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Implicit neural representations for accurate estimation of the standard model of white matter

Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments. However, due to the model its high-dimensional nature, extensive acquisition protocols with multiple b-values and diffusion tensor shapes are typically required to mitigate parameter degeneracies. Even then, accurate estimation remains challenging due to noise. This work introduces a novel estimation framework based on implicit neural representations (INRs), which incorporate spatial regularization through the sinusoidal encoding of the input coordinates. The INR method is evaluated on both synthetic and in vivo datasets and compared to parameter estimates using cubic polynomials, supervised neural networks, and nonlinear least squares. Results demonstrate superior accuracy of the INR method in estimating SM parameters, particularly in low signal-to-noise conditions. Additionally, spatial upsampling of the INR can represent the underlying dataset anatomically plausibly in a continuous way, which is unattainable with linear or cubic interpolation. The INR is fully unsupervised, eliminating the need for labeled training data. It achieves fast inference ($\sim$6 minutes), is robust to both Gaussian and Rician noise, supports joint estimation of SM kernel parameters and the fiber orientation distribution function with spherical harmonics orders up to at least 8 and non-negativity constraints, and accommodates spatially varying acquisition protocols caused by magnetic gradient non-uniformities. The combination of these properties along with the possibility to easily adapt the framework to other dMRI models, positions INRs as a potentially important tool for analyzing and interpreting diffusion MRI data.

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