General construction of transform-domain filters, filtering methods for electronic speckle pattern interferometry, and comparative analyses

Xia Chen; Chen Tang; Wenjun Xu; Yonggang Su; KaiLeung Su

doi:10.1364/AO.55.002214

Applied Optics
Vol. 55,
Issue 9,
pp. 2214-2222
(2016)
•https://doi.org/10.1364/AO.55.002214

General construction of transform-domain filters, filtering methods for electronic speckle pattern interferometry, and comparative analyses

Xia Chen, Chen Tang, Wenjun Xu, Yonggang Su, and KaiLeung Su

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Xia Chen, Chen Tang, Wenjun Xu, Yonggang Su, and KaiLeung Su, "General construction of transform-domain filters, filtering methods for electronic speckle pattern interferometry, and comparative analyses," Appl. Opt. 55, 2214-2222 (2016)

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Abstract

In this paper, we first present a general method for the construction of transform-domain filters for the removal of speckle noise in electronic speckle pattern interferometry (ESPI) wrapped phase patterns. Then we review the construction of previously published representative transform-domain filters, including the Fourier transform (FT), the wavelet transform, windowed Fourier filtering, and the localized FT filter. Furthermore, we fully evaluate the performance of the four filters via a variety of test cases and a comparable mean square error. Lastly, we also propose three new transform-domain filters for the removal of speckle noise in ESPI based on the general method. The three new methods are developed by selecting the input image function and filter function with better performance. The filtering results of the three proposed methods have been demonstrated via comparisons with four previously published filters.

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Algorithm	Figures	Parameters	Times	MSE
FT	Fig. 4(a-1)	$thr = 1000$	1.24	0.0152
	Fig. 4(a-2)	$thr = 900$	0.52	0.3180
	Fig. 4(a-3)	$thr = 700$	0.51	0.5546
	Fig. 4(a-4)	$thr = 500$	0.50	0.6065
	Fig. 4(b-1)	$thr = 1600$	1.03	0.0034
	Fig. 4(b-2)	$thr = 1200$	1.34	0.0081
	Fig. 4(b-3)	$thr = 1000$	0.71	0.3117
	Fig. 4(c)	$thr = 1400$	1.07
WT	Fig. 6(a-1)	$thr = 1.2$	0.32	0.0215
	Fig. 6(a-2)	$thr = 1.4$	0.32	0.1547
	Fig. 6(a-3)	$thr = 1.4$	0.34	0.4023
	Fig. 6(a-4)	$thr = 1.4$	0.31	0.5387
	Fig. 6(b-1)	$thr = 1.4$	0.29	0.0056
	Fig. 6(b-2)	$thr = 1.1$	0.32	0.0335
	Fig. 6(b-3)	$thr = 1.2$	0.33	0.1060
	Fig. 6(c)	$thr = 1.6$	0.22
WFF	Fig. 8(a-1)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	245	0.0015
	Fig. 8(a-2)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	242	0.0022
	Fig. 8(a-3)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	247	0.0040
	Fig. 8(a-4)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	242	0.0051
	Fig. 8(b-1)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 7$	231	0.0013
	Fig. 8(b-2)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	238	0.0016
	Fig. 8(b-3)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 3$	255	0.0051
	Fig. 8(c)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	246
LFF	Fig. 10(a-1)	$w = 29$ , $α = 1$ , $σ = 0.0001$	137.82	0.0022
	Fig. 10(a-2)	$w = 39$ , $α = 1$ , $σ = 0.0001$	213.76	0.0033
	Fig. 10(a-3)	$w = 51$ , $α = 1$ , $σ = 0.0001$	386.05	0.0048
	Fig. 10(a-4)	$w = 63$ , $α = 1$ , $σ = 0.0001$	506.24	0.0080
	Fig. 10(b-1)	$w = 45$ , $α = 1$ , $σ = 0.0001$	300.51	0.0017
	Fig. 10(b-2)	$w = 33$ , $α = 1$ , $σ = 0.0001$	174.60	0.0027
	Fig. 10(b-3)	$w = 17$ , $α = 1$ , $σ = 0.0001$	68.72	0.0047
	Fig. 10(c)	$w = 39$ , $α = 1$ , $σ = 0.008$	141.20

Algorithm	Figures	Parameters	Times	MSE
WFLPF	Fig. 12(a-1)	$w = 23$ , $thr = 100$	148.12	0.0032
	Fig. 12(a-2)	$w = 27$ , $thr = 90$	199.07	0.0053
	Fig. 12(a-3)	$w = 29$ , $thr = 90$	244.48	0.0438
	Fig. 12(a-4)	$w = 33$ , $thr = 90$	303.28	0.0908
	Fig. 12(b-1)	$w = 23$ , $thr = 100$	139.41	0.0030
	Fig. 12(b-2)	$w = 23$ , $thr = 90$	138.25	0.0036
	Fig. 12(b-3)	$w = 17$ , $thr = 60$	74.78	0.0049
	Fig. 12(c)	$w = 33$ , $thr = 110$	215.39
CLPF	Fig. 14(a-1)	$thr = 0.8$	4.95	0.0046
	Fig. 14(a-2)	$thr = 0.9$	4.88	0.0073
	Fig. 14(a-3)	$thr = 1.0$	5.03	0.0110
	Fig. 14(a-4)	$thr = 1.0$	6.63	0.0176
	Fig. 14(b-1)	$thr = 0.8$	5.02	0.0027
	Fig. 14(b-2)	$thr = 0.7$	5.74	0.0055
	Fig. 14(b-3)	$thr = 0.7$	5.90	0.0067
	Fig. 14(c)	$thr = 1.4$	4.10
WFMF	Fig. 16(a-1)	$w = 41$ , $α = 1$ , $thr = 180$	58.87	0.0013
	Fig. 16(a-2)	$w = 43$ , $α = 1$ , $thr = 180$	73.00	0.0020
	Fig. 16(a-3)	$w = 47$ , $α = 1$ , $thr = 180$	76.17	0.0029
	Fig. 16(a-4)	$w = 49$ , $α = 1$ , $thr = 180$	83.65	0.0042
	Fig. 16(b-1)	$w = 49$ , $α = 1$ , $thr = 180$	86.97	0.0016
	Fig. 16(b-2)	$w = 47$ , $α = 1$ , $thr = 180$	74.48	0.0021
	Fig. 16(b-3)	$w = 41$ , $α = 1$ , $thr = 180$	64.33	0.0045
	Fig. 16(c)	$w = 63$ , $α = 1$ , $thr = 180$	51.74

Algorithm	Figures	Parameters	Times	MSE
FT	Fig. 4(a-1)	$thr = 1000$	1.24	0.0152
	Fig. 4(a-2)	$thr = 900$	0.52	0.3180
	Fig. 4(a-3)	$thr = 700$	0.51	0.5546
	Fig. 4(a-4)	$thr = 500$	0.50	0.6065
	Fig. 4(b-1)	$thr = 1600$	1.03	0.0034
	Fig. 4(b-2)	$thr = 1200$	1.34	0.0081
	Fig. 4(b-3)	$thr = 1000$	0.71	0.3117
	Fig. 4(c)	$thr = 1400$	1.07
WT	Fig. 6(a-1)	$thr = 1.2$	0.32	0.0215
	Fig. 6(a-2)	$thr = 1.4$	0.32	0.1547
	Fig. 6(a-3)	$thr = 1.4$	0.34	0.4023
	Fig. 6(a-4)	$thr = 1.4$	0.31	0.5387
	Fig. 6(b-1)	$thr = 1.4$	0.29	0.0056
	Fig. 6(b-2)	$thr = 1.1$	0.32	0.0335
	Fig. 6(b-3)	$thr = 1.2$	0.33	0.1060
	Fig. 6(c)	$thr = 1.6$	0.22
WFF	Fig. 8(a-1)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	245	0.0015
	Fig. 8(a-2)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	242	0.0022
	Fig. 8(a-3)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	247	0.0040
	Fig. 8(a-4)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	242	0.0051
	Fig. 8(b-1)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 7$	231	0.0013
	Fig. 8(b-2)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 9$	238	0.0016
	Fig. 8(b-3)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 3$	255	0.0051
	Fig. 8(c)	$ξ_{l} = ξ_{h} = - 1$ , $ξ_{i} = 0.05$ , $η_{l} = η_{h} = - 1$ , $η_{i} = 0.05$ , $σ_{x} = σ_{y} = 20$ , $thr = 4$	246
LFF	Fig. 10(a-1)	$w = 29$ , $α = 1$ , $σ = 0.0001$	137.82	0.0022
	Fig. 10(a-2)	$w = 39$ , $α = 1$ , $σ = 0.0001$	213.76	0.0033
	Fig. 10(a-3)	$w = 51$ , $α = 1$ , $σ = 0.0001$	386.05	0.0048
	Fig. 10(a-4)	$w = 63$ , $α = 1$ , $σ = 0.0001$	506.24	0.0080
	Fig. 10(b-1)	$w = 45$ , $α = 1$ , $σ = 0.0001$	300.51	0.0017
	Fig. 10(b-2)	$w = 33$ , $α = 1$ , $σ = 0.0001$	174.60	0.0027
	Fig. 10(b-3)	$w = 17$ , $α = 1$ , $σ = 0.0001$	68.72	0.0047
	Fig. 10(c)	$w = 39$ , $α = 1$ , $σ = 0.008$	141.20

Algorithm	Figures	Parameters	Times	MSE
WFLPF	Fig. 12(a-1)	$w = 23$ , $thr = 100$	148.12	0.0032
	Fig. 12(a-2)	$w = 27$ , $thr = 90$	199.07	0.0053
	Fig. 12(a-3)	$w = 29$ , $thr = 90$	244.48	0.0438
	Fig. 12(a-4)	$w = 33$ , $thr = 90$	303.28	0.0908
	Fig. 12(b-1)	$w = 23$ , $thr = 100$	139.41	0.0030
	Fig. 12(b-2)	$w = 23$ , $thr = 90$	138.25	0.0036
	Fig. 12(b-3)	$w = 17$ , $thr = 60$	74.78	0.0049
	Fig. 12(c)	$w = 33$ , $thr = 110$	215.39
CLPF	Fig. 14(a-1)	$thr = 0.8$	4.95	0.0046
	Fig. 14(a-2)	$thr = 0.9$	4.88	0.0073
	Fig. 14(a-3)	$thr = 1.0$	5.03	0.0110
	Fig. 14(a-4)	$thr = 1.0$	6.63	0.0176
	Fig. 14(b-1)	$thr = 0.8$	5.02	0.0027
	Fig. 14(b-2)	$thr = 0.7$	5.74	0.0055
	Fig. 14(b-3)	$thr = 0.7$	5.90	0.0067
	Fig. 14(c)	$thr = 1.4$	4.10
WFMF	Fig. 16(a-1)	$w = 41$ , $α = 1$ , $thr = 180$	58.87	0.0013
	Fig. 16(a-2)	$w = 43$ , $α = 1$ , $thr = 180$	73.00	0.0020
	Fig. 16(a-3)	$w = 47$ , $α = 1$ , $thr = 180$	76.17	0.0029
	Fig. 16(a-4)	$w = 49$ , $α = 1$ , $thr = 180$	83.65	0.0042
	Fig. 16(b-1)	$w = 49$ , $α = 1$ , $thr = 180$	86.97	0.0016
	Fig. 16(b-2)	$w = 47$ , $α = 1$ , $thr = 180$	74.48	0.0021
	Fig. 16(b-3)	$w = 41$ , $α = 1$ , $thr = 180$	64.33	0.0045
	Fig. 16(c)	$w = 63$ , $α = 1$ , $thr = 180$	51.74

Abstract

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Figures (18)

Tables (2)

Equations (12)

Applied Optics