P-SER: Physical Consistency-Constrained Scattering Expandable Representation for Class-Incremental HRRP Target Recognition

Fangyi Wang; Peng Zhao; Haipeng Wang

cs.CVNov 3, 2026

P-SER: Physical Consistency-Constrained Scattering Expandable Representation for Class-Incremental HRRP Target Recognition

Authors: Fangyi Wang, Peng Zhao, Haipeng Wang

Organizations: Key Laboratory of Information Science of Electromagnetic Waves (MOE), and the Discipline and Technology Center of Microwave Vision Intelligent Sensing, Fudan University, Shanghai 200433, China

Abstract

High-resolution range profiles (HRRPs) provide compact radar target representations but exhibit strong aspect sensitivity, complicating class-incremental recognition when historical data are unavailable. Changes in viewing aspect shift scattering-peak locations and amplitudes, while reflector groups may produce responses resembling ships. Existing dynamic expansion methods can also incur substantial parameter and memory overhead. To address these challenges, we propose P-SER, a Physical Consistency-Constrained Scattering Expandable Representation framework for exemplar-free class-incremental HRRP recognition. P-SER reconstructs dominant scattering points from complex-valued sum- and azimuth-difference-channel HRRPs and observation geometry. The reconstructed spatial structure, target extent, and energy distribution are used to derive class-level scattering prototypes and sample-level saliency priors, providing physically grounded constraints for feature learning and old-class knowledge retention. A primitive scatterer dictionary further characterizes local strong-scattering mechanisms and calibrates uncertain ship--reflector predictions at inference. Meanwhile, lightweight residual adapters are incrementally introduced into a shared HRRP backbone to learn new classes with limited model growth. Experiments on simulated and measured HRRP datasets show that P-SER delivers competitive recognition performance without retaining old-class exemplars, while maintaining physical consistency, interference robustness, knowledge retention, and model scalability.

Figures & tables

Fig. 1: Illustration of continual class-incremental HRRP observation and its physical scattering response. Target classes expand progressively, while the HRRP imaging mechanism remains intrinsically sensitive to viewing aspect. Dominant responses are formed by the range projection of physical scattering centers, motivating the use of stable physical properties for incremental recognition.

Fig. 2: Key challenges in class-incremental HRRP recognition and the corresponding solutions in P-SER.

Fig. 3: Overall framework of the proposed P-SER. The framework consists of three complementary components: physical-consistency scattering prototype constraint (PCSP), PSD-guided scattering-component inference calibration (PSD-SCIC), and lightweight residual adapter expansion (LRAE).

Fig. 4: Overview of PCSP, which reconstructs physically consistent scattering points from HRRP observations and uses the resulting class-level prototypes and sample-level saliency priors to constrain incremental recognition.

Fig. 5: Representative samples from the simulation and measured datasets: (a) HRRP profiles of the ten simulated target classes, including ships and reflector groups; and (b) measured target images with their corresponding HRRP profiles.

Dataset	Target type	Length & width (m)	Training	Test
Simulation dataset
	Bulk carrier	(152.14, 16.07)	3240	810
	Container	(139.37, 23.37)	3240	810
	Passenger	(178.82, 26.01)	3240	810
	General cargo	(121.50, 21.72)	3240	810
	Dredger	(79.52, 15.42)	3240	810

TABLE I: Simulation and Measured HRRP Datasets

Fig. 6: Accuracy comparison of different incremental learning methods across incremental stages on the self-constructed simulation dataset.

Method	Exemplars per class	8-stage			4-stage			2-stage
Method	Exemplars per class	Params. (M)	$\mathcal{A}_{B}$ (%)	$\bar{\mathcal{A}}$ (%)	Params. (M)	$\mathcal{A}_{B}$ (%)	$\bar{\mathcal{A}}$ (%)	Params. (M)	$\mathcal{A}_{B}$ (%)	$\bar{\mathcal{A}}$ (%)
LwF [ 29 ]	0	11.17	47.89	61.50	11.17	51.29	66.15	11.17	55.23	68.93
iCaRL [ 38 ]	150	11.18	43.28	62.42	11.18	48.45	64.57	11.18	49.11	65.69
PODNet [ 9 ]	150	11.18	56.34	69.01	11.18	59.03	72.15	11.18	60.05	72.18
DER [ 50 ]	150	89.39	60.41	73.12	44.71	63.37	77.98	22.37	69.41	78.45
VAE+DER [ 10 , 50 ]	150	89.44	65.55	76.69	44.74	69.97	80.91	22.40	71.06	83.03

TABLE II: Performance Comparison on the Self-Constructed Simulation Dataset

Fig. 7: Final-round confusion matrices of P-SER. The top row reports the simulation results under the (a) 8-stage, (b) 4-stage, and (c) 2-stage settings; the bottom row reports the measured results under the (d) 4-stage and (e) 2-stage settings.

Fig. 8: Accuracy comparison of different incremental learning methods across incremental stages on the measured dataset.

Method	Exemplars per class	4-stage			2-stage
Method	Exemplars per class	Params. (M)	$\mathcal{A}_{B}$ (%)	$\bar{\mathcal{A}}$ (%)	Params. (M)	$\mathcal{A}_{B}$ (%)	$\bar{\mathcal{A}}$ (%)
LwF [ 29 ]	0	11.17	43.75	63.25	11.17	51.63	67.44
iCaRL [ 38 ]	150	11.18	53.14	65.47	11.18	55.29	68.07
PODNet [ 9 ]	150	11.18	48.62	63.81	11.18	52.81	64.90
DER [ 50 ]	150	44.71	60.47	69.32	22.37	65.47	72.12
VAE+DER [ 10 , 50 ]	150	44.74	61.72	71.34	22.40	64.38	74.77

TABLE III: Performance Comparison on the Measured Dataset

Setting	Component			Recognition accuracy (%)									Avg.
Setting	PCSP	PSD-SCIC	LRAE	Base	Stage-1	Stage-2	Stage-3	Stage-4	Stage-5	Stage-6	Stage-7	Stage-8	Avg.
Ablation Exp-1	$\times$	$\times$	$\times$	83.44	67.36	63.84	61.11	57.47	55.82	49.34	47.93	46.59	59.21
Ablation Exp-2	$\checkmark$	$\times$	$\times$	96.29	89.37	87.24	84.68	80.15	77.92	73.46	67.81	65.29	80.25
Ablation Exp-3	$\checkmark$	$\checkmark$	$\times$	96.29	89.37	85.76	83.18	82.64	78.31	75.87	74.22	72.59	82.03
Ablation Exp-4	$\checkmark$	$\times$	$\checkmark$	96.29	93.72	87.35	85.72	84.19	81.63	77.84	75.27	74.51	84.06
Ablation Exp-5	$\times$	$\checkmark$	$\times$	83.44	67.36	73.28	69.91	65.43	59.75	55.12	53.86	50.34	64.28

TABLE IV: Ablation study of the proposed components.

Fig. 9: Target reconstruction results for representative observations from the simulation test set. The dots denote the retained dominant scattering points, and the orange rectangles indicate the reconstructed target extents in the range and cross-range directions.

Target	GT $(L,W)$ (m)	Reconstructed $(\widehat{L},\widehat{W})$ (m)	$\epsilon_{L}$ (%)	$\epsilon_{W}$ (%)
Bulk carrier	(152.14, 16.07)	(149.38, 18.62)	1.81	15.87
Container	(139.37, 23.37)	(141.66, 25.97)	1.64	11.13
Passenger	(178.82, 26.01)	(186.59, 29.50)	4.35	13.42
General cargo	(121.50, 21.72)	(117.67, 23.09)	3.15	6.31
Dredger	(79.52, 15.42)	(83.25, 17.84)	4.69	15.69
Fishing	(46.85, 8.60)	(50.13, 11.81)	7.00	37.33

TABLE V: Full-Test-Set Reconstruction Statistics on the Simulation Dataset

Fig. 10: Hyperparameter sensitivity on the measured 4-stage protocol: final-round accuracy with respect to (a)

\lambda_{\mathrm{sp}}

and

\lambda_{\mathrm{p}}

, and (b)

\tau_{p}

and

\mu_{\mathrm{sc}}

Class-Incremental Learning

Class-incremental learning studies how models can add new categories over time while retaining the ability to recognize previously learned classes.

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Polarimetric Scattering-Structure Contrastive Learning for Few-Shot HRRP Recognition

Fangyi Wang, Peng Zhao, Haipeng Wang

Fudan University, China

Few-Shot Learning Contrastive Learning

Open paper AskPDF arXiv

Few-shot high-resolution range profile (HRRP) recognition is challenged by strong aspect-dependent variation and sparse novel-class support. We propose polarimetric scattering-structure contrastive learning (PSS-CL), which supplies an episodic HRRP encoder with a structured physical training view. Dominant local responses are represented by their soft affinities to canonical polarimetric mechanisms, normalized range locations, and energy contributions. A symmetric cross-view objective transfers this scattering structure to the learned HRRP representation, while episodic prototype learning supports novel-class inference without the physical branch. We conduct Random-aspect and Cross-aspect experiments on a six-class measured dataset. In Cross-aspect 1-, 3-, and 5-shot recognition, PSS-CL achieves 81.73%, 86.92%, and 90.98% mean class accuracy (MCA), respectively, outperforming the best competing results by 5.62%, 3.09%, and 3.56%.

Abstract

Class-Incremental Learning

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