Lorentz Encoding is proposed, a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning via implicit continuous coordinate learning that significantly outperforms state-of-the-art methods.
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).
A model-driven bilevel optimization framework that couples SENSE-based image reconstruction with SPIRiT-based k-space calibration through shared CSMs, and introduces a deep-prior-guided regularization strategy that preserves the structure of classical linear regularizers while adaptively learning spatially varying regularization weights from denoised intermediate reconstructions.
Weipeng Chen, Yan-Ran Li, Raymond H. Chan et al.· Journal of Mathematical Imag...· 0 citations
Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.
Zheng Zhang, Hao Tang, Yingying Hu et al.· 0 citations
Quantitative Susceptibility Mapping (QSM) reconstructs tissue magnetic susceptibility from MR phase data but remains highly ill-posed in the single-orientation setting due to the cone-null region of the dipole kernel in the Fourier domain. To address this challenge, we propose QSMnet-INR, a physics informed framework that integrates an implicit neural representation (INR) into k-space modeling. The INR learns a continuous dipole response to improve stability in ill-conditioned regions, while a frequency-aware dipole loss enforces consistency with the physical model. Experiments on the 2016 QSM Reconstruction Challenge, a multi-orientation GRE dataset, and clinical data demonstrate improved reconstruction quality and reduced artifacts compared with existing methods, particularly under single orientation settings. Ablation and sensitivity analyses further support the complementary roles of INR-based modeling and frequency-aware regularization. While performance under more extreme susceptibility conditions or unseen acquisition settings warrants further investigation, the results indicate that integrating implicit representations with physics-informed constraints provides an effective approach for stabilizing ill-posed QSM reconstruction.
X. Cai, Ruo-Mi Guo, K. Zheng et al.· IEEE Transactions on Pattern...· 0 citations
The proposed K-space Gaussian Representation (KGR), the first explicit continuous representation formulated directly in the native k-space domain, suggests that explicit continuous parameterization of native k-space provides a principled framework for integrating continuous signal modeling with structured low-rank reconstruction.
I2SB-Inversion is proposed, a multi-contrast guided reconstruction framework based on the Schrödinger Bridge that achieves a a high acceleration factor of R=11.38 and consistently outperforms existing methods in both quantitative and qualitative evaluations.
Yue Wang, Yuanbiao Yang, Zhuo-xu Cui et al.· IEEE Transactions on Medical...· 0 citations
Resolving complex fiber geometries in brain white matter requires high-resolution diffusion MRI at the cost of long acquisition times. This leads many clinical protocols to opt for low-resolution scans, making downstream microstructure estimation and tractography challenging. Implicit neural representations (INRs) can model the diffusion signal continuously, enabling native single-subject super-resolution by querying the network at arbitrary spatial coordinates, yet existing methods often suffer from long training times and lack a mechanism to incorporate anatomical priors to regularize super-resolution by constraining the space of plausible reconstructions. To address these limitations, we propose a novel transfer-learning framework that pre-trains an INR on a high-resolution template and then adapts it to subject-specific scans via registration and fine-tuning. For $4\times$ through-plane super-resolution from 5 mm to 1.25 mm on Human Connectome Project (HCP) data, our method reduces NRMSE by 36-49% and increases FSIM by 24-43% over a recent baseline with $6\times$ faster training, outperforming competing INR-based methods across both image quality and domain-specific metrics. Code is available on the project page at https://abdulkaderghandoura.github.io/research/msc-thesis/ .
Abdulkader Ghandoura, Marsil Zakour, William Consagra et al.· 0 citations