Low-field NMR has evolved into a widely used tool in various industrial applications to quantify liquid distributions in porous media and characterize complex systems. Low-field NMR systems such as the NMR-MOUSE measure non-oscillatory time dependent exponential signal decays and build-up curves to obtain relaxation times and diffusion coefficients.
Various signal processing methods have been applied to relaxation and diffusion signals to reveal distributions of relaxation constants in systems with multiple relaxation components. A commonly applied approach for quantitative relaxometry analysis is solving a Fredholm integral of the first kind, often also referred to as the Inverse Laplace Transformation (ILT).
In 2020 Fricke et al. proposed an alternative approach using the Matrix Pencil Method (MPM). For this a nxm matrix is divided into two submatrices. This pair is defined as a matrix pencil and the generalized eigenvalue problem for them is solved. For a 2D data set n and m are defined by the increments in the direct and indirect detection dimensions, respectively. 1D measurements require transformation into a squared matrix to get an array in form of a 2D data set. Advantages of this method compared to ILT are higher resolution, less computational requirements as well as less sensitivity to noise.
In this work, the MPM approach is used on T1 saturation recovery data obtained with a single sided NMR-MOUSE system to probe the temporal resolution limit. Therefore, 0.9% brine solutions were doped with different amounts of Gd-DTPA as contrast agent to achieve a variety of relaxation species. The solutions were kept in separated containers and were measured individually. Afterwards combinations of two solutions were placed on top of the detector. Gradually the difference in relaxation times of the two components was reduced to test the minimum difference between relaxation times that still can be resolved using MPM.
MPM was able to quantitatively resolve two components with a relative difference of 50% in T1 relaxation time. The calculated relaxation time of the longer component matched the value obtained for the individual measurement (180 ms), while the shorter was calculated to be 22% higher (95 ms). It was not possible to resolve the two components using ILT and the computation even introduced artifacts, if now pre-processing was applied to the data.
Systems with more than two components and varying component ratios as well as T2 and Diffusion data sets will be addressed in future work. These results show a potential superiority of MPM vs. ILT in context of quantitative single sided NMR-MOUSE relaxometry.