{"id":"abc1a45d-d628-4b7e-92b0-7a187a826336","arxiv_id":"1908.06749","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Using signal magnitude in diffusion MRI forces the recovered displacement distribution to be symmetric, so asymmetric microstructural environments are misrepresented.","lead":"The paper shows that taking the magnitude of the diffusion MRI signal, as standard q-space methods do, removes the asymmetry of the underlying particle displacement distribution. Simulations near a reflective wall and a corner demonstrate that the reconstructed distribution is symmetric and therefore distorted, which can mislead microstructure inference.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Generalization from idealized wall/corner simulations to practical microstructural inference is unsupported; Eq. (12) is correct but its impact on inference in tissue-like geometries is not demonstrated.","rationale":"The reader's verdict is CONDITIONAL with low correctness risk, and I agree. The mathematical core (Eqs. 6–12) is sound: the signal is the Fourier transform of a real distribution, so the magnitude is symmetric and its inverse transform is symmetric, while the true distribution is asymmetric. The simulations are appropriate as a proof of principle for the mathematical property. The soft spot is the leap from a mathematical inequality to a claim about microstructural inference. The paper's own caveat in Section 1 limits the geometries to 'solid test beds' and explicitly says they are 'not necessarily representatives of biological tissue's microstructure,' yet Section 4 draws a general recommendation for future diffusion imaging research. The missing piece is a quantitative demonstration that, in a realistic acquisition/inversion pipeline, magnitude processing produces meaningful errors in estimated microstructural parameters. Without that, Eq. (12) is a cautionary note rather than a demonstrated impediment to inference. My proposed test directly checks whether the distortion survives in tissue-like geometries and whether it matters for estimated parameters. If it survives, the CONDITIONAL verdict stands or strengthens; if not, the conclusion should be narrowed to the mathematical property only. Setting verdict_should_be to UNCHANGED reflects that the reader already captured this concern and that no new issue changes the verdict.","tokens_in":8732,"tokens_out":6581,"duration_ms":67762,"concrete_test":"Simulate a voxel-scale tissue phantom containing closed, randomly oriented cylindrical and spherical compartments with realistic size and permeability distributions (e.g., a MISST- or NeuroVIESA-style phantom). Generate noiseless complex PGSE signals S(k) and magnitude signals |S(k)| over the same k-space sampling. (1) Reconstruct displacement distributions via inverse Fourier transform and compare pointwise; (2) fit standard models (DTI, NODDI, or a q-space metric such as return-to-origin probability) to both data sets and compare estimated indices to ground truth. Repeat with Rician noise at SNR 20–40 and with a linear bulk-motion phase. If the magnitude-based parameter estimates differ from the complex-based estimates by less than the noise-induced uncertainty, the paper's conclusion that magnitude usage impedes inference does not hold for tissue-like geometries.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (12) is mathematically correct: for any asymmetric real displacement-integral distribution P, |F{P}| is real and symmetric, so F^{-1}(|F{P}|) is real and symmetric and cannot equal P. The simulations confirm this for an infinite reflecting wall and an orthogonal corner. However, the paper's central claim, stated in the abstract and Section 4, is that magnitude usage 'impedes DW–MR from accurately inferring microstructural information.' That inference is not demonstrated by the simulations, which compare distributions only visually and never run a model-fitting or parameter-estimation pipeline. The chosen geometries are open, one-sided boundaries that generate strongly asymmetric displacement integrals; the paper itself concedes in Section 1 that they 'are not necessarily representatives of biological tissue's microstructure.' In tissue, barriers are largely closed membranes (cell walls, myelin sheaths); for particles inside closed compartments, displacement distributions are often symmetric or become nearly symmetric after orientation averaging over a voxel. Thus the practical relevance of the demonstrated distortion for typical diffusion MRI inference (DTI, NODDI, q-space) is an extrapolation, not a proven consequence. The conditional recommendation to prefer complex-valued methods may be reasonable, but the claim that magnitude processing impedes inference in real tissue requires quantitative support.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper addresses the common practice in diffusion MR of using the magnitude of the complex MR signal in q-space and related analyses. The author shows that for a real-valued displacement-integral distribution P, the noiseless NMR signal S is its Fourier transform and is Hermitian. Taking |S| before inverse Fourier transformation yields a real, symmetric function F^{-1}(|S|), which generally differs from the true asymmetric P. The paper supports this with random-walk simulations of particles near a reflecting wall and an orthogonal corner, comparing the true P with F^{-1}(|S|). The visual results show that magnitude processing produces symmetric reconstructions that resemble a tube instead of a wall and a box instead of a corner, and it adds an artificial spike at the origin. The author recommends using complex-valued processing as in the CFD-MRI framework.","tokens_in":8994,"tokens_out":6852,"duration_ms":76065,"significance":"If correct, the paper provides a clear, elementary demonstration that magnitude-based q-space analysis cannot recover asymmetric displacement-integral distributions. The core identity, Eq. (12), is a direct consequence of Fourier transform properties and is correctly implemented and visualized in the simulations. The paper is honest about the idealized nature of the simulations and explicitly notes that the chosen geometries are not representative of biological tissue. Its practical significance for diffusion MRI inference, however, is not yet established: the simulations show distribution mismatch but do not quantify its effect on any parameter-estimation task, and the extrapolation to tissue is not supported. The paper would be a useful cautionary note and a motivation for complex-valued methods, provided the inference claims are strengthened.","major_comments":[{"comment":"The central claim that magnitude usage 'impedes DW-MR from accurately inferring microstructural information' is not supported by the evidence presented. Eq. (12) is a correct Fourier-theoretic statement, and Figures 2 and 3 visually confirm the distribution mismatch, but no inference or parameter-estimation is performed. The statements that a wall 'is inferred as a vertically oriented tube' and a corner 'appears as a box' are qualitative visual labels, not results of any model-fitting procedure. To substantiate the inference claim, the authors should run a downstream estimation task (e.g., fitting wall position, tube radius, or compartment size) on the simulated complex signal and on its magnitude, and report bias or error for both. As written, the paper establishes a distribution-reconstruction mismatch, not an inference failure.","section":"Section 4, Eq. (12)"},{"comment":"The generalization from the two open-boundary geometries to biological tissue is acknowledged by the authors as unsupported: Section 1 states that these geometries 'are not necessarily representatives of biological tissue's microstructure.' Nevertheless, Section 4 recommends abandoning magnitude processing in future in and ex vivo diffusion imaging research. This extrapolation requires either additional simulations in tissue-like geometries with closed boundaries (e.g., cylinders or spheres) or an explicit argument for why the open-boundary asymmetry persists after orientation averaging in a voxel. Without such support, the practical relevance of the demonstrated distortion to typical diffusion MRI inference remains an open question.","section":"Sections 1 and 4"}],"minor_comments":[{"comment":"The simulations use 120000 particles but no random seeds or repeated runs are reported; please provide reproducibility details (seed or code) and, if possible, error bars on the displayed distributions to rule out single-realization artifacts.","section":"Section 2.2"},{"comment":"The statement that 'taking the magnitude transfers the imaginary portion to the real axis, thereby adding a positive constant to the signal' is imprecise: |S| - Re(S) is nonnegative pointwise but is not a constant. The spike at the origin is the zero-frequency consequence of the integral of |S|, rather than of adding a constant to the signal; please rephrase.","section":"Section 3"},{"comment":"The phrase 'the signal magnitude becomes a symmetric' is missing a noun; it should read 'a symmetric function.'","section":"Section 2.1"},{"comment":"The exponential phase term appears malformed in the submitted manuscript; please check the typesetting of the term -iγΩ_i.","section":"Eq. (2)"}],"recommendation":"major_revision","confidential_remarks":"The mathematical core of this paper is standard Fourier transform theory; the contribution is the application to diffusion MR and the accompanying simulations. The author promotes his own CFD-MRI framework as the solution, which is a promotional element but not a circularity or correctness problem. The novelty is modest, but the paper could be acceptable as a methods note after the inference gap is addressed and the presentation issues are fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, what you should know: this is a mathematically sound but conceptually elementary cautionary note. The central inequality—Eq. (12)—says that inverse Fourier transforming the magnitude of the diffusion MR signal cannot recover an asymmetric displacement distribution, because the magnitude is real and symmetric. That is a direct consequence of Hermitian symmetry of the Fourier transform of a real function; the paper clearly derives it and then verifies it with simple random-walk simulations near a reflecting wall and a corner.\n\nCredit where due: the explanation of the Fourier relationships is precise, and the simulations visually show that magnitude processing turns a wall into a tube and a corner into a box, including an artificial zero-displacement spike. The paper is honest enough to say in Section 1 that the chosen geometries are not necessarily representative of biological tissue. It also makes a fair point that q-space methods that take the magnitude to remove bulk motion inadvertently discard more information than intended.\n\nThe soft spots are in proportion to the overreach. The main issue is the final conclusion: that magnitude processing 'impedes DW-MR from accurately inferring microstructural information' in general. That is not demonstrated by the simulations. The paper never runs a model-fitting or parameter-estimation pipeline; it only compares the reconstructed distribution to the true one by eye. There are no error bars, repeated seeds, or noise. In tissue, barriers are mostly closed membranes, and after orientation averaging the asymmetry may be much smaller. So the practical relevance is an extrapolation, not a proven result. The recommendation to use complex-valued methods, especially the author's own CFD-MRI, is plausible but self-promotional.\n\nWho is this for? A diffusion MRI researcher who uses magnitude in q-space or DSI would find this a useful reminder that phase information carries asymmetry content. It is not a new principle, but it is a clean demonstration. With revisions (add noise, error bars, a fitted model, and a more careful generalization) it would be a solid methods note. As is, I would send it to peer review because the core message is correct and worth publishing if the inference claim is tempered. I would not cite it as a primary reference, but I might point colleagues to it.","headline":"A mathematically correct but textbook-level cautionary note: magnitude processing in diffusion MRI forces symmetry, and the simulations illustrate it well, but the practical inference claim is overreached.","tokens_in":9443,"tokens_out":2381,"would_cite":false,"duration_ms":25480,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using the magnitude of the diffusion MR signal forces the reconstructed displacement distribution to be symmetric, erasing asymmetric microstructure.","keywords":["diffusion MRI","signal magnitude","displacement integral","Fourier transform","Hermitian symmetry","restricted diffusion","reflective wall","q-space imaging"],"falsifier":"Take any real, asymmetric displacement-integral distribution $P$, compute $F^{-1}(|F(P)|)$, and compare with $P$; the paper's central identity says they differ whenever $P$ is asymmetric, so an example where they are equal would falsify the mathematical claim, while a biological phantom with known asymmetric microstructure whose magnitude-based and complex-based inferences agree would falsify the practical-impact claim.","tokens_in":8547,"feed_emoji":"🧲","tokens_out":5386,"duration_ms":47333,"temperature":0.7,"pith_summary":"This paper argues that a standard step in diffusion magnetic resonance imaging — taking the magnitude of the measured signal before Fourier inversion — destroys information about asymmetric molecular motion. In the noiseless Fourier model, the physically meaningful displacement-integral distribution is recovered from the complex signal, and replacing that signal by its magnitude forces the recovered distribution to be real and symmetric. The author demonstrates the mismatch by simulating water-like particles diffusing near a reflective wall and around an orthogonal corner, two geometries that produce asymmetric displacement distributions. If the claim holds, every magnitude-based diffusion MR method, even in ideal noiseless conditions, distorts inferred microstructure whenever the true environment is asymmetric.","feed_headline":"Signal magnitude hides asymmetric diffusion in MRI","feed_subtitle":"Simulations show wall and corner geometries are misread as tubes and boxes when magnitude replaces the complex signal.","key_machinery":"The load-bearing object is the displacement integral $W^d_i$, the difference between the time integrals of a magnetic moment's path during the two pulsed gradients of a PGSE sequence; its distribution $P^{nmr}_{cfd}$ is real-valued and is the physical quantity of interest. Equations (7) and (8) express the noiseless complex signal as the Fourier transform of this distribution, so Hermitian symmetry is the mechanism: since $P^{nmr}_{cfd}$ is real, $S^{nmr}_{cfd}$ is Hermitian, and taking $|S^{nmr}_{cfd}|$ before the inverse transform collapses the phase and symmetrizes the recovered distribution.","core_discovery":"The central claim is the inequality in Eq. (12): $F^{-1}(|S^{nmr}_{cfd}|) \\neq P^{nmr}_{cfd} = F^{-1}(S^{nmr}_{cfd})$, where $S^{nmr}_{cfd}$ is the complex diffusion MR signal and $P^{nmr}_{cfd}$ is the distribution of displacement integrals. Because $P^{nmr}_{cfd}$ is real, its Fourier transform is Hermitian, so its magnitude is real and symmetric; the inverse Fourier transform of that magnitude is therefore real and symmetric and cannot reproduce an asymmetric distribution. The paper shows this concretely in simulations: a wall appears as a tube, a corner appears as a box, and a spurious spike at zero displacement integral suggests stationary spins that are not there. The conclusion is that magnitude processing, often used to remove bulk motion, removes asymmetry as well and should be replaced by complex-valued processing with phase correction.","pith_inferences":["By the same Fourier argument, any real asymmetric displacement distribution will be symmetrized by magnitude processing, so the wall and corner results are instances of a general mathematical fact rather than geometry-specific accidents.","A testable extension would be to quantify how much the inferred microstructure is distorted as a function of asymmetry strength and signal-to-noise ratio; the paper establishes the noiseless floor but not the practical error size.","If biological tissue contains asymmetric restrictions such as curved axons, branching, or boundaries at multiple scales, magnitude-based estimates of axon diameter and density could be systematically biased in those regions.","The linear-phase signature of bulk motion, which magnitude processing was meant to remove, could instead be estimated and corrected from the complex signal; the paper leaves that phase-correction algorithm as open future work."],"forward_implications":["Magnitude-based diffusion MR models cannot recover asymmetric displacement distributions, so they bias microstructure inference in any geometry where motion is asymmetric.","The spurious zero-displacement peak introduced by magnitude processing can be misinterpreted as stationary or trapped water, inflating estimates of restricted compartments.","The distortion is present in ideal noiseless simulations, so it is intrinsic to the magnitude operation rather than a noise artifact.","Complex-valued processing that restores Hermitian symmetry, such as phase correction, avoids this distortion and also removes the Rician noise assumption.","The paper's recommendation is to let data analysis reveal symmetry or its absence instead of imposing symmetry through signal magnitude or symmetric basis expansions."],"supporting_citations":[{"why":"Establishes the complex-valued Fourier relationship between the DW-MR signal and the displacement-integral distribution that the paper's argument builds on.","marker":"[4]"},{"why":"The target practice: diffusion spectrum imaging that uses signal magnitude with the stated aim of filtering out bulk motion.","marker":"[9]"},{"why":"Supplies the Fourier transform properties, Hermitian symmetry and real-even symmetry, that make magnitude processing force a symmetric reconstructed distribution.","marker":"[16]"},{"why":"Represents the q-space methodology that processes the signal magnitude before Fourier inversion, the approach being criticized.","marker":"[8]"},{"why":"An example of a complex-valued model that recognizes asymmetry in the DW-MR signal, used as the alternative standard.","marker":"[2]"},{"why":"Another complex-valued model, generalized diffusion tensors, that also avoids forcing symmetry.","marker":"[3]"},{"why":"Earlier simulation of diffusion in restricted geometries that motivates the numerical approach used here.","marker":"[19]"},{"why":"Earlier work on surface-normal mapping with diffusion imaging near macroscopic boundaries, related to the wall simulations.","marker":"[20]"},{"why":"Supplies the PGSE timing parameters (delta = 15 ms, Delta = 30 ms) that the simulations match.","marker":"[18]"}],"fun_headline_variants":["Magnitude MRI misreads walls as tubes","Diffusion MRI magnitude erases asymmetry","Phase loss in diffusion MRI distorts geometry","Signal magnitude flattens diffusion MRI detail","Magnitude processing hides diffusive asymmetry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The asymmetric displacement distributions produced by a single reflective wall and an orthogonal corner are representative of the asymmetry that matters in biological tissue, so that the demonstrated distortion actually impedes microstructure inference in practice.","fun_headline_variants_meta":{"raw":{"variants":["Magnitude MRI misreads walls as tubes","Diffusion MRI magnitude erases asymmetry","Phase loss in diffusion MRI distorts geometry","Signal magnitude flattens diffusion MRI detail","Magnitude processing hides diffusive asymmetry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000202,"raw_usage":{"total_tokens":1328,"prompt_tokens":835,"completion_tokens":493,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":451,"completion_tokens_details":{"reasoning_tokens":429}},"tokens_in":451,"tokens_out":493,"duration_ms":5600,"temperature":1.0,"reasoning_tokens":429,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:35:14.497769+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take any real, asymmetric displacement-integral distribution $P$, compute $F^{-1}(|F(P)|)$, and compare with $P$; the paper's central identity says they differ whenever $P$ is asymmetric, so an example where they are equal would falsify the mathematical claim, while a biological phantom with known asymmetric microstructure whose magnitude-based and complex-based inferences agree would falsify the practical-impact claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The target practice: diffusion spectrum imaging that uses signal magnitude with the stated aim of filtering out bulk motion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Fourier transform properties, Hermitian symmetry and real-even symmetry, that make magnitude processing force a symmetric reconstructed distribution."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Represents the q-space methodology that processes the signal magnitude before Fourier inversion, the approach being criticized."},{"cited_title":"¨Ozarslan, C","cited_arxiv_id":null,"evidence_quote":"An example of a complex-valued model that recognizes asymmetry in the DW-MR signal, used as the alternative standard."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Another complex-valued model, generalized diffusion tensors, that also avoids forcing symmetry."},{"cited_title":"¨Ozarslan, C","cited_arxiv_id":null,"evidence_quote":"Earlier simulation of diffusion in restricted geometries that motivates the numerical approach used here."},{"cited_title":"¨Ozarslan, U","cited_arxiv_id":null,"evidence_quote":"Earlier work on surface-normal mapping with diffusion imaging near macroscopic boundaries, related to the wall simulations."},{"cited_title":"¨Ozcan, J","cited_arxiv_id":null,"evidence_quote":"Supplies the PGSE timing parameters (delta = 15 ms, Delta = 30 ms) that the simulations match."}],"review_version":1}