Compact hyperspectral cameras enable scanning a scene with both a large spectral and spatial resolution. However, they use Fabry-Perot filter (FPf) arrays with different cavity heights. The transmittance of each FPf basically produces two peaks coming from the harmonics of the filter. However, the exit pupil of the device together with the pixel position degrades the perfect transmittance. We propose here to model the whole degradation of the datacube pixels extracted from the raw images according to extending Goossens et al.'s physical model. In this article, in order to recover the luminance of one pixel, we propose to invert this physical model by solving a non-negative ill-posed problem. It turns out that our whole method outperforms state-of-the-art approaches, especially, the one proposed by the manufacturer.