Two parabolic&#x2013;hyperbolic oriented partial differential equations for denoising in electronic speckle pattern interferometry fringes

Wenjun Xu; Chen Tang; Junjiang Zhang; Yonggang Su; Ray Kai Leung Su

doi:10.1364/AO.54.004720

Applied Optics
Vol. 54,
Issue 15,
pp. 4720-4726
(2015)
•https://doi.org/10.1364/AO.54.004720

Two parabolic–hyperbolic oriented partial differential equations for denoising in electronic speckle pattern interferometry fringes

Wenjun Xu, Chen Tang, Junjiang Zhang, Yonggang Su, and Ray Kai Leung Su

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Wenjun Xu, Chen Tang, Junjiang Zhang, Yonggang Su, and Ray Kai Leung Su, "Two parabolic–hyperbolic oriented partial differential equations for denoising in electronic speckle pattern interferometry fringes," Appl. Opt. 54, 4720-4726 (2015)

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Abstract

Oriented partial differential equation (OPDE)-based filtering methods have been demonstrated to be a powerful tool for denoising while preserving all fringes. In this paper we propose new OPDE-filtering models, named parabolic–hyperbolic oriented partial differential equations (PH-OPDEs), based on variational methods. We test the proposed PH-OPDEs on two computer-simulated and two experimentally obtained ESPI fringe patterns with poor quality, and compare our models with related OPDE models. The experimental results have demonstrated that the new models have significantly better performance in numerical stability and computational efficiency as compared with the previous OPDE models.

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Methods	Figures	Parameters	Time(s)
SOOPDE	Fig. 3(a)	$N = 50, Δ t = 0.2$	2.07
PH-SOOPDE	Fig. 3(b)	$N = 10, Δ t = 1, λ = 0.6$	0.50
CEDPDE	Fig. 4(a)	$N_{0} = 20, N = 115$ ,	4.83
		$Δ t = 0.1, α = 0.005$
PH-CEDPDE	Fig. 4(b)	$N_{0} = 8, N = 11, Δ t = 1$ ,	0.53
		$λ = 0.6, α = 0.005$

Figures	Methods	Filtered Images	Parameters	Time(s)
Fig. 1(c)	SOOPDE	Fig. 5(a)	$N = 500, Δ t = 0.4$	32.45
	PH-SOOPDE	Fig. 5(b)	$N = 84, Δ t = 2.5, λ = 5.1$	5.80
	CEDPDE	Fig. 5(c)	$N_{0} = 200, N = 700$ ,	93.73
			$Δ t = 0.2, α = 0.005$
	PH-CEDPDE	Fig. 5(d)	$N_{0} = 40, N = 70, Δ t = 2$ ,	9.61
			$λ = 6, α = 0.005$
Fig. 1(d)	SOOPDE	Fig. 6(a)	$N = 2000, Δ t = 0.4$	127.26
	PH-SOOPDE	Fig. 6(b)	$N = 270, Δ t = 3, λ = 7.6$	18.02
	CEDPDE	Fig. 6(c)	$N_{0} = 600, N = 1500$ ,	193.37
			$Δ t = 0.2, α = 0.005$
	PH-CEDPDE	Fig. 6(d)	$N_{0} = 10, N = 100, Δ t = 3$ ,	13.24
			$λ = 14.4, α = 0.005$

Methods	Figures	Parameters	Time(s)
SOOPDE	Fig. 3(a)	$N = 50, Δ t = 0.2$	2.07
PH-SOOPDE	Fig. 3(b)	$N = 10, Δ t = 1, λ = 0.6$	0.50
CEDPDE	Fig. 4(a)	$N_{0} = 20, N = 115$ ,	4.83
		$Δ t = 0.1, α = 0.005$
PH-CEDPDE	Fig. 4(b)	$N_{0} = 8, N = 11, Δ t = 1$ ,	0.53
		$λ = 0.6, α = 0.005$

Figures	Methods	Filtered Images	Parameters	Time(s)
Fig. 1(c)	SOOPDE	Fig. 5(a)	$N = 500, Δ t = 0.4$	32.45
	PH-SOOPDE	Fig. 5(b)	$N = 84, Δ t = 2.5, λ = 5.1$	5.80
	CEDPDE	Fig. 5(c)	$N_{0} = 200, N = 700$ ,	93.73
			$Δ t = 0.2, α = 0.005$
	PH-CEDPDE	Fig. 5(d)	$N_{0} = 40, N = 70, Δ t = 2$ ,	9.61
			$λ = 6, α = 0.005$
Fig. 1(d)	SOOPDE	Fig. 6(a)	$N = 2000, Δ t = 0.4$	127.26
	PH-SOOPDE	Fig. 6(b)	$N = 270, Δ t = 3, λ = 7.6$	18.02
	CEDPDE	Fig. 6(c)	$N_{0} = 600, N = 1500$ ,	193.37
			$Δ t = 0.2, α = 0.005$
	PH-CEDPDE	Fig. 6(d)	$N_{0} = 10, N = 100, Δ t = 3$ ,	13.24
			$λ = 14.4, α = 0.005$

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Applied Optics