arXiv:2606.00126eess.IV2026-06

无需真值即可预测信号压缩误差,给出可计算的理论边界。

Bounding Global and Local Compression Error of Signal Parameterizations

论文配图:Bounding Global and Local Compression Error of Signal Parameterizations
图 1 · 摘自论文原文
  • 通过不同压缩层级模型输出差值,构造误差上界。
  • 在合成与真实信号上,误差预测与实际误差高度吻合。
  • 适用于图像、辐射场、MRI等重建任务,适合无真值场景。

可微分信号参数化(如隐式神经表示和混合模型)在计算成像中日益重要,但当缺乏真实信号时,对有限模型规模下的重建保真度评估仍缺乏系统方法。本文提出一种框架,可在不依赖真实信号的情况下,高效计算非渐近、信号相关的重建误差上界。我们证明,当参数化压缩满足特定自然性质时,任意压缩等级的误差可由不同压缩层级模型预测值之差的缩放形式界定。该性质在插值网格、傅里叶特征网络、多分辨率哈希编码及张量分解等典型模型中成立。实验表明,由此导出的最坏情况保证可高效转化为紧致且可泛化的信号特异性误差预测器,在直接拟合合成与自然信号,以及辐射场和MRI重建等反问题中,能准确追踪全局误差曲线并生成局部误差热图,且无需真值。代码已开源。

原文摘要 · Abstract (English)

Differentiable signal parameterizations such as implicit neural representations (INRs) and hybrid models are increasingly central to computational imaging, yet principled tools for evaluating reconstruction fidelity at finite model size remain limited when ground truth is unavailable. We introduce a framework for predicting the reconstruction error of compressive signal parameterizations, yielding non-asymptotic, signal-specific bounds that are both theoretically sound and efficiently computable without access to the ground truth signal. Specifically, we prove that when parameterization-based compression satisfies certain natural properties, the compression error at any compression level is bounded by a simple scaled difference between model predictions at different compression levels. We verify these properties for representative model families including interpolated grids, Fourier feature networks, multi-resolution hash encodings, and tensor factorizations, and show empirically that the resulting worst-case guarantees can be efficiently adapted into signal-specific error predictors that are tight and generalizable. Across direct fitting of synthetic and natural signals, and inverse problems including radiance field and MRI reconstruction, our method closely tracks global error curves and yields informative local error heatmaps without ground-truth access. Code is available at https://github.com/voilalab/global_error_bound.

信号压缩误差估计无真值神经表示

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