[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84888-en":3,"doc-seo-84888-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84888,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding","Multi-pool chemical exchange saturation transfer (CEST) MRI offers valuable metabolic biomarkers but suffers from long acquisition times, and sparse sampling makes dense Z-spectrum reconstruction an ill-posed inverse problem. Generic implicit neural representations (INRs) lack physical constraints, often yielding spectral artifacts and signals that violate physical validity. This work introduces Lorentz Encoding (LE), a physics-informed self-supervised framework that learns continuous coordinate mappings using Lorentzian-parametric bases with learnable components. Experiments on in vivo human brain data show strong gains under 21–39 point sampling, enabling accurate APT/NOE/MT quantification.","Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding  \nDexuan Li\\#, Yupeng Wu\\#, Chenglong Wang, Hanlin Liu, Hui Zheng, Jianqi Li, and  \nGuang Yang*  \nShanghai Key Laboratory of Magnetic Resonance, Institute of Magnetic Resonance and Molecular Imaging in Medicine, East China Normal University  \n[gyang@phy.ecnu.edu.cn](gyang@phy.ecnu.edu.cn)  \nAbstract. 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 Representations (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 metabolite mapping (APT, NOE, MT) .  \nKeywords: CEST MRI, Implicit Neural Representation, Image Reconstruction, Physics-Informed Deep Learning.  \n1 Introduction  \nMulti-Pool Chemical Exchange Saturation Transfer (CEST) MRI has emerged as a vital tool for molecular imaging, enabling the non-invasive detection of low-concentration endogenous metabolites[1] . Its diagnostic capability relies on the Z-spectra to quantify molecular effects such as Amide Proton Transfer (APT), Nuclear Overhauser enhancement (NOE) effect, and Magnetization Transfer (MT) . Fundamentally, CEST exploits frequency-selective radiofrequency (RF) irradiation to saturate dilute exchangeable solute protons; through continuous chemical exchange, this saturation state is transferred to the abundant bulk water pool, resulting in an amplified attenuation of the water signal that is recorded as a function of the frequency offset to form the Zspectrum[1,2] . However, capturing these subtle spectral features typically requires dense  \n2 Dexuan Li et al.  \nsampling (e.g., >50 frequency offsets), leading to long acquisition times that severely limit clinical translation[3] .  \nWhile sparse sampling offers a method to accelerate scanning, it renders the Z-spectra reconstruction an ill-posed inverse problem. Traditional model-based approaches such as Multi-Pool Lorentzian Fitting (MPLF) are theoretically sound but numerically unstable when data are sparse. Recently, deep learning approaches such as variants of U-Net[4, 5] and generic Implicit Neural Representation (INR)[6–8] have demonstrated the capability to model continuous spectral signals from sparse data. In the INR paradigm, the reconstruction of 2D CEST is typically formulated as learning a continuous function mapping spatial-spectral coordinates (􀀢, 􀀤, ∆􀀦) to the normalized Z-spectra intensity. However, standard INRs utilizing generic encodings (e.g., Fourier[9] or Hash Encoding[10]) treat all dimensions equally and lack physical constraints. By treating the Zspectra as an arbitrary continuous function, they force the network to search for solutions in an unconstrained high-dimensional space. Consequently, they often overfit high-frequency noise or produce spectral oscillations that","cbCaieQTtaqhaXMG","https://ap.wps.com/l/cbCaieQTtaqhaXMG","pdf",5278719,2,1,10,"English","en",105,"# Introduction\n## Problem of sparse CEST reconstruction\n## Motivation for physics-informed implicit learning\n# Method\n## Overall architecture","[{\"question\":\"Why does sparse sampling make CEST Z-spectra reconstruction difficult?\",\"answer\":\"Sparse sampling turns the task into an ill-posed inverse problem, where many reconstructions can fit the limited measurements, causing instability and artifacts.\"},{\"question\":\"What problem do generic implicit neural representations cause in this setting?\",\"answer\":\"Generic INRs use unconstrained encodings and treat dimensions without physics priors, which can lead to overfitting to noise and physically invalid spectral oscillations.\"},{\"question\":\"How does Lorentz Encoding (LE) improve reconstruction quality?\",\"answer\":\"LE injects Lorentzian physical priors into the encoding layer and restricts the continuous spectral mapping to physically valid basis combinations, reducing noise and enforcing model consistency for accurate APT/NOE/MT mapping.\"}]",1784199037,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"self-supervised-implicit-cest-reconstruction-via-physics-informed-lorentz-encoding","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/self-supervised-implicit-cest-reconstruction-via-physics-informed-lorentz-encoding/84888/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does sparse sampling make CEST Z-spectra reconstruction difficult?","Question",{"text":75,"@type":76},"Sparse sampling turns the task into an ill-posed inverse problem, where many reconstructions can fit the limited measurements, causing instability and artifacts.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What problem do generic implicit neural representations cause in this setting?",{"text":80,"@type":76},"Generic INRs use unconstrained encodings and treat dimensions without physics priors, which can lead to overfitting to noise and physically invalid spectral oscillations.",{"name":82,"@type":73,"acceptedAnswer":83},"How does Lorentz Encoding (LE) improve reconstruction quality?",{"text":84,"@type":76},"LE injects Lorentzian physical priors into the encoding layer and restricts the continuous spectral mapping to physically valid basis combinations, reducing noise and enforcing model consistency for accurate APT/NOE/MT 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