Optimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimization

Xuyang Xu; Enrong Li; Xia Shen; Shensheng Han

doi:10.3788/COL201513.071101

Journals >Chinese Optics Letters >Volume 13 >Issue 7 >Page 071101 > Article

Chinese Optics Letters
Vol. 13, Issue 7, 071101 (2015)

Optimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimization

Xuyang Xu, Enrong Li^*, Xia Shen, and Shensheng Han

Author Affiliations

Key Laboratory for Quantum Optics and Center for Cold Atom Physics of the Chinese Academy of Science, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Science, Shanghai 201800, China

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DOI: 10.3788/COL201513.071101 Cite this Article Set citation alerts

Xuyang Xu, Enrong Li, Xia Shen, Shensheng Han, "Optimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimization," Chin. Opt. Lett. 13, 071101 (2015) Copy Citation Text

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Abstract

In this Letter the problem of optimization of speckle patterns in a ghost imaging (GI) system is addressed. The mutual coherence between the measuring matrix and the sparsifying dictionary matrix is minimized to obtain the required speckle patterns. Simulation and experimental results are presented, both showing that the quality of the reconstructed results obtained with the optimized speckle patterns is much improved in comparison with that obtained with the general unoptimized ones. We expect this method can be used to design GI systems with high performance.

Y = AX + σ,

(1)

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\tilde{A} = \arg \min_{X} \frac{1}{2} {‖ Y - AX ‖}_{2}^{2} + τ {‖ θ ‖}_{1}, s.t. X = Ψ θ,

(2)

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μ_{i j} = \frac{| d_{i}^{T} d_{j} |}{{∥ d_{i} ∥}_{2} {∥ d_{j} ∥}_{2}}, 1 < i, j < N, i \neq j,

(3)

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μ = \sum_{i \neq j} μ_{i j}^{2} .

(4)

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A_{opt} = \arg \min_{A} E, s.t. A \geq 0,

(5)

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RMSE = \sum_{i j} {(I_{i j}^{'} - I_{i j})}^{2} / \sum_{i j} I_{i j}^{2},

(6)

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MSE = \frac{1}{m n} \sum_{i = 0}^{m - 1} \sum_{j = 0}^{n - 1} {‖ I^{'} (i, j) - I (i, j) ‖}^{2} PSNR = 10 \cdot \log_{10} (\frac{{MAX}_{I}^{2}}{MSE}),

(7)

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Xuyang Xu, Enrong Li, Xia Shen, Shensheng Han, "Optimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimization," Chin. Opt. Lett. 13, 071101 (2015)

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