# Spectral Reconstruction

Computational hyperspectral imaging must hold highlights and shadows in one shot, but the encoding mask's channels have unequal spectral responsivities, so no single exposure keeps every channel in its reliable range. A Zhejiang University team moves multi-exposure fusion ahead of spectral inversion, into the encoded measurement domain, where an analytical reliability prior and a learned channel-specific adjustment jointly set fusion weights, and measurement-domain spectral-angle supervision constrains relative channel responses. On a 9-channel broadband-encoded camera, an optical-density target gives a spectral reconstruction dynamic range of 42.8 dB, 16.0 dB above the best fixed single exposure at 26.8 dB.

Computational hyperspectral imaging must hold highlights and shadows in one shot, but the encoding mask's channels have unequal spectral responsivities, so no single exposure keeps every channel in its reliable range. A Zhejiang University team moves multi-exposure fusion ahead of spectral inversion, into the encoded measurement domain, where an analytical reliability prior and a learned channel-specific adjustment jointly set fusion weights, and measurement-domain spectral-angle supervision constrains relative channel responses. On a 9-channel broadband-encoded camera, an optical-density target gives a spectral reconstruction dynamic range of 42.8 dB, 16.0 dB above the best fixed single exposure at 26.8 dB.

Using Fisher information and random matrix theory, the authors derive a closed-form expression for the noise-induced error of chaotic/diffusive reconstructive spectrometers, linking the variance bound σ²_ε Tr[(AᵀA)⁺] to the spectral correlation length Γ_corr, mean transmittance T₀, and the numbers of frequency channels N and measurement channels M, establish conditions for super-resolution, and validate the theory with a random matrix model and full-wave FDTD simulations, where the predicted optimal on-chip cavity size is about 17.9 µm.

Using Fisher information and random matrix theory, the authors derive a closed-form expression for the noise-induced error of chaotic/diffusive reconstructive spectrometers, linking the variance bound σ²_ε Tr[(AᵀA)⁺] to the spectral correlation length Γ_corr, mean transmittance T₀, and the numbers of frequency channels N and measurement channels M, establish conditions for super-resolution, and validate the theory with a random matrix model and full-wave FDTD simulations, where the predicted optimal on-chip cavity size is about 17.9 µm.