Effect of basis choice on quantitative parameter estimation in accelerated subspace reconstructions

This work assesses the effects of different simulated and data-driven subspaces on quantitative parameter estimation in highly accelerated subspace reconstructions. Three different methods for generating basis were applied in a locally low rank subspace reconstruction: (1) a data-driven basis derived from fully sampled low-resolution data, (2) a simulated basis from a dictionary with uniform $T_2$ tissue distribution, and (3) a simulated basis with white matter (WM) and gray matter (GM) oversampled. Obtaining basis vectors from a dictionary with non-uniform tissue distributions can be interpreted as obtaining basis vectors using a weighted singular value decomposition to a dictionary generated with uniform tissue spacings. Fully sampled echo planar spectroscopic imaging (EPSI) datasets of six subjects (including three brain tumor patients) were retrospectively undersampled with 9-shot and 3-shot $k_y-t$ traversals. The effect of regularization was assessed by comparing $T_2$ maps and qualitative images of fully sampled and retrospectively undersampled images. Under 3-shot retrospective undersampling, images reconstructed with the basis generated from a uniform $T_2$ distribution basis had altered signal evolutions, resulting in statistically significant WM/GM $T_2$ overestimations with mean differences of 10-15 ms. Applying a WM/GM oversampled basis improved $T_2$ accuracy but still induced $T_2$ bias. The data-driven basis provided the most accurate $T_2$ estimates. Highly accelerated subspace reconstructions cause bias in quantitative relaxation maps. Data-driven subspaces can reduce this bias.