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 (Westin et al. 2016) and three-term diffusion skewness tensor imaging (Ning et al. 2021), 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 (Reymbaut et al. 2020). Alternatively, diffusion tensor distribution imaging (DTD, Topgaard 2019) 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 (Reymbaut et al. 2020).
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 (Ning et al. 2019), the DTD framework can also be adapted to includes relaxation weighting (de Almeida Martins et al. 2020). As for time-dependent diffusion effects, they are incorporated in correlation tensor MRI (Henriques et al. 2020), a two-term cumulant expansion, and in a recently introduced extension of the DTD framework (Narvaez et al. 2021). 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, Veraart et al. 2016) denoising on multidimensional diffusion data reduces the noise-induced biases of the DTD approach (Martin et al. 2021). Similar work should be done for other inversion techniques.