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Proceedings Paper

An optimal algorithm for reconstructing images from binary measurements
Author(s): Feng Yang; Yue M. Lu; Luciano Sbaiz; Martin Vetterli
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Paper Abstract

We have studied a camera with a very large number of binary pixels referred to as the gigavision camera [1] or the gigapixel digital film camera [2, 3]. Potential advantages of this new camera design include improved dynamic range, thanks to its logarithmic sensor response curve, and reduced exposure time in low light conditions, due to its highly sensitive photon detection mechanism. We use maximum likelihood estimator (MLE) to reconstruct a high quality conventional image from the binary sensor measurements of the gigavision camera. We prove that when the threshold T is "1", the negative loglikelihood function is a convex function. Therefore, optimal solution can be achieved using convex optimization. Base on filter bank techniques, fast algorithms are given for computing the gradient and the multiplication of a vector and Hessian matrix of the negative log-likelihood function. We show that with a minor change, our algorithm also works for estimating conventional images from multiple binary images. Numerical experiments with synthetic 1-D signals and images verify the effectiveness and quality of the proposed algorithm. Experimental results also show that estimation performance can be improved by increasing the oversampling factor or the number of binary images.

Paper Details

Date Published: 27 January 2010
PDF: 12 pages
Proc. SPIE 7533, Computational Imaging VIII, 75330K (27 January 2010); doi: 10.1117/12.850887
Show Author Affiliations
Feng Yang, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Yue M. Lu, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Luciano Sbaiz, Google (Switzerland)
Martin Vetterli, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of California, Berkeley (United States)


Published in SPIE Proceedings Vol. 7533:
Computational Imaging VIII
Charles A. Bouman; Ilya Pollak; Patrick J. Wolfe, Editor(s)

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