Abstract:
In this work, we shed light on the issue of estimating Intravoxel Incoherent Motion (IVIM)
for diffusion and perfusion estimation by characterizing the objective function using
simplicial homology tools. We provide a robust solution via topological optimization of
this model so that the estimates are more reliable and accurate. Estimating the tissue
microstructure from diffusion MRI is in itself an ill-posed and a non-linear inverse problem.
Using variable projection functional (VarPro) to fit the standard bi-exponential IVIM model
we perform the optimization using simplicial homology based global optimization to
better understand the topology of objective function surface. We theoretically show
how the proposed methodology can recover the model parameters more accurately
and consistently by casting it in a reduced subspace given by VarPro. Additionally
we demonstrate that the IVIM model parameters cannot be accurately reconstructed
using conventional numerical optimization methods due to the presence of infinite
solutions in subspaces. The proposed method helps uncover multiple global minima by
analyzing the local geometry of the model enabling the generation of reliable estimates
of model parameters.
