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Spectral point transformer for significant wave height estimation from sea clutter

Yi Zhou, Li Wang, Hang Su, Tian Wang

TL;DR

The paper addresses the challenge of estimating the significant wave height $H_s$ from sea clutter radar data by introducing the Spectral Point Transformer (SPT), which leverages sparse high-energy spectral points aligned with dispersion relations. It processes 3D-FFT spectra to extract $N$ points with features $f=[z, k_x, k_y, u, p]$, then uses an embedding module, RMSNorm-enabled transformer blocks, and a regression head to predict $H_s$ with a robust Huber loss. The approach achieves competitive or superior accuracy with far fewer parameters and FLOPs than full-spectrum CNN/ViT baselines, and exhibits learned features that align with physical dispersion curves, indicating a meaningful physics-informed representation. This enables efficient, real-time capable radar wave monitoring with reduced data and computational requirements, offering lower deployment costs and scalable insights for ocean state estimation. $H_s$ estimation remains data-limited in nearshore scenarios, prompting future work to collect more diverse data and extend the method to other oceanographic parameters such as current speed and direction.

Abstract

This paper presents a method for estimating significant wave height (Hs) from sparse S_pectral P_oint using a T_ransformer-based approach (SPT). Based on empirical observations that only a minority of spectral points with strong power contribute to wave energy, the proposed SPT effectively integrates geometric and spectral characteristics of ocean surface waves to estimate Hs through multi-dimensional feature representation. The experiment reveals an intriguing phenomenon: the learned features of SPT align well with physical dispersion relations, where the contribution-score map of selected points is concentrated along dispersion curves. Compared to conventional vision networks that process image sequences and full spectra, SPT demonstrates superior performance in Hs regression while consuming significantly fewer computational resources. On a consumer-grade GPU, SPT completes the training of regression model for 1080 sea clutter image sequences within 4 minutes, showcasing its potential to reduce deployment costs for radar wave-measuring systems. The open-source implementation of SPT will be available at https://github.com/joeyee/spt

Spectral point transformer for significant wave height estimation from sea clutter

TL;DR

The paper addresses the challenge of estimating the significant wave height from sea clutter radar data by introducing the Spectral Point Transformer (SPT), which leverages sparse high-energy spectral points aligned with dispersion relations. It processes 3D-FFT spectra to extract points with features , then uses an embedding module, RMSNorm-enabled transformer blocks, and a regression head to predict with a robust Huber loss. The approach achieves competitive or superior accuracy with far fewer parameters and FLOPs than full-spectrum CNN/ViT baselines, and exhibits learned features that align with physical dispersion curves, indicating a meaningful physics-informed representation. This enables efficient, real-time capable radar wave monitoring with reduced data and computational requirements, offering lower deployment costs and scalable insights for ocean state estimation. estimation remains data-limited in nearshore scenarios, prompting future work to collect more diverse data and extend the method to other oceanographic parameters such as current speed and direction.

Abstract

This paper presents a method for estimating significant wave height (Hs) from sparse S_pectral P_oint using a T_ransformer-based approach (SPT). Based on empirical observations that only a minority of spectral points with strong power contribute to wave energy, the proposed SPT effectively integrates geometric and spectral characteristics of ocean surface waves to estimate Hs through multi-dimensional feature representation. The experiment reveals an intriguing phenomenon: the learned features of SPT align well with physical dispersion relations, where the contribution-score map of selected points is concentrated along dispersion curves. Compared to conventional vision networks that process image sequences and full spectra, SPT demonstrates superior performance in Hs regression while consuming significantly fewer computational resources. On a consumer-grade GPU, SPT completes the training of regression model for 1080 sea clutter image sequences within 4 minutes, showcasing its potential to reduce deployment costs for radar wave-measuring systems. The open-source implementation of SPT will be available at https://github.com/joeyee/spt
Paper Structure (15 sections, 11 equations, 4 figures, 3 tables)

This paper contains 15 sections, 11 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methodology
  4. Pre-processing
  5. SPT Network Architecture
  6. Embedding Module
  7. Transformer Block
  8. Regression Head
  9. Experiments
  10. Experimental Setup and Radar Parameters
  11. Model Comparison
  12. Analysis of SPT Characteristics
  13. Ablation Study
  14. conclusion
  15. Acknowledgment

Figures (4)

  • Figure 1: (a) Top 512 sea clutter spectral points in the wavenumber-frequency domain and the underlying dispersion shell. (b) Energy distribution of the sparse points compared with the empirical PM and JONSWAP wave spectra.
  • Figure 2: The framework of Spectral Point Transformer (SPT).
  • Figure 3: On-site experimental environment as viewed from the radar location. The white-dashed circle marks the wave-measuring buoy, and the rectangles indicate three observed sea zones ($z_1, z_2, z_3$), with their corresponding raw sea clutter images displayed on the right.
  • Figure 4: Alignment of SPT features with physical dispersion relations. The left column shows $w$-$k_y$ planes for different $H_s$ values. Solid lines represent dispersion relations, and dashed lines indicate aliasing effects. The right column highlights feature similarity scores, with higher intensities indicating stronger influence on regression.