Proximity operators for phase retrieval

Soulez, Ferréol; Thiébaut, Éric; Schutz, Antony; Ferrari, A.; Courbin, F.; Unser, Michaël

doi:10.1364/ao.55.007412

Cited by 39 publications

(43 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most of the phase retrieval algorithms are based on the Gerchberg-Saxton algorithm [8]: ER [2], HIO [2], shrinkwrap [9], charge-flipping algorithm [25], relaxed averaged alternating reflections (RAAR) algorithm [26], noise tolerant HIO algorithm [18], and many others [10]. The main differences between these algorithms are the various constraints applied in real space [2,9,20,24] and reciprocal space [27][28][29], which can be optimized depending on the particular sample and experiment. Moreover, a combination of phase retrieval algorithms (ER and HIO algorithms [2,24,30]) is often applied in an alternating fashion to avoid stagnation or oscillation of the iterative process and to stabilize the final reconstruction.…”

Section: Optimized Phase Retrieval Algorithmsmentioning

confidence: 99%

Iterative phase retrieval in coherent diffractive imaging: practical issues

Latychevskaia

2018

Appl. Opt.

View full text Add to dashboard Cite

In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.

show abstract

Section: Optimized Phase Retrieval Algorithmsmentioning

confidence: 99%

Iterative phase retrieval in coherent diffractive imaging: practical issues

Latychevskaia

2018

Appl. Opt.

View full text Add to dashboard Cite

show abstract

“…This was rigorously demonstrated by Bauschke et al [41] since Fienup's BIO and HIO are shown to be instances of Dykstra and Douglas-Rachford algorithms. In [12], alternating projections strategies are reformulated as proximity operators derived from the maximum likelihood point of view.…”

Section: The Alternating Projections Point Of Viewmentioning

confidence: 99%

“…Most phase retrieval techniques are still derived from the methods of alternating projections initially proposed by Gerchberg and Saxton [3] and popularized and extended by Fienup [4,5]. This class of methods is still widely used today [6][7][8][9][10][11][12][13], with improvements to enforce a priori knowledge (support of the objects, admissible values domain, sparsity constraints) [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

Momey¹,

Denis²,

Thomas³

et al. 2019

J. Opt. Soc. Am. A

View full text Add to dashboard Cite

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is made on the connections between the numerous alternating projection strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projection techniques to the inverse problems formulation is straightforward and advantageous.

show abstract

“…Here, we benefit from the closed-form expressions that have been recently derived for Gaussian likelihood in [49]. In the present work, we consider the weighted quadratic data-fidelity term…”

Section: Proximity Operator For Phase-retrievalmentioning

confidence: 99%

Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering

Pham¹,

Soubies²,

Goy³

et al. 2018

Opt. Express

Self Cite

View full text Add to dashboard Cite

Taking benefit from recent advances in both phase retrieval and estimation of refractive indices from holographic measurements, we propose a unified framework to reconstruct them from intensity-only measurements. Our method relies on a generic and versatile formulation of the inverse problem and includes sparsity constraints. Its modularity enables the use of a variety of forward models, from simple linear ones to more sophisticated nonlinear ones, as well as various regularizers. We present reconstructions that deploy either the beam-propagation method or the iterative Lippmann-Schwinger model, combined with total-variation regularization. They suggest that our proposed (intensity-only) method can reach the same performance as reconstructions from holographic (complex) data. This is of particular interest from a practical point of view because it allows one to simplify the acquisition setup.

show abstract

Proximity operators for phase retrieval

Cited by 39 publications

References 38 publications

Iterative phase retrieval in coherent diffractive imaging: practical issues

Iterative phase retrieval in coherent diffractive imaging: practical issues

From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering

Contact Info

Product

Resources

About