Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding

Chenglong Wang; Dexuan Li; Guang Yang; Hanlin Liu; Hui Zhen; Jianqi Li; Yupeng Wu

arxiv: 2607.06132 · v1 · pith:PRYVLVHI · submitted 2026-07-07 · cs.LG · cs.AI· physics.med-ph

Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding

Dexuan Li , Yupeng Wu , Chenglong Wang , Hanlin Liu , Hui Zhen , Jianqi Li , Guang Yang This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 15:30 UTCglm-5.2pith:PRYVLVHI record.json open to challenge →

classification cs.LG cs.AIphysics.med-ph

keywords cestcontinuousimplicitphysics-informedreconstructiondataencodingencodings

0 comments

The pith

Lorentzian priors cut CEST MRI scan time by 78% with high fidelity

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper claims that CEST MRI Z-spectra can be reconstructed from as few as 21 sampled frequency offsets (down from 97) with high fidelity, by constraining the spectral encoding of an implicit neural representation to a learnable Lorentzian subspace. The central object is Lorentz Encoding (LE), which replaces generic positional encodings (Fourier, hash, wavelet) with a set of parametric Lorentzian basis functions whose amplitude, center frequency, and peak width are initialized to known physical pools (Water, APT, NOE, MT) and bounded during optimization. The paper argues that this single design choice transforms the reconstruction from unconstrained regression—where the network may fit noise or produce physically invalid oscillations—into physics-informed optimization, where the solution space is restricted to superpositions of Lorentzian line shapes. The paper reports PSNR of 54.19 dB at 21 points and 57.58 dB at 39 points on in vivo human brain data, substantially above all tested baselines, and shows that downstream metabolite maps (APT, NOE, MT) derived from LE reconstructions are correspondingly more accurate.

Core claim

The paper's central claim is that the performance gap between LE and generic INR encodings is caused by the Lorentzian constraint itself, not by network capacity or training procedure. The authors provide an ablation (LE vs. MHE with identical 16-dimensional spectral encoding and 32-dimensional spatial encoding, same MLP, same training) showing LE at 54.19 dB vs. MHE at 33.56 dB under 21-point sampling. They attribute this to the fact that generic encodings operate in an unconstrained high-dimensional space and lack the inductive bias to bridge wide spectral gaps (e.g., the >10 ppm region), producing physically invalid oscillations. LE, by contrast, forces the network to follow the smooth, d

What carries the argument

Lorentz Encoding (LE): a spectral encoding that projects frequency offsets onto N learnable Lorentzian basis functions L_i(Δω) = A_i * γ_i² / (γ_i² + (Δω - μ_i)²), each parameterized by amplitude A_i, center frequency μ_i, and peak width γ_i. The N=16 bases are partitioned equally among four physical pools (Water, APT, NOE, MT) with parameters initialized and bounded to physiologically determined ranges. Spatial coordinates are encoded separately via Multi-resolution Hash Encoding (MHE). The two encoding streams are concatenated and decoded by a 6-layer MLP (128 hidden units, ReLU). The entire system is optimized per-subject via self-supervised L2 loss over sparse acquired points only.

If this is right

If the Lorentzian-constraint principle generalizes, other MRI modalities with known line-shape physics (e.g., MRS, ASL) could benefit from encoding-level physical priors rather than post-hoc regularization.
The finding that encoding constraints matter more than network capacity for ill-posed spectral reconstruction suggests that INR design should prioritize domain-specific basis functions over generic frequency mappings.
Clinical CEST protocols could reduce acquisition from ~9 minutes to under 2 minutes (21 offsets) if reconstruction quality holds in multi-center validation, potentially enabling CEST in stroke or acute settings where scan time is critical.
The per-subject optimization paradigm (~5 min/slice) may limit clinical adoption; a meta-learned initialization or amortized variant could preserve the physics-informed constraint while reducing inference time.

Load-bearing premise

The experimental comparison may not be structurally fair: LE is optimized directly on each test subject's sparse data (per-subject self-supervised INR), while it is unclear whether U-Net was trained across subjects and tested on held-out subjects. If so, LE has direct access to the test subject's spatial information at every frequency, while a cross-subject U-Net does not, and the large performance margins could partially reflect this asymmetry rather than the Lorentzian enc

What would settle it

If the U-Net baseline were also trained per-subject (self-supervised on the same sparse data) and the PSNR gap between LE and U-Net narrowed substantially, the claimed superiority of Lorentzian encoding over generic approaches would be weakened. Alternatively, if LE reconstructions were shown to fail on pathological tissue with non-Lorentzian spectral features (e.g., tumors with altered exchange rates), the physical constraint would be revealed as a limitation rather than a universal advantage.

read the original abstract

Multi-Pool Chemical Exchange Saturation Transfer (CEST) MRI provides valuable metabolic information but is clinically limited by long acquisition times. Although sparse sampling reduces scanning time, reconstructing high-resolution Z-spectra from limited data remains an ill-posed inverse problem. Conventional interpolation and generic Implicit Neural Rep-resentations (INRs) often lack physical constraints, leading to spectral artifacts and physically invalid signals. To address this, we propose Lorentz Encoding (LE), a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning. Unlike generic positional encodings, LE regularizes the continuous spectral mapping by projecting sparse coordinates into a physically constrained space governed by a combination of parametric Lorentzian profiles with learnable basis functions. This mechanism effectively reduces noise and enforces consistency with physical models. Experiments on in vivo human brain data demonstrate that LE significantly outperforms state-of-the-art methods. Specifically, under a 39-point sampling strategy, LE achieves a PSNR of 57.58 dB and an SSIM of 0.9994. Furthermore, the learned physics-informed encodings form a continuous, geometrically ordered trajectory in the latent space, ensuring accurate quantitative metabo-lite mapping (APT, NOE, MT).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Lorentzian spectral encoding for CEST INR is a solid idea; the experimental comparison needs clarification before the performance claims hold up.

read the letter

The core idea — replacing generic positional encoding on the spectral axis with a learnable Lorentzian basis initialized to physical pool parameters — is genuinely new and well-motivated. Z-spectra are physically superpositions of Lorentzians, so constraining the encoding to that subspace is a natural inductive bias. The decoupled architecture (hash encoding for spatial, Lorentz encoding for spectral) is clean, and the code is public. The PCA visualization of learned features forming a smooth V-shaped trajectory is a nice supporting result. Credit where due: the method design is sound and the physical initialization in Table 1 is a good touch. Chen et al. [7] uses Lorentzian models in a different architectural role, so the novelty claim is legitimate. The stress-test concern about the U-Net comparison is valid and is the main issue. The paper says LE follows per-subject self-supervised optimization but does not specify whether U-Net was trained the same way or cross-subject with supervised loss. If U-Net was trained across subjects while LE optimizes directly on each test subject's sparse data, the 11+ dB gap is partly an apples-to-oranges comparison. This needs explicit clarification. The MHE ablation is the closest controlled comparison (matched capacity, same INR paradigm), and the 20+ dB gap there is the strongest evidence for the Lorentzian encoding itself being the causal factor. But the paper does not confirm matched optimization hyperparameters (learning rate, epochs, scheduler) between LE and MHE. A gap this large between two per-subject INR methods warrants that confirmation. The PSNR values of 54-57 dB are high but not implausible for normalized Z-spectral intensities that are smooth and bounded — this is less concerning to me than the comparison fairness. No statistical tests are reported, which is a minor gap given 18 subjects. This paper is for researchers working on CEST MRI reconstruction and INR methods. The core idea is worth a serious referee. I'd recommend peer review conditional on the authors clarifying the U-Net training protocol and confirming matched hyperparameters for the MHE ablation. The method contribution is real; the evaluation just needs to be tightened.

Referee Report

3 major / 6 minor

Summary. This paper proposes Lorentz Encoding (LE), a physics-informed implicit neural representation (INR) framework for reconstructing CEST Z-spectra from sparsely sampled MRI data. The core idea is to constrain the spectral encoding subspace to a superposition of learnable Lorentzian basis functions (parameterized by amplitude, center frequency, and peak width), while using multi-resolution hash encoding for spatial features. The method is evaluated on in vivo human brain data across three sampling strategies (21, 29, 39 points) and compared against U-Net, WIRE, Fourier PE, MHE, and Direct MPLF. The authors report substantial PSNR improvements (e.g., 54.19 dB vs. 42.98 dB for U-Net at 21 points) and demonstrate improved downstream APT, NOE, and MT parameter mapping. Code is publicly available.

Significance. The paper addresses a clinically relevant problem (accelerating CEST acquisition) with a methodologically interesting approach. Embedding Lorentzian priors directly into the encoding layer of an INR is a principled way to inject physics-informed inductive bias, and the decoupled spatial-spectral architecture is well-motivated. The authors provide publicly available code, which is a notable strength. The visualization of learned encoding topology (Fig. 5) and the per-frequency PSNR analysis (Fig. 4) add interpretability value. The downstream parameter map evaluation (APT, NOE, MT) grounds the work in clinical utility.

major comments (3)

§3.3, Table 2: The U-Net baseline is described only as 'A standard 4-stage encoder-decoder mapping sparse inputs to dense spectra' (§3.3). The paper does not specify whether U-Net was trained per-subject (self-supervised on the same sparse data, analogous to LE) or across subjects (supervised on fully-sampled data from training subjects, tested on held-out subjects). This is load-bearing for the central claim that LE 'significantly outperforms state-of-the-art methods including U-Net.' If U-Net was trained across subjects while LE optimizes directly on each test subject's sparse coordinates, the comparison is structurally asymmetric — LE has direct access to the test subject's spatial information at every frequency, while a cross-subject U-Net does not. The 11+ dB gap (54.19 vs. 42.98 dB, Strategy 1) could be partially or largely attributable to this asymmetry. The authors must clarify U
§3.3, Table 2: The MHE ablation is described as using 'identical network capacity for a fair comparison' (§3.3), but the paper does not confirm that LE and MHE shared identical optimization settings (learning rate, epoch count, scheduler, random seed). The 20+ dB gap between LE (54.19 dB) and MHE (33.56 dB) under Strategy 1 is the most direct evidence for the central claim that the Lorentzian encoding — rather than some other aspect of the pipeline — is the causal factor. Without confirmation of matched optimization hyperparameters, this gap cannot be cleanly attributed to the encoding strategy alone. Please confirm that LE and MHE used identical optimization settings, or provide an ablation that varies only the encoding while holding all else fixed.
§3.1, §3.2: The evaluation uses 18 healthy subjects, but the paper does not specify how many subjects were used for training (if any cross-subject baselines were trained), how many for testing, or whether results in Table 2 are averaged across all subjects or a subset. The standard deviations are reported, but the subject-level experimental design is unclear. This affects the interpretability of all quantitative results. Please specify the train/test split and how the reported metrics were aggregated.

minor comments (6)

§2.2, Eq. (2): The Lorentzian basis function is written as L_k(Δω) = A_k · γ_k² / (γ_k² + (Δω − μ_k)²), but the equation as rendered in the manuscript appears garbled ('A+1!/31!/34(∆789!)'). Please verify the formula is correctly typeset.
§2.3: The GPU is listed as 'NVIDIA RTX 5080 GPU (16GB VRAM)'. The RTX 5080 is not a widely available or standard GPU model as of the manuscript date; please verify this specification.
Table 1: The Water pool center frequency range is [-0.5, 0.5] ppm with peak width [1, 2] ppm. Please clarify whether the water pool is treated as a direct saturation pool or a separate exchange pool, as this affects the physical interpretation.
Fig. 2: The frequency offset lists for each strategy are dense and hard to parse. Consider presenting these in a cleaner tabular format or marking sampled points on a visual frequency axis.
§4.2: The authors note that strong spectral constraints can lead to over-smoothing of fine spatial details. It would strengthen the paper to show a concrete example or quantitative evidence of this trade-off, rather than only mentioning it as a limitation.
References [4] and [5] cite U-Net-based CEST methods; it would be helpful to clarify how the U-Net baseline in this paper relates to these prior works — whether it is a re-implementation or a direct comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. All three major concerns are valid and point to insufficient experimental detail in the current manuscript. We address each below and confirm revisions.

read point-by-point responses

Referee: §3.3, Table 2: U-Net training protocol (per-subject self-supervised vs. cross-subject supervised) is unspecified, making the LE–U-Net comparison potentially structurally asymmetric.

Authors: The referee is correct that this is unclear in the current manuscript and that it is load-bearing for our central claim. To clarify: U-Net was trained per-subject in a self-supervised manner, analogous to LE and all other INR baselines. Specifically, for each test subject, the U-Net was trained to map the M sparse input images to their corresponding known intensities (i.e., the same sparse coordinate-intensity pairs used by the INR methods), and the remaining 97−M frequency offsets served as the unseen test set. No cross-subject training was performed for any method. Thus, all methods—U-Net, WIRE, Fourier PE, MHE, and LE—had identical access to the test subject's sparse data and were evaluated on the same held-out frequency offsets. The comparison is structurally symmetric. We acknowledge that this was not stated in the manuscript and will add explicit clarification of the training protocol for every baseline in §3.2–3.3. revision: yes
Referee: §3.3, Table 2: MHE ablation — confirmation that LE and MHE shared identical optimization settings (learning rate, epochs, scheduler, seed) is missing; the 20+ dB gap cannot be cleanly attributed to encoding strategy alone without this.

Authors: We confirm that LE and MHE used identical optimization settings: the same Adam optimizer, learning rate (1×10⁻³), epoch count (10,000), random seed, and no scheduler. The only difference between the two configurations is the spectral encoding module: LE uses 16 learnable Lorentzian basis functions, while MHE uses a 16-dimensional 1D multi-resolution hash encoding for the spectral axis. The spatial encoding (32-dimensional MHE), MLP architecture (6 layers, 128 hidden units, ReLU), loss function (L2), and training data sampling (10,000 random points per epoch from the sparse set) are all identical. We agree this information should have been stated explicitly and will add a sentence in §3.3 confirming that all INR variants (WIRE, Fourier PE, MHE, LE) shared identical optimization hyperparameters, with the sole difference being the spectral encoding strategy. revision: yes
Referee: §3.1, §3.2: Train/test split and subject-level aggregation are unspecified. It is unclear how many subjects were used for training vs. testing and how the reported metrics in Table 2 were computed.

Authors: This is a fair concern. Because all methods in our evaluation follow the subject-specific (per-subject) self-supervised paradigm described in §3.2, there is no cross-subject train/test split: all 18 subjects are test subjects. For each subject, each method is independently optimized on that subject's sparse data and evaluated on the held-out frequency offsets. The metrics reported in Table 2 are the mean ± standard deviation across all 18 subjects. We will revise §3.1 and §3.2 to state explicitly: (1) that all 18 subjects serve as independent test cases under the per-subject optimization paradigm, (2) that no subject-level train/test split exists because no cross-subject training was performed, and (3) that the reported metrics are averaged across all 18 subjects with standard deviations reflecting inter-subject variability. revision: yes

Circularity Check

0 steps flagged

No significant circularity found; derivation is self-contained with external physical priors and independent evaluation

full rationale

The paper's core derivation chain is not circular. The physical prior (Z-spectra are superpositions of Lorentzians) is well-established CEST physics from external literature, not a self-cited result. The Lorentz Encoding parameters (A_k, μ_k, γ_k) are learnable intermediate encoding parameters, not predictions — the actual predictions (reconstructed Z-spectra) are evaluated against independent fully-sampled ground truth via PSNR/SSIM. No self-citations appear in the load-bearing argument. The downstream parameter maps (APT, NOE, MT) are generated by applying standard MPLF to all methods' outputs equally, so the evaluation protocol does not structurally favor LE. While there is a structural affinity between the Lorentzian encoding and the MPLF used downstream, the MLP combines Lorentzian features with spatial hash features in learned, non-trivial ways, so the output is not a pure Lorentzian fit by construction. The experimental fairness concerns (U-Net training protocol, MHE hyperparameter matching) are correctness risks, not circularity. Score 1 reflects the minor structural affinity between encoding and downstream evaluation method, which is an expected consequence of using physically-motivated priors rather than a formal circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 0 invented entities

No new physical entities are postulated. The Lorentzian pools correspond to known CEST exchange pools.

free parameters (5)

Lorentzian amplitudes A_k = learned, bounded [0, 0.5] or [0.5, 1.0] per pool
16 learnable amplitude parameters (4 pools × 4 bases each), optimized end-to-end per subject
Lorentzian center frequencies μ_k = learned, bounded per pool (e.g., [3.0, 4.0] ppm for APT)
16 learnable center frequency parameters, initialized within physical bounds from Table 1
Lorentzian peak widths γ_k = learned, bounded per pool (e.g., [3, 4] ppm for APT)
16 learnable width parameters, bounded per Table 1
MLP weights Θ = 6 layers × 128 units
Standard neural network parameters, optimized per-subject
Hash encoding parameters = n_levels=16, 32-dimensional spatial features
Multi-resolution hash encoding for spatial coordinates

axioms (3)

domain assumption Z-spectra are adequately modeled as a superposition of Lorentzian line shapes
§2.1: 'a Z-spectrum is essentially a superposition of multiple Lorentzian line shapes.' This is the standard CEST model but real spectra can deviate due to B1 inhomogeneity, T2 effects, and asymmetric MT.
domain assumption Four distinct pools (Water, APT, NOE, MT) sufficiently characterize the Z-spectrum
§2.2 Table 1: the encoding subspace is partitioned equally among these four pools. Additional pools (e.g., amine, hydroxyl) are not included.
domain assumption Per-subject INR optimization generalizes from sparse samples to unseen frequencies
§3.2: the framework assumes that optimizing on M sparse points produces accurate interpolation at 97-M unseen points. This is validated empirically but is an inductive assumption.

pith-pipeline@v1.1.0-glm · 11185 in / 4248 out tokens · 273506 ms · 2026-07-08T15:30:04.547820+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 1 internal anchor

[1]

Ward, K.M., Aletras, A.H., Balaban, R.S.: A new class of contrast agents for MRI based on proton chemical exchange dependent saturation transfer (CEST). J. Magn. Reson. 143, 79–87 (2000). https://doi.org/10.1006/jmre.1999.1956

work page doi:10.1006/jmre.1999.1956 2000
[2]

Van Zijl, P.C.M., Yadav, N.N.: Chemical exchange saturation transfer (CEST): what is in a name and what isn’t? Magn. Reson. Med. 65, 927–948 (2011). https://doi.org/10.1002/mrm.22761

work page doi:10.1002/mrm.22761 2011
[3]

Vinogradov, E., Sherry, A.D., Lenkinski, R.E.: CEST: from basic principles to applications, challenges and opportunities. J. Magn. Reson. 229, 155–172 (2013). https://doi.org/10.1016/j.jmr.2012.11.024

work page doi:10.1016/j.jmr.2012.11.024 2013
[4]

Chen, L., Xu, H., Gong, T., Jin, J., Lin, L., Zhou, Y., Huang, J., Chen, Z.: Accelerating multipool CEST MRI of parkinson’s disease using deep learning–based Z‐spectral com-pressed sensing. Magn. Reson. Med. mrm.30233 (2024). https://doi.org/10.1002/mrm.30233

work page doi:10.1002/mrm.30233 2024
[5]

Cheema, K., Han, P., Lee, H., Xie, Y., Christodoulou, A.G., Li, D.: Accelerated CEST im-aging through deep learning quantification from reduced frequency offsets. Magn. Reson. Med. 93, 301–310 (2025). https://doi.org/10.1002/mrm.30269

work page doi:10.1002/mrm.30269 2025
[6]

https://doi.org/10.1109/ISBI56570.2024.10635440

Chen, C., Liu, Y., Park, S.W., Li, J., Chan, K.W.Y., Chan, R.H.F.: Implicit Regression in Subspace for High-Sensitivity CEST Imaging. https://doi.org/10.1109/ISBI56570.2024.10635440. 10 Dexuan Li et al

work page doi:10.1109/isbi56570.2024.10635440 2024
[7]

IEEE Trans

Chen, C., Liu, Y., Park, S.W., Li, J., Chan, K.W.Y., Huang, J., Morel, J.-M., Chan, R.H.: High-quality CEST mapping with lorentzian-model informed neural representation. IEEE Trans. Bio-Med. Eng. 1–11 (2025). https://doi.org/10.1109/TBME.2025.3574238

work page doi:10.1109/tbme.2025.3574238 2025
[8]

IEEE Trans

Liu, B., She, H., Du, Y.P.: Scan-Specific Unsupervised Highly Accelerated Non-Cartesian CEST Imaging Using Implicit Neural Representation and Explicit Sparse Prior. IEEE Trans. Biomed. Eng. 71, 3032–3045 (2024). https://doi.org/10.1109/TBME.2024.3407092

work page doi:10.1109/tbme.2024.3407092 2024
[9]

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains

Tancik, M., Srinivasan, P.P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J.T., Ng, R.: Fourier features let networks learn high frequency functions in low dimensional domains, http://arxiv.org/abs/2006.10739, (2020). https://doi.org/10.48550/arXiv.2006.10739

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2006.10739 2006
[10]

ACM Trans

Müller, T., Evans, A., Schied, C., Keller, A.: Instant neural graphics primitives with a mul-tiresolution hash encoding. ACM Trans. Graphics. 41, 1–15 (2022). https://doi.org/10.1145/3528223.3530127

work page doi:10.1145/3528223.3530127 2022
[11]

In: 2023 IEEE/CVF Conference on Com-puter Vision and Pattern Recognition (CVPR)

Saragadam, V., LeJeune, D., Tan, J., Balakrishnan, G., Veeraraghavan, A., Baraniuk, R.G.: WIRE: wavelet implicit neural representations. In: 2023 IEEE/CVF Conference on Com-puter Vision and Pattern Recognition (CVPR). pp. 18507–18516. IEEE, Vancouver, BC, Canada (2023). https://doi.org/10.1109/CVPR52729.2023.01775

work page doi:10.1109/cvpr52729.2023.01775 2023

[1] [1]

Ward, K.M., Aletras, A.H., Balaban, R.S.: A new class of contrast agents for MRI based on proton chemical exchange dependent saturation transfer (CEST). J. Magn. Reson. 143, 79–87 (2000). https://doi.org/10.1006/jmre.1999.1956

work page doi:10.1006/jmre.1999.1956 2000

[2] [2]

Van Zijl, P.C.M., Yadav, N.N.: Chemical exchange saturation transfer (CEST): what is in a name and what isn’t? Magn. Reson. Med. 65, 927–948 (2011). https://doi.org/10.1002/mrm.22761

work page doi:10.1002/mrm.22761 2011

[3] [3]

Vinogradov, E., Sherry, A.D., Lenkinski, R.E.: CEST: from basic principles to applications, challenges and opportunities. J. Magn. Reson. 229, 155–172 (2013). https://doi.org/10.1016/j.jmr.2012.11.024

work page doi:10.1016/j.jmr.2012.11.024 2013

[4] [4]

Chen, L., Xu, H., Gong, T., Jin, J., Lin, L., Zhou, Y., Huang, J., Chen, Z.: Accelerating multipool CEST MRI of parkinson’s disease using deep learning–based Z‐spectral com-pressed sensing. Magn. Reson. Med. mrm.30233 (2024). https://doi.org/10.1002/mrm.30233

work page doi:10.1002/mrm.30233 2024

[5] [5]

Cheema, K., Han, P., Lee, H., Xie, Y., Christodoulou, A.G., Li, D.: Accelerated CEST im-aging through deep learning quantification from reduced frequency offsets. Magn. Reson. Med. 93, 301–310 (2025). https://doi.org/10.1002/mrm.30269

work page doi:10.1002/mrm.30269 2025

[6] [6]

https://doi.org/10.1109/ISBI56570.2024.10635440

Chen, C., Liu, Y., Park, S.W., Li, J., Chan, K.W.Y., Chan, R.H.F.: Implicit Regression in Subspace for High-Sensitivity CEST Imaging. https://doi.org/10.1109/ISBI56570.2024.10635440. 10 Dexuan Li et al

work page doi:10.1109/isbi56570.2024.10635440 2024

[7] [7]

IEEE Trans

Chen, C., Liu, Y., Park, S.W., Li, J., Chan, K.W.Y., Huang, J., Morel, J.-M., Chan, R.H.: High-quality CEST mapping with lorentzian-model informed neural representation. IEEE Trans. Bio-Med. Eng. 1–11 (2025). https://doi.org/10.1109/TBME.2025.3574238

work page doi:10.1109/tbme.2025.3574238 2025

[8] [8]

IEEE Trans

Liu, B., She, H., Du, Y.P.: Scan-Specific Unsupervised Highly Accelerated Non-Cartesian CEST Imaging Using Implicit Neural Representation and Explicit Sparse Prior. IEEE Trans. Biomed. Eng. 71, 3032–3045 (2024). https://doi.org/10.1109/TBME.2024.3407092

work page doi:10.1109/tbme.2024.3407092 2024

[9] [9]

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains

Tancik, M., Srinivasan, P.P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J.T., Ng, R.: Fourier features let networks learn high frequency functions in low dimensional domains, http://arxiv.org/abs/2006.10739, (2020). https://doi.org/10.48550/arXiv.2006.10739

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2006.10739 2006

[10] [10]

ACM Trans

Müller, T., Evans, A., Schied, C., Keller, A.: Instant neural graphics primitives with a mul-tiresolution hash encoding. ACM Trans. Graphics. 41, 1–15 (2022). https://doi.org/10.1145/3528223.3530127

work page doi:10.1145/3528223.3530127 2022

[11] [11]

In: 2023 IEEE/CVF Conference on Com-puter Vision and Pattern Recognition (CVPR)

Saragadam, V., LeJeune, D., Tan, J., Balakrishnan, G., Veeraraghavan, A., Baraniuk, R.G.: WIRE: wavelet implicit neural representations. In: 2023 IEEE/CVF Conference on Com-puter Vision and Pattern Recognition (CVPR). pp. 18507–18516. IEEE, Vancouver, BC, Canada (2023). https://doi.org/10.1109/CVPR52729.2023.01775

work page doi:10.1109/cvpr52729.2023.01775 2023