A mask-modulated LDR image captured with our prototype scan camera (a). The pattern introduced by the mask and saturated regions are enlarged on the upper left. The Fourier transform of the captured image (b) contains nine copies, of which three (b, top) are individually transformed into the spatial domain and reveal saturation artifacts (see below for enlargement). The tone-mapped result of our reconstruction (c) does not contain the mask pattern or Fourier copies. The right part shows a linearly mapped exposure sequence of an unmodulated LDR image (d) and our reconstruction (e) compared to ground truth images (f).


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.


Fourier Multiplexed Imaging. A simulated, band-limited optical signal is filtered with a semi-transparent mask. According to the convolution theorem, this multiplication corresponds to a convolution in the frequency domain. Fourier multiplexing approaches exploit the resulting copy mechanism to capture several differently filtered versions of a scene in different frequency bands of a photograph.
Artifacts from Partial Saturation. A band-limited signal (upper left), consisting of a single scanline taken from a high dynamic range image, and the same signal clipped at 0.8 maximum intensity level (upper right). The Fourier transform of the original scanline is band-limited (lower left), while the Fourier transform of the clipped version of the same scanline is corrupted by high frequency components.
Artifacts from Full Saturation. A constant signal captured through a 3x3 pattern of neutral density filters and its Fourier transform (left pair). Partial saturation of this sensor image causes changes in the magnitudes of the signal`s Fourier copies (right pair). Peak magnitudes are color-coded.
Sensor saturation yields ringing and other artifacts in Fourier multiplexed data. This image is the spatial version of one of the higher frequency tiles in the teaser above.


Our prototype is a large format high-resolution scanner camera. The filters are mounted under a diffuser on the scanner`s glass plate.

A comparison of color imaging through a standard Bayer color filter array (center left column), an RGBW CFA with the same light transmission (center right column), and our CFA with the proposed reconstruction (right column). A sensor image was simulated for all three cases with a dynamic range of 4% of that of the photographed scene. The upper row shows the tone mapped original image and the three reconstructions with linearized magnifications. The lower row shows color coded logarithmic intensities and linear intensities in the magnifications.

A sensor image captured with our prototype through a novel CFA with saturated regions in red (a). The mask creates two differently scaled luma and two chroma copies in the Fourier transform (b). The dynamic range of the captured image can be significantly extended using our optimization approach as seen in the recolored magnifications in the lower images.


Erratum Equation 5 is incorrect in the paper. Please find the derivation here.
Paper [pdf] [bib]
Video [mov]

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