurately characterizes pore structure and captures its subtle evolution over time.