Multi-Regularization Reconstruction of One-Dimensional T₂ Distributions in Magnetic Resonance Relaxometry

Measurements of T₂ relaxation time distributions in magnetic resonance relaxometry are increasingly used to probe microstructural details of materials or tissues. However, extracting the model from the acquired data is a severely ill-conditioned problem. Tikhonov regularization and related methods are widely used to address this. Methods such as the L-curve and generalized cross-validation (GCV) select a single regularizer to obtain an optimal approximation to the underlying distribution. However, this procedure does not make use of the information content of the non-selected regularized results; given the lack of definitive criteria for regularization parameter selection, this represents a potential loss of substantial information. In contrast, we propose a new reconstruction method, Multi-Reg, incorporating a range of calculated regularized solutions. Multi-Reg is based on a dictionary of noise-corrupted regularized reconstructions of distribution basis functions. We demonstrate that Multi-Reg can out-perform the L-curve or GCV methods in simulation analyses of Gaussian distribution components, and present experimental results on mouse spinal cord and human muscle tissue.