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

Referee: [§3.2] §3.2 (INR architecture and encoding): The claim that sinusoidal coordinate encoding supplies an effective spatial prior sufficient to stabilize recovery of the full SM parameter vector (including SH coefficients up to order 8) under realistic noise is central to the accuracy advantage. However, no ablation is presented on the frequency schedule, network depth/width, or the trade-off between regularization strength and boundary preservation; without these controls it remains unclear whether the reported gains arise from the implicit prior or from other implementation choices.

Authors: We agree that systematic ablations are needed to isolate the role of the sinusoidal positional encoding. In the revised manuscript we will add a dedicated supplementary section reporting results for (i) different frequency schedules (number of frequencies and scaling factor), (ii) network depths from 3 to 8 layers and widths from 64 to 256 units, and (iii) quantitative measures of boundary preservation (edge sharpness metrics) versus regularization strength on both synthetic phantoms and in-vivo data. These experiments will be performed with the same self-supervised loss and will be accompanied by tables of parameter error. revision: yes

Referee: [§4.1–4.2] §4.1–4.2 (synthetic and in vivo results): Superior accuracy is asserted for low-SNR regimes, yet the text provides neither per-parameter bias/variance tables nor error bars across repeated noise realizations. Because the central claim is that the INR recovers parameters more accurately than existing methods, the absence of these quantitative metrics prevents readers from judging the magnitude and statistical reliability of the improvement.

Authors: We acknowledge the omission of these statistics. The revised version will include new tables (main text and supplementary) that report, for each SM parameter (intra- and extra-axonal diffusivities, volume fractions, and SH coefficients up to order 8), the mean bias and standard deviation across 50 independent noise realizations at each SNR level. Corresponding error bars will be added to all bar plots and maps in Sections 4.1 and 4.2. revision: yes

Referee: [§4.3] §4.3 (comparison to baselines): The manuscript compares against voxel-wise fitting and a supervised network, but does not include a simple spatial-smoothing baseline (e.g., Gaussian or total-variation regularization applied after voxel-wise fitting). Such a control would isolate whether the INR’s advantage exceeds what can be achieved by explicit spatial regularization of comparable computational cost.

Authors: We accept that an explicit spatial-regularization baseline would strengthen the comparison. In the revision we will add results for two post-processing baselines applied to the voxel-wise fits: (1) Gaussian smoothing with kernel widths matched to the effective receptive field of the INR, and (2) total-variation regularization with regularization parameters chosen to yield comparable smoothness. We will report both accuracy metrics and wall-clock times for these baselines on the same synthetic and in-vivo datasets. revision: yes