Optimal Multispectral Imaging using RGB Cameras

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.