Proximity operators for phase retrieval. Soulez, F., Thiébaut, É., Schutz, A., Ferrari, A., Courbin, F., & Unser, M. Applied Optics, 55(26):7412–7421, OSA, September, 2016.
abstract   bibtex   
We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical “noise-free” projection in any projection-based algorithm. They are derived from a maximum-likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to under-sampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg–Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators always perform better than using the classical intensity projector, while their computational overhead is moderate.
@article{art_osa16,
	Abstract = {We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical \&\#x201C;noise-free\&\#x201D; projection in any projection-based algorithm. They are derived from a maximum-likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to under-sampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg--Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators always perform better than using the classical intensity projector, while their computational overhead is moderate.},
	Author = {F. Soulez and \'{E}. Thi\'{e}baut and A. Schutz and A. Ferrari and F. Courbin and M. Unser},
	Date-Added = {2017-02-16 13:46:38 +0000},
	Date-Modified = {2017-02-16 13:48:01 +0000},
	Journal = {Applied Optics},
	Month = sep,
	Number = {26},
	Pages = {7412--7421},
	Publisher = {OSA},
	Title = {Proximity operators for phase retrieval},
	Volume = {55},
	Year = {2016},
	Bdsk-Url-1 = {http://ao.osa.org/abstract.cfm?URI=ao-55-26-7412},
	Bdsk-Url-2 = {http://dx.doi.org/10.1364/AO.55.007412}}

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