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}}
Downloads: 0
{"_id":"FNPmYwrQK2d9pYjzN","bibbaseid":"soulez-thibaut-schutz-ferrari-courbin-unser-proximityoperatorsforphaseretrieval-2016","authorIDs":["5e0da6e9675bf1de010000c7","5e60e833839e59df010000ec","5e6136b497c182e9010000f4","K847C6Zc7Ag8rsChn","P4WmyAJaE3F8naWCx","THjgf8ekSN8mfQsQs","TKmMmXLcb4B7nAhiz","j5urj5TECvJG89z2X","m7sJiveByRfLiaYdt","xY3fr5C45Gy6ZdXTn"],"author_short":["Soulez, F.","Thiébaut, É.","Schutz, A.","Ferrari, A.","Courbin, F.","Unser, M."],"bibdata":{"bibtype":"article","type":"article","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 “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.","author":[{"firstnames":["F."],"propositions":[],"lastnames":["Soulez"],"suffixes":[]},{"firstnames":["É."],"propositions":[],"lastnames":["Thiébaut"],"suffixes":[]},{"firstnames":["A."],"propositions":[],"lastnames":["Schutz"],"suffixes":[]},{"firstnames":["A."],"propositions":[],"lastnames":["Ferrari"],"suffixes":[]},{"firstnames":["F."],"propositions":[],"lastnames":["Courbin"],"suffixes":[]},{"firstnames":["M."],"propositions":[],"lastnames":["Unser"],"suffixes":[]}],"date-added":"2017-02-16 13:46:38 +0000","date-modified":"2017-02-16 13:48:01 +0000","journal":"Applied Optics","month":"September","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","bibtex":"@article{art_osa16,\n\tAbstract = {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.},\n\tAuthor = {F. Soulez and \\'{E}. Thi\\'{e}baut and A. Schutz and A. Ferrari and F. Courbin and M. Unser},\n\tDate-Added = {2017-02-16 13:46:38 +0000},\n\tDate-Modified = {2017-02-16 13:48:01 +0000},\n\tJournal = {Applied Optics},\n\tMonth = sep,\n\tNumber = {26},\n\tPages = {7412--7421},\n\tPublisher = {OSA},\n\tTitle = {Proximity operators for phase retrieval},\n\tVolume = {55},\n\tYear = {2016},\n\tBdsk-Url-1 = {http://ao.osa.org/abstract.cfm?URI=ao-55-26-7412},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1364/AO.55.007412}}\n\n","author_short":["Soulez, F.","Thiébaut, É.","Schutz, A.","Ferrari, A.","Courbin, F.","Unser, M."],"key":"art_osa16","id":"art_osa16","bibbaseid":"soulez-thibaut-schutz-ferrari-courbin-unser-proximityoperatorsforphaseretrieval-2016","role":"author","urls":{},"metadata":{"authorlinks":{"ferrari, a":"https://bibbase.org/show?bib=dl.dropboxusercontent.com/s/is80a9wjw4k1qps/monbibarticles.bib"}},"downloads":0},"bibtype":"article","biburl":"https://dl.dropboxusercontent.com/s/is80a9wjw4k1qps/monbibarticles.bib","creationDate":"2019-12-25T04:43:34.009Z","downloads":0,"keywords":[],"search_terms":["proximity","operators","phase","retrieval","soulez","thiébaut","schutz","ferrari","courbin","unser"],"title":"Proximity operators for phase retrieval","year":2016,"dataSources":["bWKYCxXhmHxgkrrcy","66A76SGjs5ZdQX2dG","Bv6sHf6MRRsEJMGR3"]}