Problem
Research questions and friction points this paper is trying to address.
oscillatory wave fields
sparse reconstruction
underdetermined inverse problem
HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields
🤖 AI Summary
本文提出HarmoCore方法，通过在紧凑连续的波场潜在空间中引入生成先验，解决稀疏观测下振荡波场重建的问题。
📝 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 highly oscillatory, while costly simulation and sensing often leave only extreme-sparse observations. Existing low-rank, operator, and diffusion approaches are largely designed for real-valued, smoother fields; dense pixel-space diffusion is particularly inefficient for oscillatory complex fields and difficult to scale to 3D. We propose HarmoCore, which places a generative prior in a compact, continuous, and structured wave-field latent. HarmoCore represents joint real--imaginary channels with Functional Tucker cores over shared continuous spatial bases, learns a frequency-conditioned core diffusion prior, and performs Diffusion Posterior Sampling directly in core space. At fixed sensor coordinates, the multilinear decoder induces an explicit likelihood guidance operator, avoiding dense pixel-space correction. Optional target-equation residual guidance further promotes physical consistency. Experiments on 2D Helmholtz, 2D synthetic wave fields, and 3D Helmholtz show substantial gains under 1%--2% sensing while remaining practical in three dimensions.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Functional Latent Diffusion
Sparse Reconstruction
Oscillatory Wave Fields
Continuous Spatial Bases
Diffusion Posterior Sampling
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