Optically multiplexed image acquisition techniques have become increasingly popular for encoding different exposures, color channels, light fields, and other properties of light onto two-dimensional image sensors. Recently, Fourier-based multiplexing and reconstruction approaches have been introduced in order to achieve a superior light transmission of the employed modulators and better signal-to-noise characteristics of the reconstructed data. We show in this paper that Fourier-based reconstruction approaches suffer from severe artifacts in the case of sensor saturation, i.e. when the dynamic range of the scene exceeds the capabilities of the image sensor. We analyze the problem, and propose a novel combined optical light modulation and computational reconstruction method that not only suppresses such artifacts, but also allows us to recover a wider dynamic range than existing image-space multiplexing approaches.