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Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns

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Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns. / Krishnan, Joshin P.; Bioucas-Dias, Jose M.; Katkovnik, Vladimir.

In: Sensors, Vol. 18, No. 11, 4006, 16.11.2018.

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Krishnan, Joshin P. ; Bioucas-Dias, Jose M. ; Katkovnik, Vladimir. / Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns. In: Sensors. 2018 ; Vol. 18, No. 11.

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@article{1e9812f187464a56bc073b43ec97a504,
title = "Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns",
abstract = "This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors.",
keywords = "complex domain imaging, phase retrieval, photon-limited imaging, complex domain sparsity, dictionary learning, SPARSE, IMAGE, RECONSTRUCTION, RECOVERY, CRYSTALLOGRAPHY, ALGORITHMS",
author = "Krishnan, {Joshin P.} and Bioucas-Dias, {Jose M.} and Vladimir Katkovnik",
year = "2018",
month = "11",
day = "16",
doi = "10.3390/s18114006",
language = "English",
volume = "18",
journal = "Sensors",
issn = "1424-8220",
publisher = "MDPI",
number = "11",

}

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TY - JOUR

T1 - Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns

AU - Krishnan, Joshin P.

AU - Bioucas-Dias, Jose M.

AU - Katkovnik, Vladimir

PY - 2018/11/16

Y1 - 2018/11/16

N2 - This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors.

AB - This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors.

KW - complex domain imaging

KW - phase retrieval

KW - photon-limited imaging

KW - complex domain sparsity

KW - dictionary learning

KW - SPARSE

KW - IMAGE

KW - RECONSTRUCTION

KW - RECOVERY

KW - CRYSTALLOGRAPHY

KW - ALGORITHMS

U2 - 10.3390/s18114006

DO - 10.3390/s18114006

M3 - Article

VL - 18

JO - Sensors

JF - Sensors

SN - 1424-8220

IS - 11

M1 - 4006

ER -