This remains an open question, but let us discuss it through two key sources of estimation biases: signal representation/model assumptions and low signal-to-noise ratio (SNR). Given that models can drastically vary in terms of assumptions, let us focus on signal representations here.
Truncated cumulant expansions of the diffusion signal, such as the two-term q-space trajectory imaging () and three-term diffusion skewness tensor imaging (), imposes rather strong constraints regarding the form of the intravoxel distribution of diffusion tensors while being more general than conventional diffusion kurtosis imaging for instance. While these constraints tend to stabilize the signal inversion towards specific types of voxel contents, they also induce inherent estimation biases, even at infinite SNR (). Alternatively, diffusion tensor distribution imaging (DTD, ) describes the diffusion signal as a large sum of mono-exponential decays, i.e., as a sum of microscopic diffusion tensors. While this makes DTD more versatile than cumulant expansions, its reduced set of constraints comes at the cost of enhanced sensitivity to noise, manifesting as finite-SNR estimation biases ().
Besides, the above approaches do not account for relaxation or time-dependent diffusion. While cumulant expansions have been generalized to relaxation-diffusion cases, e.g., the joint relaxation-diffusion imaging moments (), the DTD framework can also be adapted to includes relaxation weighting (). As for time-dependent diffusion effects, they are incorporated in correlation tensor MRI (), a two-term cumulant expansion, and in a recently introduced extension of the DTD framework (). The latter approach, being the least constrained in principle, offers the highest potential for unbiased estimations at infinite SNR, even though this may require very comprehensive acquisition sampling schemes.
An obvious (maybe simplistic) solution to noise-induced biases lies in denoising data post-acquisition. To my knowledge, little work has been done to properly assess the effect of denoising strategies on multidimensional diffusion MRI signal inversions. Yet, recent work suggests that employing Marchenko-Pastur principal component analysis (MP-PCA, ) denoising on multidimensional diffusion data reduces the noise-induced biases of the DTD approach (). Similar work should be done for other inversion techniques.