Nef-Net v2: Adapting Electrocardio Panorama in the wild
Authors: Zehui Zhan
Yaojun Hu
Jiajing Zhang
Wanchen Lian
Wanqing Wu
Jintai Chen
Venue: ICLR 2026 Poster (2026)
Keywords: ECG representation
Cardiac Diagnosis
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: An enhanced variant of Nef-Net to generate panoramic ECG views, including previously unseen views.

Abstract: Conventional multi-lead electrocardiogram (ECG) systems capture cardiac signals
from a fixed set of anatomical viewpoints defined by lead placement. However, cer-
tain cardiac conditions (e.g., Brugada syndrome) require additional, non-standard
viewpoints to reveal diagnostically critical patterns that may be absent in standard
leads. To systematically overcome this limitation, Nef-Net was recently introduced
to reconstruct a continuous electrocardiac field, enabling virtual observation of
ECG signals from arbitrary views (termed Electrocardio Panorama). Despite
its promise, Nef-Net operates under idealized assumptions and faces in-the-wild
challenges, such as long-duration ECG modeling, robustness to device-specific
signal artifacts, and suboptimal lead placement calibration. This paper presents
NEF-NET V2, an enhanced framework for realistic panoramic ECG synthesis that
supports arbitrary-length signal synthesis from any desired view, generalizes across
ECG devices, and compensates for operator-induced deviations in electrode place-
ment. These capabilities are enabled by a newly designed model architecture that
performs direct view transformation, incorporating a workflow comprising offline
pretraining, device calibration tuning steps as well as an on-the-fly calibration step
for patient-specific adaptation. To rigorously evaluate panoramic ECG synthe-
sis, we construct a new Electrocardio Panorama benchmark, called Panobench,
comprising 4470 recordings with 48-view per subject, capturing the full spatial
variability of cardiac electrical activity. Experimental results show that NEF-NET
V2 delivers substantial improvements over Nef-Net, yielding an increase of around
6 dB in PSNR in real-world setting. Our data and code are publicly available at
https://github.com/HKUSTGZ-ML4Health-Lab/NEFNET-v2.

Published as a conference paper at ICLR 2026
NEF-NET V2: ADAPTING ELECTROCARDIO PANORAMA IN THE WILD
Zehui Zhan 2,, Yaojun Hu Hujinniajinn Zhang", Wanchen Lian', Wanning V Chen
1 Information Hub, Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511458, China
2 School of Biomedical Engineering. Sun Yat-sen University, Shenzhen, 518107, China
3 College of Computer Science and Technology, Zhejiang University. Hangzhou, 310012, China
4 Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, 999077, China
5 The Hong Kong University of Science and Technology, Hong Kong, 999077, China
#: Co-first authors; t: Corresponding authors
ABSTRACT
Conventional multi-lead electrocardiogram (ECG) systems capture cardiac signals from fixed set of anatomical viewpoints defined by lead placement. However, cer- tain cardiac conditions (e.g.. Brugada syndrome) require additional, non-standard viewpoints to reveal diagnostically critical patterns that may be absent in standard leads. To systematically overcome this limitation, Nef-Net was recently introduced to reconstruct continuous electrocardiac field, enabling virtual observation of ECG signals from arbitrary views (termed Electrocardio Panorama). Despite its promise, Nef-Net operates under idcalized assumptions and faces in-the-will challenges, such as long-duration ECG modeling, robustness to device-specific signal artifacts, and suboptimal lead placement calibration. This paper presents NEF-NET v2, an enhanced framework for realistic panoramic ECG synthesis that supports arbitrary-length signal synthesis from any desired view, generalizes across ECG devices, and compensates for operator-induced deviations in electrode placement. These capabilities are enabled by a newly designed model architecture that performs direct view transformation. incorporating a workflow comprising offline pretraining, device calibration tuning steps as well as an on-the-fly cal- ibration step for patient-specific adaptation. To rigorously evaluate panoramic ECG synthesis, we construct a new Electrocardio Panorama benchmark, called Panobench, comprising 4470 recordings with 48-view per subject, capturing the full spatial variability of cardiac electrical activity. Experimental results show that NEF-NET v2 delivers substantial improvements over Nef-Net, yielding increase around dB in PSNR in woal-world setting. Our code is publicly available at th-Lab/ NEFNET-v2
https:: tiitthuu thub. com www.m/HKSSGZ--BAA
INTRODUCTION
Cardiovascular diseases remain the leading cause of morbidity and mortality worldwide (Gaziano) al. 2006), claiming tens of millions of lives each year and imposing profound disability burdens that underscore an urgent clinical imperative (Tsao et al. 2023). Among diagnostic modalities, electrocardiogram (ECG) has established itself as indispensable, providing a non-invasive, cost- effective approach that offers immediate insights into the complex dynamics of cardiac electrical activity (van't 1 Hof et al. 1997).
The number of ECG observation viewpoints directly correlates with both practical complexity and the comprehensiveness of cardiac condition understanding (Kligfield et al., 2007). The standard 12-lead ECG, which is widely used in clinical practice. is generally considered a practical compromise between acquisition cost and clinical utility (Holter) 1961). The electrode placement for the standard 12-lead ECG is illustrated in Figure aa). However, this conventional setup is still insufficient for detecting certain cardiac pathologies with specialized localization patterns, and may require additional, non-standard viewpoints. For instance, posterior myocardial infarction often requires additional

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Published as a conference paper at ICLR 2026
Table I: A comparison of the synthesis performance between Nef-Net and NEF-NET+ following an
identical patient-level testing protocol.
Method ECG Length
Device
Lead Placement
Synthesis: PSNR(T)
Nef-Net
Heartbeat
Restricted
High-Precision
24.10-28.01
NEF-NET v2
Continuous
Agnostic
In-the-wild
$2.07(7.771-33482268177
posterior leads (V7-V9 for definitive diagnosis Van Gorselen al., 2007
Brugada syndrome
detection requires ECG acquisition from additional viewpoints (at 2nd/3rd ICS as these viewpoints uniquely capture the pathological signals caused by right ventricular outflow tract depolarization abnormalities (Berne & Brugada 2012).
To address the trade-off between information richness and view availability in ECGs and to advance the clinical utility of panoramic ECG analysis, Chen et (2021) introduced Electrocardio Panorama, which constructs an implicit neural representation, enabling the generation of ECG signals from arbitrary viewpoints in real time. While this pioneering approach lays an important foundation, Nef-Net nonetheless shows several limitations that constrain its adoption:
(1) Heartbeat-level modeling. Nef-Net is confined to single-heartbeat ECG reconstruction, limiting clinical utility since continuous monitoring requires long-duration signals to capture inter-beat dynamics and arrhythmia patterns. (2) Underuse of view-specifie features. Nef-Net constructs its electrocardio field representation by simply averaging the features from different viewpoints, thereby neglecting the varying relevance of each input view to the target view. This aggregation strategy blends information from all views uniformly, which not only often results in overly coarse reconstructions but also introduces unnecessary architectural complexity. This degradation is further exacerbated when only few views are available for supervision.
(3) Neglect of practical deployment factors. Training assumes idealized data, and Nef-Net overlooks two real-world challenges: inter-device shifts (e.g., variations in sensor characteristics and inter-subject differences (e.g.. electrode placement offsets introduced by clinical staff). (4) Limited validation of panoramic ECG. Due to the unavailability of dense-view datasets, evaluation has been restricted to 12-lead ECGs under narrow angular settings, which insufficient to assess the model's generalizability in reconstructing the global cardiac field. We make the following contributions to address these limitations:
pipelines across ECG devices) and
(A) Geometric View Transformer (T)o We introduce a geometry-aware cross-attention architecture that explicitly models spatial relationships between query and recorded ECG views, selectively extracting the most relevant features for direct query-view transformation. This approach overcomes the feature-averaging limitation in Nef-Net, enabling NEF-NET v2 to achieve superior synthesis performance while simplifying the modeling pipeline and reducing the overall parameter count.
(B) A New Paradigm for Model Development. We propose unified three-stage pipeline for developing and deploying NEF-NET v2 in real-world Electrocardio Panorama applications. In the initial Any-Pairs Pretraining stage, the model acquires robust cross-view transfor- mations under controlled laboratory conditions. Then, Device Calibration stage addresses feature distribution shifts arising from heterogeneity across ECG devices in clinical environ- ments. Finally, the On-the-fly Calibration stage enables rapid, geometry-awar adaptation at the level of individual examinations, compensating for variations in electrode placement.
(C) A Novel Panoramic ECG Dataset and Superior Performance. To enable comprehensive benchmarking of Electrocardio Panorama synthesis, we curated Panobench (lead positions shown in Figure [c), the first 48- ECG dataset with precisely CT-measured spherical coordinates for each view, with inter-subject angular variance quantified across 4,470 recordings. Experimental results show that NEF-NET v2 accurately synthesizes novel ECG views, offering a promising avenue toward more comprehensive clinical ECG assessment.
VV-V9 are BCG leads, beyond the standard 12-lead system, placed on the back record activity from the posterior beart wall.
"he 2nd/3ed ICS specific anatomical locations
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0
(8) The standard 12-lead positions
(b) Electrocardio Panorama
(c) Panobench lead positions
Figure 1: (a) Standard 12-lead electrode placement for conventional ECG recording. (b) Electrocar- dio Panorama enables any user-desired virtual ECG viewpoints for comprehensive visualization of cardiac electrical activity. (c) The Panobench benchmark, encompassing 48 distinet ECG viewpoints for each case, enables rigorous evaluation of Electrocardio Panorama generation models.
2 BACKGROUND AND RELATED WORK
2.1 ELECTROCARRDIGRAM (ECG)
ECG recordings are time-series signals of cardiac electrical activity. Each cardiac cycle can be decomposed into six non-overlapping deflections: the P wave, PR segment, QRS complex, ST segment, T wave, and TP segment. The standard 12-lead ECG protocol (lead positions shown in Figure a is widely used for cardiovascular screening and typically captures 10-second recordings from limb leads (I, II, III, aVR, aVL and VF) and chest leads (V1-V6) (Kligfield et al. (007). Each lead acts as a distinct sensor, providing spatially distinct views of cardiac electrical activity, analogous multi-view camera systems in computer vision. more detailed introduction ECGs is provided in Appendix
2.2 ECG VIEW RECONSTRUCTION AND SYNTHESIS
ECG view reconstruction is essential for recovering missing leads and enabling comprehensive cardiac assessment. Early methods relied on linear transformations (Nelwan al. (004),, assuming predominantly linear relationships across leads, which fails to capture the inherently nonlinear cardiac dynamics (McCulloch et al.) 1998). To address this limitation, nonlinear approaches have been developed, including recurrent neural networks (RNNs) (Hermandez-MMtamorroo et al. 2020), long short-term memory networks (LSTMs) (Kapfo et al.
2022). convolutional neural networks
(CNNs) (Gundlapalle & Acharyya 2022 Chen al.
2024
Lence al.] 2025), and conditional
generative adversarial networks (CGANs) (Seo et al. 2022 Golany & Radinsky 2019 Joo et al.,
2023), which better model complex inter-lead relationships. Yet, these methods are limited to reconstructing predefined, known views and cannot generate novel views that may be clinically valuable. Chen et al. (202T) first introduced the concept of Electrocardio Panorama, which enables the synthesis of any unseen views conditioned on viewing angles. While this represents significant conceptual advance, the approach remains unsuitable for real-world clinical applications due to its neglect of real-world challenges like operational offsets and device inconsistencies. Our method addresses these constraints and provides a more robust solution for panoramic ECG observation.
3 METHODOL.OGY
3.1 ARCHITECTURE
The key idea of NEF-NET v2 is to formulate ECG view synthesis as direct view-to-view transforma- tion problem. This is a pairwise deterministic mapping: the model converts the observed lead signals into the target lead through single-step transformation, without modeling any shared geometric prior
(e.g., the electrocardio field representation) as Nef-Net (Chen et al., 2021). NEF-NET v2 incorporates three components: Angle Embedding, View Encoder, and Geometric View Transformer (GeoVT), as illustrated in Fig. 2 ECG signals recorded from distinct viewing angles.
Formally, let X = {ø), (,),, , with each T; E R xt denote [
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Geometric Angular Attention
recorded angles (5,9%) (Pgin
Anglo Meeee
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View Encasder
Linerr
Rleernahe parausee mage!!
reconded (DCG stage!
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Gg query www.etiiieeeeeeeeeeeccc dtge.
Figure 2: NEF-NET v2 architecture for Electrocardio Panorama synthesis (illustrated for 3-input to 2-query view synthesis task as example). The NEF-NET v2 first employs a View Encoder to extract features from the Recorded ECG that are relevant to the Queried ECG. These extracted features are then fused using a Geometrie View Transformer to synthesize the query view.
Angle Embedding. We simply extend the "Angular Encoding" module of Nef-Net with an addi- tional linear projection to align feature dimensions, mapping recorded angles Aş and query angles A, into nigher-dimensional angle space, respectively.
View Encoder. Each recorded single-lead ECG signal 24 E RI is processed by a I-D ResNet basic block following (Chnn et al., 2021), yielding fa. E Rext"" This representation is then concate- nated with the query feature Fg a FiLM affine modulation (Perez et al. 2018), which amplifies signal features aligned with (0g: (Py)) and suppresses irrelevant ones. Aggregating the outputs from all I recorded leads produces the encoded feature matrix P = l, fil.
Geometric View Transformer (G)oVT), As each ECG view conveys partially redundant yet complementary information about the query view (Pipberger et al., 1961). our GeoVT is designed with three key components: Geometric Angular Attention Module (MGAA), View Transformation block, and a Reconstruction head. MGAA estimates geometric similarity between recorded and query views, the View Transformation block projects recorded features into query-aligned representations, and the Reconstruction head decodes them to reconstruct target-viev ECG signals.
(I) Geometric Angular Attention Module (MGAA) The MGAA implements coss-attention mecha- nism (Lin et al. 2022) that compares the angular embedding of the query leads Fg with recorded leads Pj. Formally, the Geometric Angular Attention map (GAA) is computed by:
Fgg (F.Wo(FAWW))) Vd
GAA softmax
where Wg, W& Rdxdd are learnable projection matrices.
(II) View Transformation Block. In GeoVT, we stack L view transformation blocks to transfer hierarchical features from recorded signals to the query signals. In block i, the recorded signal features F are projected into an angular latent space by e = Linear(Ft) and fused according to the GAA. The resulting representations integrated block by block through a spatial gating mechanism, by:
Fit1
Fr o (1- Ex. GAA) O
where G is a learnable parameter with sigmoid function. The feature extractor (Ext.) follows the design of SE blocks (Hu et al. 2018). Through this hierarchical process, GeoVT progressively refines features from the recorded ECG signals in coarse-to-fine manner, focusing on those relevant to the query view and enabling effective cross-view transformation. Notably, all blocks share the same GAA map defined in Eq. [
(III) reconstruction head. The reconstruction head maps the fused embeddings F back to the time domain using sequence of upsampling blocks. Each block performs linear interpolation, followed by a convolution module that incorporates a spectral- normalized ID convolution (Miyato et al. 2018). layer normalization, and GELU activation.
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Stage Any-Pairs Pretraining
Stage Device Calibration Tuning
Martaiee DCG
Angle
Unenetic Vve ThERIee
BoAd
Fied
Wooded ingie Yeer, Shurt
Van Franke
Siage III: On-the-fly Calibration Tuning
Stage IV: ECG Panoramic Visualization Application
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right di OP al see
Legil ba Aaggl
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Figure 3: The Development (Stage I, II, III) and Deployment (Stage IV) Workflow of NEF-NET V2.
3.2 NEF-NET v2 DEVELOPMENT AND DEPLOYMENT
To deploy an ECG analysis model in real-world settings, a central challenge lies in the heterogeneity of recording devices (Bailey et al. 1990) and the variability arising from sperator-dependee procedures and patient-specific variations (Schijvenaars al. 2008). The original Nef-Net overlooks device- specific discrepancies and case-specific variability. To ensure that our NEF-NET v2 remains robust and clinically applicable, we design a three-stage development and deployment strategy: (I) device- and case-agnostic pretraining stage, called Any-Pairs Pretraining (A (ANYPRE), which lets NEF-NET v2 learn invariant spatiotemporal representations across views under laboratory conditions: (2) Device Calibration (D-CAL), a device-specific calibration stage that adapts NEF-NET v2 to different ECG devices during deployment; and (3) On-the-fly fly Calibration OF-CAA), a case- adaptive calibration stage applied at each examination to align the model with case-level variability.
Stage I: Any-Pairs Pretraining In this phase, NEF-NET v2 is pretrained on ECG cases collected from heterogencous devices to learn fundamental ECG patterns. For each case, the available ECG views are randomly partitioned into two subsets to form the recorded query pairs (X,, Y.). All parameters are kept trainable, and we dynamically sample these recorded -uery pairs in model training. Notably, in accordance with ECG principles, two limb leads are consistently designated as recorded signals, as they provide essential reference potentials for constructing the remaining leads. Following (Chen et al. 2021). optimize the network with the mean absolute error (MAE) loss, defined as LMAB = Y; Y: |11, where Y, are synthesized by the model.
This strategy exposes the model to diverse sensor characteristies and patient demographics, mitigat- ing -pocecc--specific overfitting while compelling to infer cardiac dynamics from arbitrary lead combinations, thereby enhancing robustness and generalization to unseen electrode configurations.
Stage II: Device Calibration Due to variations in ECG acquisition protocols across de- vices-ine iices-including hardware design, electrode materials, and others- present a Device Calibration stage for local adaptation. In this stage, the model is fine-tuned on all recorded-ques pairs from the target device using LMAE. markedly improving alignment with the specific hardware configuration.
Stage II: On-the-fly Calibration Although an ideal viewing angle is defined by (Chen et al.) 2021) and this paper, the actual recorded ECG angles (Oreal: Preal) often deviate substantially from the ideal (0, up) due to two primary factors: (1) electrode placement variability arising across ECG examinations, causing viewing angle deviations; and (2) inter-subject anatomical variability, such differences in heart position, which introduce subject-specific angular offsets from the population mean for each view (e.g.. a standard deviation of up to 10.6 can be observed Panobench). However, the precise offsets are generally difficult obtain directly. To compensate for these discrepancies,
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introduce learnable angular deviation parameters (d0, dip). which are added to the ideal angles to form (0 + d0, 4 + di)), enabling NEF-NET v2 to dynamically adjust for both sources variation. In accordance with clinical ECG recording standards (minimum 10-second duration). the initial 5-second segment is allocated for model calibration on the fly. During this stage, the View Encoder and Reconstruction Head parameters remain frozen, while fine-tuning adapts the angle embeddings to -ndicic deviations.
3.3 PANOBENCH: A DENSE BENCHMARK FOR Electrocardio Panorama
To enable comprehensive evaluation of panoramic ECG view synthesis, we curated new benchmark, Panobench, which for the first time extends beyond previous datasets limited to only 8 or 12 views. Panobench comprises 4,470 ten-second recordings with 48 viewpoints (6 limb and precordial leads), each annotated with CT-derived spherical coordinates (0)4) following (Chen et al. (021). By expanding to 48 leads (views), Panobench provides a high-resolution representation of cardiac electrical dynamics, enabling signal analysis from diverse perspectives. The 48-viewpoint signals and their corresponding angular positions are illustrated in Figure T2 This design supports rigorous validation of panoramic ECG synthesis methods and establishes foundation for clinical translation. In contrast, traditional 12-lead settings require input, supervision, and synthesis to be partitioned among the same limited leads, making validation inherently less comprehensive.
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Figure 4: A representative example from Panobench, illustrating the 48 distinct ECG viewpoints.
4 EXPERIMENTS
4.1 DATASETS AND IMPLEMENTATION DETAILS
We conduct experiments the PTBXL dataset Wagner al. 2020). Tianchi ECG datase CPSC2018 dataset (Liu et al. 2018), ChinaDB dataset (Zheng et al. 2020), and our curated dataset- Panobench. All ECG recordings were resampled to 500 Hz. Each dataset is randomly split into 80 percent training and 20 percent testing. Detailed information about the datasets is provided in Appendix C
In the Any-Pairs Pretraining stage, the model is trained on the combined training sets of four public ECG datasets, with evaluation conducted on their respective test sets. In the Device Calibration stage,

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Table 2: Performance on reconstruction and synthesis tasks on the Tianchi, Chinadb, CPSC2018 and PTBXL datasets. In the synthesis tasks, the numbers of views for input, reconstruction, and synthesis are orderly listed in parentheses. The best performances are highlighted in bold.
ChinDBB
CPSC2018
Taachi
PTBXL
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
View Reconstruction
E.ISTM
(3.9)
20.56++0.38
0.811
21.3744041
0.824
22.76+40.43
0.848
20.04+0.43
0.810
ECGRecover
(3,9)
30.47+0.26
0.958
30.12+0.31
0.966
31,47+0.37
0.971
28.57+0.31
0.942
EKGAN
(3.9)
32.76+0.31
0.967
33.35=0.224
0.975
34.39:10299
0.977
31.71=0.28
0.972
SSSD
(3,9)
32.53+0.337
0.966
32.67=0.39
0.972
33.59+0.41
0.975
31.42+0047
0.972
Nef-Net
(3,9)
29,59:0.20
0.961
29.12 0.26
0.958
31.44:0.21
0.965
30.22 0.27
0.962
NEF NET
(3.9)
35.84.10.22
0.977
36.12.0.38
0.981
37.13.10.44
0.982
35.21
0.974
KIM
(8.12)
27.65
0.952
27.82
0,956
28.01
0.937
26.71
0.929
ECGRecover
(8.12)
3..96
0.983
37.74.10.73
0.985
39.72.10.41
0.986
35.92.10.79
0.985
EKGAN
(8.12)
39.43:10.52
0.976
39.56:0.49
0.976
40,37:0.71
0.981
39.83-10882
0,983
SSSD
(8.12)
39.37.0..35
0.978
38. 28..111 1.2.7
0,980
40.57.10.38
0.983
100.7
0.980
Nef-Net
(8.12)
32.74+ 0.31
0.967
31.66 31.68-+00 0.33
0.971
33.72-+ 0.29
0.961
30.58+00.30
0.977
NEP-NET V2
(8.12)
39.54
0.978
38. 08.69=0.45
0
41.52:+0.62
0.983
19-15:4.441
0,983
Unseen View Syuthesis
Nef-Net
(3.8.1)
25.24+-0.29
0.951
26.72+-0.25
0.957
27.92++0.27
0.959
24. 24+10-2
0.922
NEF NET V2
(3.8,1)
32.27
0.981
33.62.10.17
0.985
34.46.10.35
0.976
33.41 1.0.9
0.982
Nef-Net
(5.6.1)
26.06.10.31
0.954
20.13
0.948
28.01.10.30
0.959
25.37-10.34
0,942
NEP-NET v2 (5,6,1)
H-.30
0.982
32.76+-0.27
0.982
34.82-+0.41
0.977
32.07 +.335
0.986
single dataset with fixed input-lead configurations is utilized for both training and testing, In the On-the-fly Calibration stage, the first 5-second segment of each patient's ' ECG recording is used for model adaptation, with the subsequent 5-second segment reserved for performance evaluation.
All experiments are implemented using Py PyTorch 1.9 on three NVIDIA RTX2080Ti GPUs, each with 11 GB of memory. The implementation details of each experiment are shown in Appendix D
4.2 PERFORMANCE EVALUATION
In this section, evaluate NEF-NET v2's ability to generate an Electrocardio Panorama via two complementary tasks: reconstruction, in which the model regenerates ECG signals from viewpoints used in training, and synthesis, in which it produces signals for entirely unseen viewpoints, follow- ing (Chen et al., (021). Signal quality is assessed using the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM). These established metrics were chosen to ensure a fair and direct comparison with the Nef-Net baseline. All experiments were evaluated on arbitrary-length ECG segments. For the reconstruction task, Nef-Net (Chen et al., 202I), E-LSTM (Sohn et al. 2020), and KIM (Kors al.] 1990) were evaluated using the lead configuration settings adopted from previous work (Chen et 2002). ECGRecover (Lence et al. 2025). EKGAN (Joo et al., 2023). and SSSD (Alcaraz& & Strodthoff (202)) were evaluated under the setting of 3 to 9 and 8 to 12 reconstruction task. Owing to the use longer ECG recordings rather than beat-level data, our Nef-Net reproduction shows degraded performance compared to the original. For the synthesis task, we compare only with Nef-Net, as it is the only existing method capable of generating signals for unseen viewpoints. The number of views for input, supervision (reconstruction), and synthesis are listed in parentheses, in that order, All experiments were repeated multiple times for validation. We will report the standard deviation for PSNR data, while the standard deviation for SSIM omitted due to its negligible variation.
As shown Table [ our NEF-NET v2 sigmificantly outperforms previous methods on the recon- struction task under the 3-to-9-lead setting. These results provide strong reference for its synthesis capability. While under the more challenging 8-to-12-lead setting, the performance of existing state-of-the-arr models is closely matched.
The lower portion of Table 2 reveals a performance gap between the synthesis and reconstruction capabilities of both NEF-NET T v2 and Nef-Net, highlighting fundamental challenge in generalizing to novel ECG views. Despite this common challenge, NEF-NET v2 consistently surpasses Nef-Net across all datasets, achieving substantially higher PSNR and SSIM in Electrocardio Panorama synthesis. Our investigation on the Panobench dataset identified a key factor underlying these performance gap, with a detailed analysis provided in Section 4.3
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Table 3: Performance Comparison of Nef-Net and NEF-NET v2 on ECG Panoramic Synthesis with Varying Input and Supervised Leads on Panobench. Lead Types: Bipolar limb leads (I. II) measure potential between two limb electrodes. Unipolar leads (view-18, view-23) measure potential between body electrode and heart reference. Better values in bold.
Supervised Lends
Input Leads
Method
12
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
Nef-Net (Roe)
35.13:00.35
0,983
34.22:4041
0.981
34.28=
0.49
0.983
34 34.68:0.42
0,981
I. II, view-18
NEF-NET V2 (Rec)
Nef-Net (Syn)
1..13:1.15
37.25.0.400
0.891
0.989
29.19.1.37
36.22.1 0.20
0.985
0.965
31,89:2 0.33
36.15-00222
0.973
0.985
32 32.98:0.399
36.06-0.688
0.978
0.985
NEF-NET (Syn)
3166::0.43
0,973
33,05 0.31
0.973
35.13=0.44
0,983
35.57=0.23
0.983
Nef-Net (Roc)
35.77:00.25
0.986
34,80:
0.974
14:19: 0.57
0.976
35. 16:44:0.61
0.978
1. II view-18, 24, 51
NEF-NET V2 (Rec)
38.52:00331
0.992
38.18.1
0.34
0.984
36.66.00.28
0.987
38.56
0.987
Nef.Net (Syn)
21.08=0.700
0.880
30.35:00441
0.965
32.15 0.36
0.973
33.83++ 0.27
0.977
NER-NET v2 (8yn)
32.01:00.37
0.972
33.24 0.28
0.972
35.06 0.25
0.988
36.11:0.44
0.982
Nef-Net (Rec)
15.82::0.56
0.984
32.37.10.41
0.975
33,86
0.68
0.982
35. 0..34
0.982
II, viow-18, 37,
NER-NET
40.85-00.55
0.995
37.25+ 0.42
0.988
36.8--0.3
0,987
38.48-0.6
0,988
Nef-Net (Syn)
21.78::1004
0.917
28 28.06:20.35 39
0.964
31,94= 0.37
0.976
34,47:0.255
0,980
NEP-NETT V2 (8yn)
32.86-+ 0.39
0.973
33.21 +: 0.24
0.975
34.57=0.13
0.979
36.11 0.35
0,985
4.3 ELECTROCARDIO PANORAMA SYNTHESIS EVALUATION ON PANOBENCII
Most existing datasets provide only 12 views, which constrains comprehensive evaluation of panoramic synthesis. Therefore, we curated Panobench to more thoroughly assess the effectiveness of NEF-NET v2 in synthesizing Electrocardio Panorama. Our evaluation is designed to answer three questions: 1) How does NEF-NET V2 compare with Nef-Net in panoramic ECG synthesis? 2) How does the number of input leads affect reconstruction and synthesis performance? 3) How does the number of supervised leads affect reconstruction and synthesis performance?
Given the extensive combinations of input and target views, align our input configuration with the panorama training settings used for standard 12-lead ECG synthesis. Because the combinations are numerous, report representative cases in Table 3 Specifically, we select limb lead I and limb lead Il as inputs, together with precordial-like signals corresponding to the chest-lead view angles.
Figure 5 compares the synthesis and reconstruction performance of NEF-NET v2 and Nef-Net under varying levels of supervision. Notably, NEF-NET v2 achieves higher accuracy in both tasks. Across both models, reconstruction performance serves as an upper bound, quantifying the gap between each model's synthesis capability and its inherent representational limits. We observe that synthesis performance improves markedly with more supervised leads in both models, while reconstruction remains stable. This narrowing performance gap indicates enhanced generalization, as the model's s synthesis capability approaches its representational upper bound. In contrast, Nef-Net struggles under sparse-lead supervision but gradually improves as more leads are available, eventually approaching NEF-NET v2 's synthesis performance. In contrast to the significant role of supervision, the variation in the number of input leads (from 3 to 7) did not yield observable changes in the reconstruction or synthesis performance of either model.
The inferior performance of Nef- Net under sparse supervision stems from its limited use of view-specific information. Its encoder-decoder design com- presses signals into a latent car- diac field and uniformly aver- ages recorded features, neglect- ing the varying physiological rel- evance of individual views. As a result, query-irrelevant signals are mixed into the representa- tion, leading to blurred morphol- ogy and degraded fidelity, which becomes more pronounced with fewer supervised leads. In con- trast, NEF-NET v2 reformulates ECG synthesis as direct view-
3-Laads
Staa
Na5Net
No
Decorntuctio
Syrthea's
of siperi leads
Numrorro Suparvbes leacs
Deceratrution
Sytther
Manber Suparrssd koads
Numberrod Supervoed loads
Figure 5: Reconstruction and Synthesis Under Varying Inputs and Supervision.
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to-view transformation. By leveraging angular relationships. explicitly models inter-lead depen- dencies and selectively amplifies coometry-consisten features. This design preserves diagnostically relevant details and sustains high synthesis accuracy, even under sparse-lead supervision.
4.4 PERFORMANCES ON DIFFERENT DISEASES
Multi-lead ECGs capture cardiac electrical activity from spatially distinct perspectives (e.g., chest leads V1-V4 reflect the anterior wall). To rigorously assess whether NEF-NET v2 can synthesize diagnostically reliable signals across diverse cardiac conditions, we evaluate it on the CPSC2018 dataset, which encompasses nine categories of cardiac disorders, with detailed sample distributions provided in Appendix
Quantitative results in Table 4 demonstrate NEF-NET v2's superior reconstruction fidelity across all pathological categories, with an average PSNR improvement of 6.9 dB and consistent SSIM gains. Notably, its performance on Atrial Fibrillation (AF) signals improved by 7.3 dB. Beyond raw fidelity, the consistently larger margins on pathological cases (e.g., AF, I-AVB, PVC, STE) indicate that NEF-NET V2 may not only synthesize general signal morphology but also preserves key pathological signatures. The reduced performance gap between normal and abnormal rhythms suggests enhanced discase-adaptive capability, underscoring the potential of NEF-NET v2 to generate clinically reliable ECG waveforms under diverse diagnostic scenarios.
Table View Synthesis Performance on CPSC2018 across different diseases. Better in bold.
Normal
AF
I-AVB
LBBB
RBBB
PAV
PVC
STD
STE
AV
Nef-Net
PSNR
30.51
25.12
27.35
25.24
25.19
27.64
28,10
28.95
27.15
26.72
NEF-NET v2
PSNR
35.41
32.42
33.41
28.35
32.18
33.67
33.14
34.96
33.24
33.62
Nef-Net
SSIM
0.977
0,941
0.961
0,944
0.943
0.959
0.962
0,965
0.958
0.957
NEF-NET V2
SSIM
0.989
0.976
0.978
0.955
0.975
0.976
0.982
0.984
0.977
0.985
The clinical value of NEF-NET v2 lies in its ability to observe cardiac electrophysiology from arbitrary viewpoints, making the preservation of pathological features in the synthesized signals critically important. To verify this, we visualize synthesized signals at pathology-relevan viewpoints using real LBBB and RBBB cases. As these pathological characteristics typically manifest most prominently in the V1 and V6 leads, they provide the most appropriate basis for assessing the clinical relevance of NEF-NET v2's outputs. Due to space constraints, we present this analysis in Appendix E
4.5 ABLATION STUDY FOR THE THREE- STAGE DEVELOPMENT FRAMEWORK
The Any-Pairs Pretraining stage establishes a robust baseline by learning from large-scale ECG datasets. The Device Calibration stage adapts the model to specific ECG acquisition devices, while the On-the-fly Calibration stage provides case-level refinements by correcting for electrode placement variability and subject-specific anatomy. See Ta the results show that incorporating a Device Calibration step yields consistent PSNR gains of 0-1.07 dB and SSIM improvements of 0-0.004 across benchmarks, while adding On-the-Fly Calibration achieves comparable enhancements at 1.75-2.74 PSNR and 0.001-0.010 have a more pronounced impact on Electrocardio Panorama quality than inter-device variations. To further investigate this, we analyze the impact of electrode placement offsets NEF-NET v2's synthesis capability, with detailed results provided in Appendix E
SSIM. This indicates that inter-subject anatomical differences
Table 5: The impact of different stage for view synthesis tasks on the Tianchi, Chinadb, CPSC2018 and PTBXI. datasets.
ChinaDB
CPSC2018
Tianchi
PTBXL
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
Any-Pairs Pretraining
29.83++0.20
0.972
31.01+0.23
0.975
32.71=0.21
0.975
31.15++0223
0.981
Device Calibration
30.77+0..4
0.973
00.08
0.979
33.05-0.12
0.977
31.15 +0.11
0.981
On-the-fly Calibration
32.57+0..21
0.981
33.62# 0.17
0.985
34.46=0.35
0.976
33.41+0029
0.982
To further illustrate the benefits of each stage, 6 the progressive enhancements achieved by three-stage framework. Importantly, subtle variations in ECG signals are clinically critical, as

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Published as a conference paper at ICLR 2026
10 10
10
10
00
00
14 9
90
W
Stage Any-Pairs Pretraining
Stage II
Stage On-the-fly Calibration
Ground Truth
Device Calibration
Figure 6: Representative examples from CPSC2018 illustrate progressive synthesis of the V5 view by NEF-NET v2 across training stages. Green circles mark clinically relevant diagnostic details in the real signals, whereas red circles highlight their increasingly accurate recovery as our multi-stage training progresses.
even minor waveform differences may correspond to arrhythmia events or pathognomonic ST-segment changes. Consequently, even modest improvements in PSNR directly reflect the preservation of clinically salient waveform characteristics that are indispensable for accurate diagnosis and treatment. For instance, in Fig. 6 (fourth row), the heartbeat between samples 2300-2800 shows that the actual signal has a T-wave amplitude smaller than R-wave, while the synthesized signals at Stage and Stage II exhibit an ST segment higher than the R wave, a morphology that in clinical practice may indicate acute myocardial infarction, thereby potentially misleading diagnosis. The final output after on-the-Be the-fly calibration accurately reproduces the correct relationship. resulting in diagnosable-level synthesis. These findings demonstrate the necessity of the complete development-to-daee to-deployment framework: Any-Pairs Pretraining learns generalizable cardiac spatial priors, Device Calibration addresses device-level heterogeneity, and On-the-fly Calibration adapts to subject-specific anatomical variation. Together, these stages close the gap between controlled training conditions and the demands of real-world clinical deployment.
5 CONCLUSIONS
This work advances Electrocardio Panorama synthesis from controlled experimental settings to real-world applications. Our key methodological contribution reformulate ECG view synthesis, motivated by heart vector theory and the limitations of Nef-Net's feature averaging as a direct view-to- view transformation problem. Building on this formulation, we introduce three-stage development pipeline: large-scale pretraining, device-specific calibration, and on-the-fly adaptation case-specific electrode-ined indueedd viewpoint shifts. To enable rigorous evaluation, we curate Panobench, the first 48-lead ECG dataset annotated with precise CT-derived spherical coordinates (0, establishing comprehensive benchmark for Electrocardio Panorama synthesis. Experiments demonstrate that our NEF-NET v2 consistently outperforms previous works by substantial margin.
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ACKNOWLEDGMENTS
This work was partly supported by the Guangdong Basic and Applied Basic Research Foundation (2026A 10126151151111 515011793), the Youth S&T Talent Support Programme of Guangdong Provincial Associa- tion for Science and Technology (SKXRC2025467), as well as the National Key R&D Program of China (2023YFE01 10200).
ETHICAL STATEMENT
The collection of the Panobench dataset complied with standard ethical protocols, and written informed consent obtained from all participants, granting explicit permission for the academic use. All data were rigorously anonymized to safeguard participant privacy.
REPRODUCIBILITY STATEMENT
To ensure reproducibility, we provide full experimental details in the Appendix.
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A LLM USAGE
We made light use of a large language model (GPT-4, OpenAI) for grammar checking, spelling correction, and minor language polishing. The model was NOT involved in research ideation, experimental design, analysis, or interpretation. All scientific contributions and conclusions are entirely the responsibility of the authors.
B THEORETICAL FOUNDATIONS FOR MULTI-VIEY ECG GENERATION
Electrocardiograpiic (ECG) signals represent the temporal dynamics of cardiac depolarization and repolarization, recorded time-series waveforms. typical cardiac cycle consists of six characteristic deflections: the P wave, PR segment, QRS complex, ST segment, T wave, and TP segment. These deflections reflect distinct physiological processes. For example, the P wave corresponds atrial depolarization, the QRS complex captures rapid ventricular depolarization, and the T wave reflects ventricular repolarization. Clinically, subtle changes in the amplitude, duration, or morphology of these components can serve as critical biomarkers, such as ST-segment elevation indicating acute myocardial infarction or QRS widening suggesting conduction abnormalities (e.g.. bundle branch block). This fundamental structure underlies all lead systems and provides the physiological basis for both diagnostic interpretation and computational modeling.
Paren aegemant
gehcorgho STaegrant
1.0
Taaggarri
0.8
Ampltuud (a.u.
0.6
0.2
0.0
-0.2
-0.4
-.080
0.6
1.0
Time ist
Figure 7: Standard ECG waveform with six characteristic components highlighted: P wave, PR segment, QRS complex, ST segment, T wave, and TP segment.
In clinical cardiology, ECG signals are broadly categorized into two lead systems: the bipolar and unipolar lead systems. The bipolar jystem-comprinn Leads I, II, III, and the augmented limb leads aV R, L, and a F-recors the potential differences between pairs of electrodes placed on the limbs. These leads provide global yet relatively coarse projection of the heart's 's electrical activity onto the frontal plane, offering complementary directional information about the cardiac depolarization vector.
In contrast, the unipolar lead system, such as chest leads V1, V2, V3,.. and experimental leads like v view-1, vi ew-2 in Panobench, record the electrical potential at specific anatomical location relative to reference point (often Wilson's central terminal). The Wilson central terminal, defined as the average of the three limb electrodes, approximates the cardiac reference potential:
VRA + VLA + VLL
VweT
This configuration is conceptually analogous camera network in computer vision, in which each camera captures a distinct projection of a three-dimensions. scene. Similarly, each ECG lead acts as a biological "cammera, recording unique spatial projection of the heart's dynamic electrical activity over time. In standard clinical practice, for example, the precordial leads V1-V4 primarily assess the anterior wall of the heart, whereas V5-V6 provide information about the lateral wall (Anderson et al., 1994; Case et al. 1979). However, the fixed geometry of the conventional 12-lead ECG does not always capture all diagnostically relevant patterns. Clinicians frequently supplement the standard configuration with additional non-standard leads based on personal interpretation styles or case-specific requirements (Zhan et al. 2024). These observations underscore the inherent importance of examining cardiac electrical activity from multiple viewpoints.
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Theoretical Foundations of Neural Electrical Field for ECG Synthesis. From electrophysio- logical perspective, the cardiac electrical activity can be modeled as a time-varying source whose field described by multipolar expansion. As shown in Eq. 4 the extracellular potential (ax, y, 2) can be expressed as a series of dipole, quadrupole, and higher-order terms. In clinical practice, higher-order contributions are negligible at the body surface, leading to far-field dipole approximation.
1
E
r()r ps(r) f) + +...)
()),
4no
22
p
1
Σ
P4.
4
x²
1
Pa (x 20) Pyy (y) 10) + P= zo)
4
[[ xo)² (y y0) 2 + (2 20) )
where a denotes tissue conductivity, (Pz: Py. P=) are the dipole strengths along the cartesian axes, and (zo: Vo. 2o) denotes the geometric center of cardiac activity, which is not directly measurable. In clinical ECG acquisition, the Wilson central terminal is commonly adopted as practical approxi- mation to this reference potential. This formulation provides the theoretical underpinning for ECG view synthesis: from limited set of recorded leads, signals for any lead position (z, y, 2) or, equivalently, angular coordinates (0, :p).
infer the cardiac dipole and reconstruct
Building this, Nef-Net uses the relative angles between input and query leads as spatial priors to implicitly model the cardiac electrical field and synthesize the corresponding signals. Within this framework, the network parameters learn implicit representations of thoracic conductivity and field properties, enabling physiologically grounded reconstruction of signals from unobserved viewpoints.
Theoretical Foundations of View Transformation for ECG Synthesis. From the perspective of cardiac vector theory (Grant) 1950), the cardiac electrophysiological field can be represented as three-dimensional spatial vector. ECG signals from different leads can be viewed projections of this vector from various viewpoints. Therefore, a small subset of independent leads suffices to estimate the global electric field, such that the potential measured at lead can be expressed as:
Vi(t) ~ ptt) f.
(5)
where pt) is the üime-varying, cardiac dipole vector and A; is the orientation of lead i. This for- mulation highlights that multi-lead ECGs represent observations of the cardiac electrical field from different viewpoints, with varying degrees of information redundancy between these views. Synthe- sizing novel lead from recorded leads {i) can therefore be viewed learning transformation conditioned on angular relationships between f; and fy:
V₁(1) ((,.)),
Let T denote the projection operator implied by the dipole model. This formulation suggests that ECG signals from recorded views can be transformed target view through T. bypassing the need for explicit reconstruction of the underlying cardiac electrical field.
Our proposed NEF-NET v2 implements this insight by mapping angular coordinates (9, (p) into learnable representation, which enables feature projection based on spatial- relationships between recorded leads and target leads. By doing so, the network learns to approximate the theoretical operator T. effectively performing direct view-to-view transformation.
C DATASET DESCRIPTION
We evaluate NEF-NET v2 on several widely used public ECG benchmarks. PTB-XL contains 21,837 ten-second 12-lead ECGs sampled at 500 Hz and covering a wide range of cardiac pathologies. Tianchi consists of 31,779 12-lead recordings, also sampled at 500 Hz. ChinaDB provides 10,646 ten-second ECGs (5,000 samples each) at 500 Hz. CPSC2018 includes 6,877 multi multi-hospitta ECGs 500 Hz. We use CPSC2018 to assess the
with durations ranging from 6-60 seconds, sampled diagnostic reliability of synthesized signals across diverse pathological conditions: the distribution across nine diagnostic classes is summarized in Table 7
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The Panobench dataset is self-collected panoramic ECG resource comprising 4,470 ten-second recordings sampled at 250 Hz. Each sample contains 48 leads (6 limb and 42 precordial) collected under resting conditions from subjects aged 18-28. Electrode positions on CT volumes to obtain precise spherical coordinates for all leads. Compared with existing public datasets (e.g., PTB-XI. and CPSC2018), 8), Panobench offers substantially denser set of ECG viewpoints with explicit angular annotations, providing unique foundation for evaluating panoramic ECG synthesis.
manually annotated
A comprehensive comparison of dataset characteristics is provided in Table 6
Table 6: Detailed Description of the Used ECG Datasets.
Dataset
Recordings
Sampling Rate
Duration
Lead
PTBXL
21837
500/1000Hz
10s
12
Tianchi
31779
500Hz
10s
12
CPSC2018
6877
500Hz
6-60s
ChinaDB
10646
500Hz
10s
Panobench
4470
250Hz
10s
48
Table
The data description of CPSC2018
Class
Training set
%
Testing set
Total
%
Normal
734
10.6%
184
2.7%
918
13.3%
AF
878
12.8%
220
3.2%
1098
16.0%
I-AVB
563
8.2%
141
2.1%
704
10.3%
LBBB
165
2.4%
42
0.6%
207
3.0%
RBBB
1356
19.7%
339
4.9%
1695
24.6%
PAC
445
6.5%
111
1.6%
556
8.1%
PVC
538
7.8%
134
1.9%
672
9.7%
STD
9.6%
2.4%
825
12.0%
STE
162
2.4%
40
0.6%
202
3.0%
Total
5501
80.0%
1376
20.0%
6877
100.0%
In this work, lead positions were manually annotated using the ITK-SNAP software Yusskeevihh et al.) 2006). The annotation results are visualized in Figure 8 the three-dimensional rendering (lower-left panel) highlights the segmented cardiac volume (red, used as the reference center), the annotated Panobench leads (blue), and the standard 12-lead precordial electrodes (green).
subset 30 subjects was used for detailed analysis of lead orientations. Table g reports the mean angular positions derived from these annotations. The averaged limb-lead orientations are: Lead (909, 90%), Lead (150%, 90%), Lead (150;, -90%), aVR (60", -90%,, aVL (60", 90%), and VVF (180", 90%).
Table 8: Angles for Panobench
RA
0,
L.A
0.
52,88
43,-74
16
30.-7
20.70
28
30.69
34
40,80
68.78
63,61
17
54,51
23
48.42
29
54,48
35
60,71
6
90,74
12
90.54
18
90.33
Median
24
90.11
30
90.32
36
90.65
106,- 102
7
109.-75
13
113,55
19
118,40
25
122,32
31
119,41
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117.66
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112,105
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125.77
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153,63
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152,67
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http::/wwet wtw.iiikknpporrggg
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Figure 8: CT Annotation of 48-Lead ECG Electrodes, Six Precordial Leads, and Cardiac Position
D IMPLEMENTATION DETAILS OF DIFFERENT EXPERIMENTS
For easy re-implementation, this section documents the experimental configurations and implementa- tion details.
Number view transformer layers: 4;
Optimizer: AdamW;
Batch size: 32;
Weight decay: 10 10-2;
Learning rate step: 150,100,150
Gamma (a MultiStepLR hype-parameter): 0.5;
D.1 ANY PAIRS PRETRAINING
200-epoch self-supervised phase employing randomly selected lead combinations (3, 4, or 5 leads per input, excluding synthesized chest leads).
Training parameters: Exclude all parameters except a (learnable angular correction parameters used only in Stage III);
Learning rate: 10-3,
Training Datasets: All datasets;
Training epochs: 200
D.2 DEVICE CALIBRATION
Training parameters: Exclude all parameters except o;
Learning rate: * 10-4
Training Datasets: Specific dataset;
Training epochs: 200
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D.3 ON-THE-FLY CALIBRATION
Training parameters: Exclude all parameters except View Embed block and Reconstruction
Head:
Learning rate: * 10m3;
Training Datasets: Per-person;
Finetune iterations: 100
E FUTHER DISCUSSION OF THIS WORK
E IMPACT OF ON-THE-FLYY CALIBRATION ON DATA EFFICIENCY FOR VIEW SYNTHESIS
A data-driven approach is employed to develop the proposed view transformation algorithm, wherein an Any-Pairs pretraining strategy introduced enable the model to internalize the "language of ECG signals" while effectively leveraging heterogeneous ECG datasets with diverse lead config- urations. Such pretraining is critical for scaling data-driven models to robustly capture cross-lead correlations and improve generalization across varied acquisition settings.
To quantify its impact, we conducted data-efficiency study by varying the proportion of training data the CPSC2018 dataset, both with and without pretraining (Table Results demonstrate that in low-data regimes (1 percent and 5 percent), models trained from scratch exhibit severe performance degradation (c.g.. PSNR drop of up to 7.1 dB I percent data), whereas pretraining consistently mitigates this deficit, yielding stable performance even under limited data availability. Beyond 50 percent data, the performance gap narrows, underscoring pretraining's importance in resource-constrained scenarios and its role in enabling large-scale ECG view synthesis.
Table 9: CPSC201
Data volume
1% (44)
5% (223)
10% (446)
50%
(2234)
100%
(4468)
Pretrain
NO
YES
NO
YES
NO
YES
NO
YES
NO
YES
PSNR
24.68
31.75
29.04
31.91
30.05
31.89
31.07
32.14
31.67
32.06
SSIM
0.936
0.978
0.961
0.978
0.974
0.979
0.975
0.979
0.976
0.979
E.2
VALIDATING ON-THE-FLY CALIBRATION UNDER LEAD DEVIATIONS
One of the primary objectives of On-the-fly Calibration to perform individual-specife calibration of ECG signals by compensating for deviations in relative lead angles arising from two key sources: (1) variability in electrode placement introduced during manual clinical setup, and (2) inter-individual anatomical differences (e.g., variations in heart position and thoracic structure), illustrated in Fig.
To evaluate the effecttivnness of our learnable angular correction parameter (d0, dip), we introduce 10, 20%, and 30 angular deviation into the CPSC2018 dataset inputs and compare the result before and after the On-the-fly Calibration stage. As shown in Table [0] the quality of the result signals drop larger progressively the absence of correction. Once the model applied (d0,dp) and On-the- fly Calibration stage, both PSNR and SSIM returned to values close to the unperturbed baseline, demonstrating that our calibration mechanism effectively compensates for electrode misplacement and anatomical variability.
To achieve individualized model calibra- tion, NEF-NET v2 employs an Angle Embed block to encode angular informa- tion and Geometric View Transformer block to perform view transformation. Through adaptive fine-tuning of these modules, On-the-fi fly Calibration aligns recorded ECG views with their anatomi- cally consistent orientations, thereby cor- recting electrode placement enrors and
Table 10: The impact of On-the-fly Calibration on CPSC2018 (Dataset)
Uncorrected
After correction
Deviation
PSNR
SSIM
PSNR
SSIM
32.08
0.979
10
30.71
0.971
33.24
0.983
20
28.79
0.965
33.09
0,982
30
26.53
0.960
33.09
0.982
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Published as a conference paper at ICLR 2026
accounting for subject-specifer anatomical variability. This calibration step ensures that NEF-NET v2 can effectively adapt to individual physiological and acquisition-relate differences, ultimately improving its ability to synthesize accurate ECG panoramas across diverse patient populations.
PR CORPORRC
Figure 9: Illustration of inter- inter-ndiviiuall anatomical variability
E.3 ABLATION OF MODEL STRUCTURE
Based on the benchmark NEF-NET v2 (denoted as (A) in Table IT]. which averages multi-view ECG signals and employs an recoder-decoder architecture reconstruct the query view an estimated electric field, we investigate the impact of our proposed components.
Specifically, (B) incorporates the Geometric View Transformer (GeoVT), which explicitly models spatial relationships among ECG views to progressively synthesize the query view, but lacks query- guided encoding. (C) further integrates the View Encoder (VEncoder), yielding NEF-NET V2, where query-view angles guide feature extraction: the query embedding functions as angle-dependent gate that amplifies features aligned with query view while suppressing misaligned ones, thereby enhancing cross-view alignment.
Results show that Geo alone improves synthesis PSNR from 26.79 dB to 29.54 dB, demonstrating the effectiveness of explicit geometric modeling. Adding VEncoder yields substantial further gain (PSNR: 31.19 dB), validating the importance of query-aware feature encoding for precise perspective transformation. From geometric learning perspective, GeoVT captures inter-view spatial dependencies by progressively aggregating view-consistent features, while V'Ecodder leverages query- angle embeddings constrain feature extraction within the correct anatomical frame of reference. Their synergy ensures that synthesized signals remain anatomically consistent and view-coherent, even under sigmificant electrode anatomical variability.
Finally, (D) removes the noise perturbation and shows slight performance drop compared to (C), confirming the stabilizing effect of noise injection during training. Overall, these results highlight the complementary contributions of GTo VEncoder, and controlled noise perturbation in improving ECG view synthesis and transformation.
E.4 ROBUSTNESS COMMON ECG NOISE
NEF-NET v2 is intrinsically robust to common ECG distortions such as powerline interference and baseline wander. However, signals with strong motion artifacts may significantly degrade synthesis quality. This is expected because motion artifacts are nonstationary and abrupt disturbances whose frequency components heavily overlap with those of the ECG itself, making them fundamentally difficult to remove and a long-standing challenge even in the signal-processing literature. Motion artifacts typically exhibit amplitudes far exceeding those of the underlying ECG signal, effectively rendering the data unusable. Therefore, segments with severe artifacts are often discarded during data preprocessing. Moreover, mitigating such artifacts is primarily achieved through optimized
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Table 11: Ablation study CPSC2018 dataset (lead configuration: 3,8,1) evaluated in the Device Calibration stage.
Components
Synthesis
Reconstruction
GeoVT
VEncoder
PSNR
SSIM
PSNR
SSIM
A
26.79
0.958
28.47
0.960
B
V
V
29.54
0.972
32.22
0.971
CC
V
V
31.19
0.976
35.79
0.981
/
30.04
0.976
35.41
0.976
circuit-level design during signal acquisition, as algorithmic post-processing alone is often inadequate for their effective removal (Lee al. 2023 Torfs et 2014).
We first compared the synthesis performance on signals containing powerline interference and baseline wander against that clean signals. Visual inspection shows that the generated outputs effectively suppress these noise components. However, because the synthesized signals are clean while the reference signals remain noisy, the direct comparison leads to lower raw PSNR/SSIM values. To ensure a fair evaluation, we therefore denoised the reference signals and repeated the tests. The results are presented in the following table T2
Overall, noise exerts only a limited influence on the model. Since the generator tends to produce clean signals, discrepancies arise when the reference contains noise, leading lower raw metrics even when the synthesized outputs are visually superior.
Table 12: Synthesis performance (PSNR/SSIM) with noisy reference signals.
Noise Type
ChinaDB
CPSC2018
Tianchi
PTBXL
Before Filtering
Powerline interference
32.14 0.979
33.11 0.983
34.57 0.980
33.04 0.981
Baseline wander
32.53 0.982
33.47 0.983
34.69 0.981
33.25 0.981
Clear signal
33.24 / 0.986
34.18 0.987
35.14 0.987
34.17 / 0.983
After Filtering
Powerline interference
33.21 0.985
34.09 / 0.985
35.12 0.988
34.04 0.982
Baseline wander
33.08 0.984
34.13 / 0.985
34.97 0.986
33,95 / 0.982
Clear signal
33.24/ 0.986
34.18/0.987
35.14/ 0.987
34.17 0.983
E.5 CLINICAL EVALUATION
The ultimate value of synthesized ECG signals lies in their diagnostic fidelity, particularly the ability preserve pathological features across different viewing angles. In this section, we analyze the synthesized views for pathological cases of LBBB and RBBB.
As shown in the figure TO Across the core diagnostic leads (VI and V6), the panoramic ECG signals generated by NEF-NET v2 exhibit high degree of consistency with the corresponding real recordings. In the LBBB case, the synthesized V1 lead (0 = 90" o -10%) accurately reproduces the characteristic wide and deep QS/1S morphology. Likewise, the synthesized V6 lead (# 96", = 09) clearly presents the broad, notched R wave accompanied by the expected secondary ST-T changes. In the RBBB case, the synthesized VI lead (0 90" & 10%) precisely captures the hallmark rsR' "rabbit-car" pattern, reflecting the delayed right ventricular depolarization vector. These observations demonstrate that the panoramic ECG model effectively captures the pathophysiological signatures of bundle branch block and is capable of reproducing diagnostically decisive waveform features standard lead locations.
As shown in Fig. | NEF-NET v2 demonstrates strong capability in generating ECGs from nonstandard, virtual views. Given three sets of spherical coordinates: (0 90" 130%),
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NefNet v2
V1
V6
VI
V6
(9-90,
90,
68-%
Ground Truth
V1
V6
VI
V6
900
-10
9-90
(0-96.
30
LBBB
RBBB
Figure 10: ECG recordings from leads VI and V6 patients with LBBB and RBBB, along with the corresponding V1 and V6 signals synthesized by NEF-NET v2 from leads I, II, and V5.
(0 132", á -99)), and (0 140%, 100%), NEF-NET produces the corresponding synthesized views.
The results indicate that the synthesized signals consistently preserve the essential pathological characteristics across different viewpoints. For RBBB, the virtual view (0 132" 6 -99)) captures the typical rsR' morphology. For LBBB, the virtual view at (0 = 90" 130%) reveals the broad, notched R wave reflecting dominant left ventricular depolarization, while the view at = 132", Ø = -99%) presents wide and deep QS pattern. These findings show that NEF- NET v2 does not merely map waveforms but effectively reconstructs the three-dimensional cardiac depolarization vector, enabling the generation of ECG signals as if observed from any point on the cardiac sphere and thereby overcoming the physical constraints of conventional electrode placement.
Based on this principle, when diagnosing cardiovascular diseases that rely on specific lead positions, NEF-NET v2 offers distinct advantage. For example, in the diagnosis of Brugada syndrome, the characteristic ECG pattern may not appear in the standard V V1-V2 leads recorded at the fourth intercostal space. Clinically, the electrodes must be repositioned to the second third intercostal space to significantly improve detection sensitivity. In contrast, NEF-NET v2 can directly generate the corresponding virtual-view ECG simply by specifying the desired viewpoint coordinates, thereby providing clinicians with an optimized observation window without physically repositioning the electrodes.
241
200
340
e
130)
(8 =99)
10.
(a) LBBB
(0
130)
(0 -99)
Φ 1000
(b) RBBB
Figure 11: Arbitrary-view ECG signals LBBB and RBBB patients synthesized by NEF-NET from leads I, II, and V5.
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Since the pathological signatures of LBBB and RBBB manifest most prominently in leads VI and V6, we asked two independent board-certified cardiologists to evaluate the diagnostic quality of the generated V1 and V6 signals under these two conditions. Each waveform was scored 0-5 scale (5 = excellent fidelity, = clinically acceptable, 0 = misleading interpretation). Across 60 evaluations per cardiologist, all scores ranged between 3 and 5.
These evaluations show that NEF-NET v2 faithfully preserves the diagnostic morphology of bundle branch blocks, including the wide QS/iS complexes in VI and broad notched R waves in V6 for LBBB, and the characteristic rsR pattern in V1 for RBBB. Importantly, neither expert identified any clinically misleading artifacts. The consistently high ratings across both experts confirm that the synthesized signals maintain clinically meaningful fidelity, further supporting the utility of NEF-NET V2 for pathological ECG synthesis.
Table 13: Cardiologist evaluation synthesized V1/V6 signals for LBBB and RBBB. Scores range from 0-5 (higher is better).
Diagnosis
5
4
2
0
Total
Cardiologist 1
LBBB RBBB
25
5
0
0
0
30
28
2
0
30
Cardiologist 2
LBBB RBBB
25
3
2
0
0
30
29
0
0
0
30
For the panoramic dataset Panobench, further provide visual comparison between the real panoramic ECG (Fig. (2) and the panorama synthesized by NEF-NET v2 (Fig. (3). In Fig. 13] orange dashed boxes indicate the recorded input views (real signals), blue dashed boxes highlight the reconstructed views corresponding to supervised targets, and all remaining unboxed views represent fully synthesized signals. A close inspection reveals that the reconstructed views preserve finer morphological details due to direct supervision. In addition the generated views appear slightly smoother an expected behavior of generative models. Nonetheless, the generated signals remain highly consistent with the real panoramic ECG in Fig. 12 capturing the global morphology and inter-lead relationships across the full 48- view panorama.
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Figure 12: Representative example from Panobench, illustrating the full set of 48 recorded ECG viewpoints. Each view corresponds to a unique angular position, providing a dense panoramic characterization of the cardiac electrical field.
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Figure 13: Representative example synthesized by NET-NET v2 using Panobench. For intuitive comparison with the ground-truth panoramic ECG in Fig. 12, orange dashed boxes indicate the recorded ECG views, blue dashed boxes denote the views used as supervision during training, and all remaining views are synthesized by NEF-NET v2.
23


Reviews:
[{"review_id": "H1Yidr2Kia", "reviewer": "Reviewer_xHLx", "summary": "The paper presents Nef-Net+, an improved version of Nef-Net for synthesizing panoramic ECG signals from arbitrary viewpoints, addressing limitations like single-heartbeat modeling, device variability, and electrode placement errors through a new geometry-aware architecture and a three-stage workflow (pretraining, device calibration, on-the-fly calibration).\nIt also introduces Panobench, a new 48-view ECG dataset with CT-derived coordinates for benchmarking. While the enhancements show promising improvements in signal quality metrics (PSNR and SSIM), the evaluation lacks clinical validation, broader comparisons, and deeper analysis of the method's physiological fidelity, raising questions about its real-world diagnostic utility.", "questions": "o Can the authors elaborate on the rationale for employing the dipole approximation from cardiac vector theory as the foundational model, and discuss how NEF-NET+ accounts for potential higher-order multipolar contributions in scenarios involving complex cardiac\npathologies?\n\no Regarding the GeoVT module, the utilization of a shared Geometric Angular Attention (GAA) map across all blocks implies an assumption of static angular similarity; could this constrain the model's capacity to handle temporal variations in cardiac electrical activity, and were alternative dynamic attention mechanisms explored during development?\n\no Please provide details on the initialization and optimization strategy for the angular deviation parameters (dθ, dφ) in the on-the-fly calibration phase, including measures implemented to mitigate overfitting to the initial 5-second segment under conditions of signal noise or variability.\n\no In Table 4, the observed performance improvements vary across disease categories (e.g., relatively modest gains for LBBB); what factors might contribute to these disparities, and do they suggest inherent limitations in the model's representation of specific conduction\ndisorders?\n\no Could the authors explain the absence of assessments for downstream applications, such as leveraging synthesized ECG signals to enhance diagnostic model training or conducting clinician-led perceptual fidelity studies?\n\no Appendix E.2 demonstrates the efficacy of calibration for angular deviations up to 30°; what is the documented range of electrode placement errors in clinical practice, and how does the model's performance scale for deviations exceeding this threshold?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- The study is already established on a sound baseline work, and the treatment and the introduction of a geometry-aware cross-attention mechanism (GeoVT) and query-guided feature encoding are shown to be a reasonable solution, effectively addressing the limitations\nof uniform feature averaging in prior work, leading to better handling of sparse views and improved synthesis quality.\n\n- The three-stage workflow is a practical, enabling adaptation to device heterogeneity and patient-specific variations, which are critical for clinical deployment.\n\n- Panobench represents a valuable new benchmark with dense 48-view recordings and precise angular annotations, filling a gap in existing datasets and facilitating more comprehensive evaluation of panoramic ECG methods.\n\n- The visual schematics are highly informative and effectively showcases the methodology with clear annotations.", "weaknesses": "o The paper claims robustness to \"in-the-wild\" challenges but tests primarily on controlled datasets; real-world noise (e.g., motion  artifacts, baseline wander) is not explicitly simulated or evaluated beyond angular deviations.\n\no The evaluation relies heavily on PSNR and SSIM, which measure signal similarity but do not assess clinical relevance, such as the preservation of diagnostic features (e.g., arrhythmia detection or pathology-specific waveforms). Other potential metrics, like sensitivity/specificity for disease classification on synthesised signals, could strengthen claims of clinical utility.\n\no Comparisons are limited to Nef-Net and a few others (KIM and E-LSTM); the paper does not benchmark against other recent ECG synthesis methods (e.g., GAN-based or transformer-based approaches cited in related work), potentially overstating the novelty and superiority of NEF-NET+.\n\no Panobench has limited demographic diversity (subjects aged 18-28), which may not capture variations in older populations or those with comorbidities, limiting generalizability. Additionally, the dataset size (9360 recordings) is substantial but lacks details on\npathological distribution beyond basic categories.\n\no The on-the-fly calibration uses only the first 5 seconds of a 10-second recording, assuming stability; however, this may not hold for arrhythmic or dynamic ECGs, and no sensitivity analysis is provided for calibration duration or failure cases. This may highlight potential\nablation studies in this direction.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "s8UzCSwPP8", "reviewer": "Reviewer_MVub", "summary": "The paper introduces Nef-Net+, an enhanced framework for panoramic ECG synthesis. The model supports arbitrary-length signal generation from any desired view, aims to generalize across different ECG devices, and compensates for operator-induced deviations in electrode placement. To evaluate panoramic ECG synthesis, the authors also present Panobench, a new benchmark dataset including 9,369 recordings with 48 views per subject, designed to capture the spatial variability of cardiac electrical activity.", "questions": "1) Could the authors clarify what exactly *device heterogeneity* refers to in their experiments? It looks like by heterogeneity, they mean data from different datasets. \n\n2) Was the Panobench dataset curated or validated by medical professionals? \n\n3) How were the ECG datasets preprocessed before training? The paper combines recordings with different sampling frequencies (1000/500/250 Hz) and signal durations. Details regarding signal preprocessing are fundamental but completely missing from the paper.\n\n4) What is the rationale for using SSIM as an evaluation metric? Standard metrics exist for ECG synthesis and reconstruction (e.g., see [1, 2, 3]). A morphological analysis of ECG features such as peaks, waves, and segments would also be necessary to assess clinical fidelity. In addition, no statistical information (e.g., standard deviations) is reported for the quantitative results.\n \n5) It is unclear whether the experiments are conducted at the heartbeat level (as in the original Nef-Net) or on continuous ECG recordings. If the latter is the case, it becomes unclear how a fair comparison with Nef-Net is ensured, since that model was evaluated on single-beat reconstructions.\n\n6) The paper repeatedly states that Nef-Net+ supports *arbitrary-length ECG synthesis*. How is this implemented in practice? Are sequences chunked, streamed, or processed recurrently?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1) The paper addresses an important practical limitation of ECG modeling, i.e., the restricted number of observation viewpoints, and proposes an architectural improvement over Nef-Net.\n\n2) The Panobench dataset could be of interest to the biomedical ML community.", "weaknesses": "1) **The paper does not align with the conference scope**. The contribution is highly domain-specific and would be more appropriate for an applied or benchmark-oriented venueApplied/Benchmark track conference.\n\n2) Several paragraphs are written in a dense and overly technical style (e.g., 068-071, 152-155). A clearer presentation of the original Nef-Net architecture would greatly help to understand the improvements introduced in Nef-Net+, since the latter builds directly upon the former. For instance, the description of “direct view-to-view transformation” versus “neural electrocardio field reconstruction” (lines 140-142) it is important but not explained.\n\n3) Weak evaluation (see *Questions*).\n\n4) The discussion of related work on ECG reconstruction is limited and overlooks several recent and top-tier contributions in this area, to cite a few:\n\n[1] Alex Lence, Federica Granese, Ahmad Fall, Blaise Hanczar, Joe-Elie Salem, Jean-Daniel Zucker, Edi Prifti: ECGrecover: A Deep Learning Approach for Electrocardiogram Signal Completion. KDD (1) 2025: 2359-2370\n\n[2] Juan Miguel Lopez Alcaraz, Nils Strodthoff: Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models. Trans. Mach. Learn. Res. 2023 (2023)\n\n[3] Jinho Joo, Gihun Joo, Yeji Kim, Moo-Nyun Jin, Junbeom Park, Hyeonseung Im: Twelve-Lead ECG Reconstruction from Single-Lead Signals Using Generative Adversarial Networks. MICCAI (7) 2023: 184-194", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "SHo4fMwT2T", "reviewer": "Reviewer_yWqz", "summary": "The paper proposes NEF-NET+, a geometry-aware ECG transformation model that replaces field reconstruction with a direct view-to-view learning strategy. \nIt introduces a multi-stage adaptation pipeline to improve real-world robustness. \nA new 48-view dataset, Panobench, is constructed for spatially precise evaluation of cross-lead ECG reconstruction.", "questions": "It would be helpful to address the weaknesses if possible.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The combination of direct view transformation and geometry-aware attention effectively captures spatial lead dependencies while simplifying the modeling pipeline.\n- The three-stage calibration framework is well-aligned with real-world ECG acquisition and device variability.\n- The proposed 48-view Panobench dataset expands the spatial evaluation scope beyond traditional 12-lead ECGs", "weaknesses": "- Limited Validation of Geometry-Aware Attention: While the MGAA and GeoVT modules are claimed to model inter-lead angular relationships, the paper lacks quantitative evidence that these mechanisms genuinely capture geometric or biophysical correspondence. \nWhile the geometry-aware mechanism is formally defined and integrated into the architecture, the paper does not present attention-weight visualizations nor any correlation analysis between learned attention weights and actual spatial distances or electric potential gradients.\n\n- Lack of Clinical Interpretability: The performance evaluation relies heavily on signal reconstruction metrics, which do not directly reflect diagnostic or physiological relevance. \nThe absence of task-oriented evaluation metrics limits the interpretability and translational value of the proposed framework in clinical contexts.\n\n- Computational Efficiency and Deployment Feasibility: Although the architecture simplifies the overall transformation pipeline, the paper does not quantify the practical cost of on-the-fly calibration, which requires per-examination adaptation. \nThe manuscript does not report time-to-adapt (wall-clock latency from raw input to an adapted model), compute/memory budget for the calibration step on realistic hardware, or convergence stability under streaming/telemetry conditions. \nThis omission makes it difficult to assess whether the per-patient adaptation loop can meet real-time throughput constraints in clinical workflows and whether maintaining adapted parameters across encounters is feasible on resource-constrained medical devices.\n\n- Limited Accessibility of the Panobench Dataset: While the appendix provides detailed descriptions of the Panobench dataset and its construction process, the dataset itself is not publicly available at the time of writing. \nGiven that Panobench serves as a central contribution and evaluation benchmark, the lack of open access limits reproducibility and independent verification of the reported results (the paper only states that code and data “will also be released publicly”).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)