Spectrum Concentration Based Reparameterization for Light Field Denoising

Fig. 1. Light field spectrum support structure. (a) Spectrum support structure of 2D Lambert scene; (b) main energy regions $R_{1}$ and $R_{2}$ of 2D light field spectrum with texture information

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Fig. 2. Parameterization of the light field and embodiment in the real domain. (a) Two lane parameterization of 4D light field; (b) two plane parameterization of 2D light field; (c) embodiment of reparameterization in the real domain

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Fig. 3. 2D light field spectra under different parameterizations when considering scene texture information. (a) Spectrum of light field when image plane is located on one side of the scene; (b) spectrum of 2D light field when image plane is located between scenes

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Fig. 4. Slope and angle of spectrum support

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Fig. 5. Relationship between two planes distance and spectrum support structure of reparameterized light field at $2 \sqrt[]{2 Z_{m a x} Z_{m i n}} < Z_{m a x} + Z_{m i n}$ . (a) Schematic of reparameterized light field image plane located at ①-③; (b)-(d) reparameterized spectrum support structures of light field when image plane is located at ①-③

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Fig. 6. Relationship between two planes distance and spectrum support structure of reparameterized light field at $2 \sqrt[]{2 Z_{m a x} Z_{m i n}} \geq Z_{m a x} + Z_{m i n}$ . (a) Schematic of reparameterized light field image plane located at ①-③; (b)-(d) reparameterized spectrum support structures of light field when the image plane is located at ①-③

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Fig. 7. Noise power spectra and light field spectrum support. (a) Initial parameterized noise power spectrum; (b) reparameterized noise power spectrum; (c) initial parameterized light field spectrum support; (d) reparameterized light field spectrum support

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Fig. 8. Light field spectrum support and noise power spectrum. (a) Initial parameterization of the noise power spectrum and the region corresponding to the light field spectrum support; (b) initial parameterization of the light field spectrum support

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Fig. 9. Discrete light field spectra, and spectrum period extracted by the red dotted line. (a) Initial parameterized light field spectrum; (b) reparameterized light field spectrum

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Fig. 10. Spectrum support of initial and reparameterized light fields. (a) Spectrum support of initial parameterized light field; (b) spectrum support of reparameterized light field; (c) initial and reparameterized light field spectrum support boundary

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Fig. 11. PSNR and SSIM of Antinous light field with different noise levels. (a1) (a2) Based on 4D dual fan filter; (b1) (b2) based on 4D hypercone filter; (c1) (c2) based on 4D hyperfan filter

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Fig. 12. PSNR and SSIM of Cotton light field with different noise types. (a1) (a2) Based on 4D dual fan filter; (b1) (b2) based on 4D hypercone filter; (c1) (c2) based on 4D hyperfan filter

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Fig. 13. Comparison of visual effects of denoising results for Pens light field, the images from left to right are the original data center view and partial enlarged drawing, the noisy data center view with Gaussian noise and partial enlarged drawing, the direct denoising center view and partial enlarged drawing, and the reparameterized denoising center view and partial enlarged drawing. (a) Based on 4D dual fan filter; (b) based on 4D hypercone filter; (c) based on 4D hyperfan filter

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Fig. 14. Comparison of visual effects of denoising results for Cotton light field, the images from left to right are the original data center view and partial enlarged drawing, the noisy data center view with mixed noise including Poisson noise, Gaussian noise, and salt & pepper noise and partial enlarged drawing, the direct denoising center view and partial enlarged drawing, and the reparameterized denoising center view and partial enlarged drawing. (a) Based on 4D dual fan filter; (b) based on 4D hypercone filter; (c) based on 4D hyperfan filter

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Table 1. Spectrum support angle and noise signal-to-noise ratio on the support for reparameterized light field with different distances between two planes
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Table 1. Spectrum support angle and noise signal-to-noise ratio on the support for reparameterized light field with different distances between two planes
Two plane distance $D_{r e} = 4$ $D_{1} = 5$ $D_{r e} = 3$ $D_{r e} = 8$ $D_{r e} = 2$ $D_{r e} = 1$
Spectrum support angle 0.90 0.84 0.83 0.55 0.54 0.22
SNR 22.79 22.82 25.09 25.68 28.59 32.34

Table 2. Initial distance of two plane $D_{1}$ , weight parameters $α_{o p t}$ , and distance of reparametrized light field two planes $D_{r e}$ of 12 light fields

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Table 2. Initial distance of two plane $D_{1}$ , weight parameters $α_{o p t}$ , and distance of reparametrized light field two planes $D_{r e}$ of 12 light fields

Scene	Pens	Cotton	Antinous	Tomb	Dino	Platonic	Boxes	Dishes	Greek	Kitchen	Sideboard	Table
$D_{1}$	101.28	102.41	101.45	100.23	101.47	100.52	109.53	100.446	101.49	104.53	100.46	102.27
$α_{o p t}$	5.1×10⁷	2.1×10⁷	2×10⁸	1×10⁶	1.3×10⁸	9.2×10⁸	3.2×10⁴	1.1×10⁹	5.6×10⁷	5.4×10⁸	2.5×10⁶	7.3×10⁵
$D_{r e}$	101.26	102.28	101.35	100.24	101.44	100.49	108.99	100.444	101.48	104.59	100.48	102.30

Table 3. PSNR and SSIM of denoising results for 12 light fields in HCI light field dataset

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Table 3. PSNR and SSIM of denoising results for 12 light fields in HCI light field dataset

Scene	Dual fan				Hypercone				Hyperfan
	Filter		Re + filter		Filter		Re + filter		Filter		Re + filter
	PSNR /dB	SSIM	PSNR /dB	SSIM	PSNR /dB	SSIM	PSNR /dB	SSIM	PSNR /dB	SSIM	PSNR /dB	SSIM
Pens	25.01	0.47	25.68	0.66	24.97	0.47	25.68	0.66	25.01	0.47	25.68	0.66
Cotton	27.47	0.60	29.48	0.84	27.36	0.59	29.41	0.83	27.47	0.60	29.48	0.84
Antinous	25.90	0.57	28.11	0.84	25.96	0.56	28.17	0.83	25.90	0.57	28.11	0.84
Tomb	26.65	0.54	27.87	0.77	26.56	0.53	27.83	0.76	26.65	0.54	27.87	0.77
Dino	26.72	0.59	28.22	0.75	26.69	0.58	28.28	0.75	26.72	0.59	28.22	0.75
Platonic	22.50	0.41	23.10	0.60	22.49	0.40	23.11	0.60	22.50	0.41	23.10	0.60
Boxes	23.30	0.52	23.97	0.68	23.45	0.52	24.13	0.68	23.30	0.52	23.97	0.68
Dishes	21.41	0.45	21.67	0.60	21.50	0.44	21.79	0.59	21.41	0.45	21.67	0.60
Greek	23.18	0.53	23.67	0.72	23.37	0.52	23.91	0.71	23.18	0.53	23.67	0.72
Kitchen	23.57	0.53	23.92	0.65	23.66	0.52	24.04	0.64	23.57	0.53	23.92	0.65
Sideboard	19.65	0.42	21.33	0.57	19.83	0.42	21.46	0.57	19.65	0.42	21.33	0.57
Table	23.30	0.53	23.67	0.67	23.32	0.52	23.72	0.66	23.30	0.53	23.67	0.67

Table 4. PSNR and SSIM of Flowers and Amethyst in Stanford light field dataset
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Table 4. PSNR and SSIM of Flowers and Amethyst in Stanford light field dataset
Scene $σ$ Re+4D hyperfan LSI-hyperfan
PSNR /dB SSIM PSNR /dB SSIM
Flowers 0.1 30.06 0.8955 27.00 0.5963
0.2 26.03 0.8172 22.66 0.4027
Amethyst 0.1 28.62 0.8795 28.34 0.6860
0.2 25.75 0.8051 24.04 0.5237

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Tiantian Wang, Di He, Chang Liu, Jun Qiu. Spectrum Concentration Based Reparameterization for Light Field Denoising[J]. Acta Optica Sinica, 2023, 43(20): 2026001

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Paper Information

Category: Physical Optics

Received: Mar. 10, 2023

Accepted: May. 19, 2023

Published Online: Oct. 23, 2023

The Author Email: Qiu Jun (qiujun@bistu.edu.cn)

DOI:10.3788/AOS230659

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Spectrum support angle and noise signal-to-noise ratio on the support for reparameterized light field with different distances between two planes

Table 1. Spectrum support angle and noise signal-to-noise ratio on the support for reparameterized light field with different distances between two planes

Table 2. Initial distance of two plane D1, weight parameters αopt, and distance of reparametrized light field two planes Dre of 12 light fields

Table 2. Initial distance of two plane D1, weight parameters αopt, and distance of reparametrized light field two planes Dre of 12 light fields

Table 3. PSNR and SSIM of denoising results for 12 light fields in HCI light field dataset

Table 3. PSNR and SSIM of denoising results for 12 light fields in HCI light field dataset

Table 4. PSNR and SSIM of Flowers and Amethyst in Stanford light field dataset

Table 4. PSNR and SSIM of Flowers and Amethyst in Stanford light field dataset

Table 2. Initial distance of two plane $D_{1}$ , weight parameters $α_{o p t}$ , and distance of reparametrized light field two planes $D_{r e}$ of 12 light fields

Table 2. Initial distance of two plane $D_{1}$ , weight parameters $α_{o p t}$ , and distance of reparametrized light field two planes $D_{r e}$ of 12 light fields