Free water mapping using single-shell diffusion MRI has been proposed by regularizing the ill-posed problem, but the effect of this regularization has yet to be systematically investigated. Here we explore the solution space for the two-compartment free water model. Without regularization, the solution space is flat for one-shell data, and while it has a minimum for two-shell data, this minimum is not particularly steep. Regularizing the fit by exploiting smoothness of the tensor creates a steep minimum in both one- and two-shell data, demonstrating the advantage of regularization.
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