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HarmoCore Reconstructs Oscillatory Wave Fields from Sparse Data

Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang· September 2, 2026 View original

Key takeaways

  • HarmoCore reconstructs complex, oscillatory wave fields from extremely sparse data.
  • It uses a compact, continuous latent representation with Functional Tucker cores.
  • Diffusion Posterior Sampling is performed directly in the core space for efficiency.
  • The method shows significant gains with minimal sensing, even in 3D.

Who benefits

Medical ImagingGeophysicsNon-Destructive TestingAcousticsDefense

Summary

HarmoCore is a novel functional latent diffusion model designed to reconstruct complex-valued, oscillatory wave fields from extremely sparse sensor observations. It uses a compact, continuous latent representation and performs diffusion posterior sampling in core space, significantly outperforming existing methods, especially in 3D.

Reconstructing oscillatory wave fields, such as sound or electromagnetic waves, from limited sensor data is a notoriously difficult inverse problem. These fields are complex-valued, frequency-sensitive, and highly oscillatory, making them challenging for existing reconstruction methods that are often designed for real-valued, smoother data. Traditional dense pixel-space diffusion models are also inefficient and struggle to scale to three dimensions. HarmoCore introduces a new approach by placing a generative prior in a compact, continuous, and structured wave-field latent space. It represents the complex-valued channels using Functional Tucker cores over shared continuous spatial bases and learns a frequency-conditioned core diffusion prior. The method performs Diffusion Posterior Sampling directly in this core space, avoiding the inefficiencies of pixel-space correction. By incorporating optional target-equation residual guidance, HarmoCore also promotes physical consistency. Experiments show substantial gains in reconstruction accuracy with very sparse sensing (1-2%) across 2D and 3D Helmholtz and synthetic wave fields.

Why it matters

This breakthrough enables more accurate and efficient sensing and imaging in fields like medical diagnostics, non-destructive testing, and geophysical exploration, even with minimal data.

How to implement this in your domain

  1. 1Investigate HarmoCore's functional latent diffusion approach for sparse data reconstruction in your domain, especially for wave-based phenomena.
  2. 2Explore the use of Functional Tucker cores for compact representation of complex, high-dimensional data.
  3. 3Consider how diffusion posterior sampling in a latent space could improve efficiency for inverse problems.
  4. 4Collaborate with research teams to adapt HarmoCore's principles to specific sensing or imaging challenges.

Original post by Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang

"arXiv:2609.00679v1 Announce Type: new Abstract: Reconstructing oscillatory wave fields from scattered sensors is a severely underdetermined inverse problem. Beyond the challenges of general physical-field reconstruction, wave responses are complex-valued, frequency-sensitive, and…"

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Originally posted by Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang on X · view source

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