Phase Retrieval with Application to Optical Imaging: A contemporary overview

Shechtman, Yoav; Eldar, Yonina C.; Cohen, Oren; Chapman, Henry N.; Miao, Jianwei; Segev, Mordechai

doi:10.1109/msp.2014.2352673

Cited by 1,031 publications

(834 citation statements)

References 158 publications

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“…The projection P S (•) represents projection onto the support constraint. Differing from the RAAR-l 0 algorithm, the RAAR-l 1 …”

Section: Parameter Setupmentioning

confidence: 99%

“…In science and engineering fields, such as crystallography, neutron radiography, astronomy, signal processing, and optical imaging [1,2], it is difficult to design sophisticated measuring setups to allow direct recording of the phase, which carries the critical structural information of the test object or signal [1]. Interestingly, an alternative mean called algorithmic phase retrieval is arising in these fields.…”

Section: Introductionmentioning

confidence: 99%

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Sparse representation utilizing tight frame for phase retrieval

Shi

Lian

Chen

2015

EURASIP J. Adv. Signal Process.

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We treat the phase retrieval (PR) problem of reconstructing the interest signal from its Fourier magnitude. Since the Fourier phase information is lost, the problem is ill-posed. Several techniques have been used to address this problem by utilizing various priors such as non-negative, support, and Fourier magnitude constraints. Recent methods exploiting sparsity are developed to improve the reconstruction quality. However, the previous algorithms of utilizing sparsity prior suffer from either the low reconstruction quality at low oversampled factors or being sensitive to noise. To address these issues, we propose a framework that exploits sparsity of the signal in the translation invariant Haar pyramid (TIHP) tight frame. Based on this sparsity prior, we formulate the sparse representation regularization term and incorporate it into the PR optimization problem. We propose the alternating iterative algorithm for solving the corresponding non-convex problem by dividing the problem into several subproblems. We give the optimal solution to each subproblem, and experimental simulations under the noise-free and noisy scenario indicate that our proposed algorithm can obtain a better reconstruction quality compared to the conventional alternative projection methods, even outperform the recent sparsity-based algorithms in terms of reconstruction quality.

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“…The projection P S (•) represents projection onto the support constraint. Differing from the RAAR-l 0 algorithm, the RAAR-l 1 …”

Section: Parameter Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse representation utilizing tight frame for phase retrieval

Shi

Lian

Chen

2015

EURASIP J. Adv. Signal Process.

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“…In the literature, this criterion generally turns out to be the optical intensity specified over multiple parallel planes for monochromatic scalar optical fields [1,2]. As a result of these algorithms, the computed scalar field may end up with a wide angle field so the propagation directions of the plane wave components may lie in a large cone.…”

Section: Introductionmentioning

confidence: 99%

Phase Retrieval from Electric Field Intensity for Wide Angle Optical Fields

Kulce¹,

Onural²

2017

Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP)

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“…It is based on the assumption that there exists a small number of items such that image can be represented exactly or approximately with a good accuracy. Here we wish refer to the recent overview [2] of the complex domain sparsity concentrated on applications in optics.…”

Section: Introductionmentioning

confidence: 99%

Complex domain nonlocal block-matching denoising based on high-order singular value decomposition (HOSVD)

Katkovnik

Ponomarenko

Егиазарян

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Block matching 3D collaborative filtering (BM3D) is one of the most popular denoising technique based on data sparsity concept applied to specially structured data. In this paper we develop this technique for complex domain, i.e. for application to complex-valued data. Sparsity as an approximation technique can be addressed directly to complex-valued variables or to real-valued pairs phase/amplitude and real/imaginary parts of complex-valued variables. As a result we arrive to various ways of development and obtain a set of quite different algorithms. The algorithms proposed in this paper are composed from two components: nonlocal patch-wise grouping and highorder singular value decomposition (HOSVD) for grouped data processing. The latter gives data adaptive complex-valued bases for complex-valued data or real-valued bases for joint processing of the pairs phase/amplitude, real/imaginary parts of complexvalued variables. Comparative study of the developed algorithms is produced in order to select the most efficient ones.

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Phase Retrieval with Application to Optical Imaging: A contemporary overview

Cited by 1,031 publications

References 158 publications

Sparse representation utilizing tight frame for phase retrieval

Sparse representation utilizing tight frame for phase retrieval

Phase Retrieval from Electric Field Intensity for Wide Angle Optical Fields

Complex domain nonlocal block-matching denoising based on high-order singular value decomposition (HOSVD)

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