Convex optimization-based mesoscopic 3D reconstruction method for fluorescence-free light fields

Changmiao WANG; Hui LI; Chenbo SU; Yuntao WU

doi:10.5768/JAO202445.0602002

Journal of Applied Optics, Volume. 45, Issue 6, 1179(2024)

Convex optimization-based mesoscopic 3D reconstruction method for fluorescence-free light fields

Changmiao WANG1...2,3, Hui LI1,3,*, Chenbo SU1,3, and Yuntao WU13 |Show fewer author(s)

Author Affiliations

¹School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan 430205, China

²Swan college, Central South University of Forestry and Technology, Changsha 410211, China

³Hubei Key Laboratory of Intelligent Robot, Wuhan 430205, China

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Figures & Tables(8)

Fig. 1. Schematic diagram of system flow

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Fig. 2. Schematic diagram of mesoscopic imaging of light field and reconstruction process

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Fig. 3. Non-fluorescent RGB-MesoLFM light field acquisition system

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Fig. 4. Light field data self-view angle extraction and system PSF

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Fig. 5. Results of fluorescence-free reconstruction of US Air Force-1951 resolution target under different depth slices (grayscale map)

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Fig. 6. Comparison of reconstruction results of 72-hour non-fluorescent 3D RGB slices of egg embryos by three algorithms

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Table 1. Algorithm iteration steps

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Table 1. Algorithm iteration steps

Algorithm 1
Input: $h_{c} (x, y, z_{})$ 、 $g_{c} (x, y, z_{})$ 、 $α$ 、 $μ$ .
Output: $f_{z_{*}} = {f_{z_{1}}, f_{z_{2}}, \dots, f_{z_{n}}}$ .
Ensure:
$\begin{matrix} L_{ρ} (Φ_{z_{}}, f_{z_{}}, λ) = T_{data} (Φ_{z_{*}}) \\ + α \sum_{i = 1}^{n} \sum_{j = 1}^{k} \sum_{j^{'} \neq j}^{k} {‖ H_{j}^{j^{'}} (F_{j}^{j^{'}} P h_{c, j} (x, y, z_{i}) f_{c, j} (x, y, z_{i}) - g_{c, j^{'}} (x, y, z_{i})) ‖}_{2}^{2} \\ + μ \sum_{i = 1}^{n} {‖ \nabla f_{c} (x, y, z_{i}) ‖}_{2}^{2} \end{matrix}$
1: $Φ_{z_{}}^{0} = f_{z_{}}^{0} = g_{c} (x, y, z_{*}), λ^{0} = 0, l = 0$ .
2:for $l = 0$ to $i t e r$ do
3: $Φ_{z_{}}^{l + 1} = \underset{Φ_{z_{}}}{\arg \min} L_{ρ} (Φ_{z_{}}, f_{z_{}}^{l}, φ_{z}^{l})$ ;
4： $f_{z_{}}^{l + 1} = \underset{f}{\arg \min} L_{ρ} (Φ_{z_{}}^{l + 1}, f_{z_{*}}, φ_{z}^{l})$ ;
5: $λ^{l + 1} = λ^{l} + ρ (Φ_{z_{}}^{l + 1} - f_{z_{}}^{l + 1})$ ;
7: $l \leftarrow l + 1$ ;
8: stopping criteria met;
9:end for
10:return $f_{z_{*}}$ .

Table 2. Comparison of evaluation indicators

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Table 2. Comparison of evaluation indicators

Method	Depth/μm	SSIM	PSNR	Brenner	Energy
Non-cyclical extraction	−0	0.9001	29.84	172.35	99.74
	−10	0.8876	27.44	167.93	94.66
	−20	0.8622	26.51	164.54	93.35
LI H	−0	0.9149	31.34	179.24	95.71
	−10	0.8901	28.12	173.87	93.45
	−20	0.8721	27.80	168.46	92.16
Our	−0	0.9256	34.59	206.36	128.25
	−10	0.9013	32.51	202.45	116.36
	−20	0.9116	31.00	199.60	108.14

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Changmiao WANG, Hui LI, Chenbo SU, Yuntao WU. Convex optimization-based mesoscopic 3D reconstruction method for fluorescence-free light fields[J]. Journal of Applied Optics, 2024, 45(6): 1179

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