An optimal algorithm for reconstructing images from binary measurements

Feng Yang; Yue M. Lu; Luciano Sbaiz; Martin Vetterli

doi:10.1117/12.850887

27 January 2010 An optimal algorithm for reconstructing images from binary measurements

Feng Yang, Yue M. Lu, Luciano Sbaiz, Martin Vetterli

Proceedings Volume 7533, Computational Imaging VIII; 75330K (2010) https://doi.org/10.1117/12.850887
Event: IS&T/SPIE Electronic Imaging, 2010, San Jose, California, United States

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.

Citation Download Citation

Feng Yang, Yue M. Lu, Luciano Sbaiz, and Martin Vetterli "An optimal algorithm for reconstructing images from binary measurements", Proc. SPIE 7533, Computational Imaging VIII, 75330K (27 January 2010); https://doi.org/10.1117/12.850887

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