Parameter Optimization Wavelet Denoising Algorithm for Full-Waveforms Data of Laser Altimetry Satellite

Jun Liu; Yumu Yao; Peinan Li; Jingyun Liu

doi:10.3788/CJL202148.2310001

Journals >Chinese Journal of Lasers >Volume 48 >Issue 23 >Page 2310001 > Article

Chinese Journal of Lasers
Vol. 48, Issue 23, 2310001 (2021)

Parameter Optimization Wavelet Denoising Algorithm for Full-Waveforms Data of Laser Altimetry Satellite

Jun Liu^1、*, Yumu Yao¹, Peinan Li², and Jingyun Liu¹

Author Affiliations

¹College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China

²College of Environmental Science and Engineering, Donghua University, Shanghai 201620, China

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DOI: 10.3788/CJL202148.2310001 Cite this Article Set citation alerts

Jun Liu, Yumu Yao, Peinan Li, Jingyun Liu. Parameter Optimization Wavelet Denoising Algorithm for Full-Waveforms Data of Laser Altimetry Satellite[J]. Chinese Journal of Lasers, 2021, 48(23): 2310001 Copy Citation Text

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Waveform comparison of soft and hard thresholds. (a) Waveform processing result under soft threshold; (b) waveform processing result under hard threshold

Fig. 1. Waveform comparison of soft and hard thresholds. (a) Waveform processing result under soft threshold; (b) waveform processing result under hard threshold

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Fig. 2. Approximate components of GLAS full-waveform wavelet decomposition

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Fig. 3. Detail components of GLAS full-waveform wavelet decomposition

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Fig. 4. Center points of ICESat laser altimetry footprint

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Fig. 5. Original echo waveform

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Fig. 6. Comparison of filtering effects under various filtering methods

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Fig. 7. Verification of the inflection point extraction of the waveform

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Family	Short name	Orthogonal	Biorthogonal	Compact support	Support width	Filters length	Symmetry	Vanishing moment
Haar	haar	Yes	Yes	Yes	1	2	Symmetry	1
Dmeyer	dmey	Yes	Yes	Yes	—	—	Symmetry	—
Fejer-korovkin	fk	Yes	—	Yes	—	—	—	—
Daubechies	db	Yes	Yes	Yes	2n-1	2n	Asymmetry(except db1)	N
Symlets	sym	Yes	Yes	Yes	2n-1	2n	Approximately symmetry	N
Coiflets	coif	Yes	Yes	Yes	6n-1	6n	Approximately symmetry	2N
Biorthogonal	bior	No	Yes	Yes	Decompose: 2n_r+1Reconstruct: 2n_d+1	max(2n_r, 2^nd)+2	Symmetry	N_r
Reversebior	rbio	No	Yes	Yes	Decompose: 2N_r+1Reconstruct: 2N_d+1	max(2N_r, 2^nd)+2	Symmetry	N_d

Table 1. Parameter characteristics of commonly used wavelet basis function name

Short name	Specific order	Number
haar	haar	1
dmey	dmey	1
fk	fk4, fk6, fk8, fk14, fk18, fk22	6
db	db1, db2, db3, db4, db5, db6, db7, db8, db9, db10	10
sym	sym1, sym2, sym3, sym4, sym5, sym6, sym7, sym8	8
coif	coif1, coif2, coif3, coif4, coif5	5
Short name	Specific order	Number
bior	bior1.1, bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9, bior4.4, bior5.5, bior6.8	15
rbio	rbio1.1, rbio1.3, rbio1.5, rbio2.2, rbio2.4, rbio2.6, rbio2.8, rbio3.1, rbio3.3, rbio3.5, rbio3.7, rbio3.9, rbio4.4, rbio5.5, rbio6.8	15

Table 2. Order of wavelet basis functions used in this paper

No.	TPTR	SORH	SCAL	NBD	WNAME	SNR /dB
1	Rigrsure	h	sln	3	rbio3.3	34.00
2	Rigrsure	h	sln	3	db4	42.56
3	Rigrsure	h	sln	3	bior2.6	39.38
4	Rigrsure	h	sln	3	bior2.4	43.90
5	Rigrsure	h	sln	3	bior2.4	40.99
6	Rigrsure	h	sln	3	rbio5.5	48.40
7	Rigrsure	h	sln	3	sym2	43.65
8	Rigrsure	h	sln	3	bior3.9	39.45
9	Rigrsure	h	sln	3	db4	33.23
10	Rigrsure	h	sln	3	bior6.8	38.42

Table 3. Combination of ten optimal control parameters

No.	SNR /dB			PSNR			MSE			MAE
No.	PGF	GF	WF	PGF	GF	WF	PGF	GF	WF	PGF	GF	WF
1	6.70	12.55	34.00	26.83	31.26	52.01	0.84×10^-2	0.51×10^-2	0.46×10^-3	0.38×10^-2	0.51×10^-2	0.32×10^-3
2	4.13	15.19	42.56	27.30	36.47	63.10	3.62×10^-2	1.26×10^-2	0.59×10^-3	0.52×10^-2	0.90×10^-2	0.41×10^-3
3	4.92	16.54	39.38	28.11	37.56	59.76	4.64×10^-2	1.56×10^-2	1.21×10^-3	0.61×10^-2	1.15×10^-2	0.85×10^-3
4	8.39	18.59	43.90	27.61	37.04	61.86	5.86×10^-2	1.98×10^-2	1.14×10^-3	0.76×10^-2	1.39×10^-2	0.73×10^-3
5	7.89	19.16	40.99	28.00	38.27	59.68	4.59×10^-2	1.41×10^-2	1.20×10^-3	0.76×10^-2	1.59×10^-2	0.82×10^-3
6	12.29	18.65	48.40	28.42	34.26	63.63	5.48×10^-2	2.80×10^-2	0.95×10^-3	1.12×10^-2	1.85×10^-2	0.64×10^-3
7	13.63	18.42	43.65	31.42	35.87	60.63	3.84×10^-2	2.31×10^-2	1.33×10^-3	0.91×10^-2	1.40×10^-2	0.94×10^-3
8	3.93	14.48	39.45	27.62	35.86	60.07	2.27×10^-2	0.88×10^-2	0.54×10^-3	0.43×10^-2	0.73×10^-2	0.32×10^-3
9	7.48	13.88	33.23	27.77	33.32	52.08	0.89×10^-2	0.47×10^-2	0.54×10^-3	0.33×10^-2	0.49×10^-2	0.36×10^-3
10	8.05	18.41	38.42	27.49	36.86	56.50	3.18×10^-2	1.08×10^-2	1.12×10^-3	0.52×10^-2	0.94×10^-2	0.82×10^-3

Table 4. Quantitative evaluation of noise reduction effect of each filtering method

No.	Elevation /m
No.	Measured	By GLAH14	By GD-OE	By GD-OE and WF	By EPE	By EPE and WF	By EPC	By EPC and WF
1	9.20	7.64	8.25	7.80	8.25	7.80	7.67	7.71
2	80.70	78.84	6.90	31.05	82.05	82.05	80.70	80.70
3	80.50	0.00	0.60	4.05	81.45	81.45	81.39	81.47
4	80.90	3.91	8.10	22.80	79.50	78.90	78.90	79.21
5	19.30	6.38	4.35	7.50	3.45	4.35	18.65	19.05
6	18.70	20.01	20.10	20.85	20.10	19.95	20.06	20.24
7	18.60	17.26	18.60	18.00	18.60	18.00	18.60	18.60
8	18.60	17.84	0.00	0.00	18.30	18.00	17.85	18.10
9	19.00	0.00	19.05	18.60	18.90	21.60	18.53	18.46
10	12.90	12.30	13.20	13.05	15.15	15.15	12.36	12.45
Mean	35.84	16.42	9.92	14.37	34.58	34.73	35.47	35.60
MSE	—	35.98	42.07	29.00	5.14	5.10	1.02	0.98

Table 5. Altimetry results of seven decomposition methods

Jun Liu, Yumu Yao, Peinan Li, Jingyun Liu. Parameter Optimization Wavelet Denoising Algorithm for Full-Waveforms Data of Laser Altimetry Satellite[J]. Chinese Journal of Lasers, 2021, 48(23): 2310001

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