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Non-Linear Fresnelet Approximation for Interference Term Suppression in Digital Holography

M. Liebling, T. Blu, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, August 4-8, 2003, vol. 5207, part II, pp. 553-559.

We present a zero-order and twin image elimination algorithm for digital Fresnel holograms that were acquired in an off-axis geometry. These interference terms arise when the digital hologram is reconstructed and corrupt the result. Our algorithm is based on the Fresnelet transform, a wavelet-like transform that uses basis functions tailor-made for digital holography. We show that in the Fresnelet domain, the coefficients associated to the interference terms are separated both spatially and with respect to the frequency bands. We propose a method to suppress them by selectively thresholding the Fresnelet coefficients. Unlike other methods that operate in the Fourier domain and affect the whole spacial domain, our method operates locally in both space and frequency, allowing for a more targeted processing.

AUTHOR="Liebling, M. and Blu, T. and Unser, M.",
TITLE="Non-Linear {F}resnelet Approximation for Interference Term
        Suppression in Digital Holography",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical
        Imaging: {W}avelet Applications in Signal and Image Processing {X}",
address="San Diego CA, USA",
month="August 3-8,",
note="Part {II}")

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