arXiv:2604.19460eess.SPeess.IV2026-04

用RGB相机+滤光片实现高精度多光谱成像,优化波长分配提升重建稳定性。

Optimal Multispectral Imaging using RGB Cameras

论文配图:Optimal Multispectral Imaging using RGB Cameras
图 1 · 摘自论文原文
  • 基于物理模型建模相机响应,通过滤光片与感光特性匹配设计系统矩阵。
  • 在12个目标波长下,找到使条件数最小的配置,显著提升抗噪能力。
  • 支持冗余测量设计,适合低资源环境下需要高鲁棒性的多光谱应用。

本文提出一种基于物理驱动的框架,利用低成本的现成RGB相机与窄带多波段光学滤光片构建多光谱成像系统。通过建立线性测量模型,将相机响应表示为未知光谱成分的线性组合,混合系数由相机光谱敏感度与滤光片透射率重叠决定。多相机配置下,各相机模型被整合为全局系统,其结构完全由目标波长在相机-滤光片单元间的分配决定。将波长分配视为确定性设计问题,选择使系统矩阵谱条件数最小的配置。该准则在框架理论指导下,可提升数值稳定性、最大化最差情况信噪比并增强光谱重构鲁棒性。由于设计空间有限,可在实际约束下评估所有可行配置。实验以12个目标波长和四组三波段滤光片为例,识别出最稳定且抗噪能力强的波长分配方案。所提框架包含冗余配置,即单个波长由多个相机测量,进一步增加自由度以改善抗噪性能。

原文摘要 · Abstract (English)

We present a physics-driven framework for accurate evaluation of discrete spectral bands using a low-cost multispectral setup built from off-the-shelf RGB cameras and narrow multi-band optical filters. The approach starts by explicitly formulating a linear measurement model. The camera responses are expressed as linear mixtures of unknown spectral components, with mixing coefficients determined by the overlap between the camera spectral sensitivities and the filter transmittances. For a multi-camera configuration, the per-camera models are stacked into a single global system whose structure is fully determined by the allocation of target wavelengths across the camera--filter units. We pose wavelength allocation as a deterministic design problem and select the configuration that minimizes the spectral condition number of the resulting system matrix. Guided by a frame-theoretic interpretation, this criterion promotes numerical stability, maximizes worst-case output signal-to-noise ratio, and improves the robustness of spectral reconstruction. The design space is finite, enabling the evaluation of all feasible configurations under practical constraints. We demonstrate the method on a representative example with 12 target wavelengths and four triband filters, and identify the wavelength allocation that yields the most stable and noise-robust recovery. The proposed framework includes redundant configurations, in which individual wavelengths are measured by multiple cameras, thereby providing additional degrees of freedom that further improve noise robustness.

多光谱成像光学设计信号重建噪声鲁棒

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