Low-Rank-Matrix-Completion-Based Method for Suppressing Background Fluorescence

Fig. 4. Reconstruction using two methods at noise level of 0.06/50 in single light source experiment. (a) 2D reconstruction using IVTCG-NO method; (b) 2D reconstruction using IVTCG-LR method; (c) 3D reconstruction using IVTCG-NO method; (d) 3D reconstruction using IVTCG-LR method

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Fig. 5. Reconstruction using two methods at noise level of 0.06/50 in double light sources. (a) 2D reconstruction using IVTCG-NO method; (b) 2D reconstruction using IVTCG-LR method; (c) 3D reconstruction using IVTCG-NO method; (d) 3D reconstruction using IVTCG-LR method

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Table 1. Optical parameters of the organs of digital mouse

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Table 1. Optical parameters of the organs of digital mouse

Organ	$\begin{matrix} {μ_{ax}}_{} \end{matrix}$ /mm^-¹	μ' $\begin{matrix} {_{sx}}_{} \end{matrix}$ /mm^-¹	$\begin{matrix} {μ_{am}}_{} \end{matrix}$ /mm^-¹	μ' $\begin{matrix} {_{sm}}_{} \end{matrix}$ /mm^-¹	g
Muscle	0.075	0.412	0.043	0.350	0.90
Heart	0.051	0.944	0.030	0.870	0.85
Stomach	0.010	1.417	0.007	1.340	0.92
Liver	0.304	0.668	0.176	0.629	0.90
Kidneys	0.058	2.204	0.034	2.021	0.86
Lungs	0.170	2.157	0.097	2.093	0.90

Table 2. Reconstruction using two methods at different noise levels

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Table 2. Reconstruction using two methods at different noise levels

Method	NL	(τ,ε)	LE /mm	CNR	Time /s
IVTCG-LR	0.06/50	(10^-12,10^-12)	0.4679±9.2×10^-3	20.5455±1.8	71.0230±4.4
IVTCG-NO	0.06/50	(10^-14,10^-12)	0.7528±0	13.7432±0	74.3608±3.2
IVTCG-LR	0.06/60	(10^-12,10^-12)	0.4409±8.7×10^-3	25.2068±2.0	62.6312±4.3
IVTCG-NO	0.06/60	(10^-14,10^-12)	0.7420±0	14.2688±0	69.7136±1.3
IVTCG-LR	0.06/70	(10^-12,10^-12)	0.4154±1.1×10^-2	27.9832±3.3×10^-1	61.4392±7.0
IVTCG-NO	0.06/70	(10^-14,10^-12)	0.7313±0	14.8315±0	68.2468±0.6
IVTCG-LR	0.06/80	(10^-12,10^-12)	0.3928±3.9×10^-3	28.8322±4.0×10^-1	52.3152±3.5
IVTCG-NO	0.06/80	(10^-14,10^-12)	0.7134±0	16.1134±0	68.2628±1.9
IVTCG-LR	0.06/90	(10^-12,10^-13)	0.3810±4.4×10^-4	17.4285±1.2×10^-2	51.3362±4.8
IVTCG-NO	0.06/90	(10^-14,10^-12)	0.7031±0	16.1723±0	67.9030±1.5
IVTCG-LR	0.06/100	(10^-12,10^-13)	0.3591±3.9×10^-4	18.3511±5.9×10^-3	45.3048±1.9
IVTCG-NO	0.06/100	(10^-14,10^-12)	0.6915±0	16.4278±0	66.2242±0.5

Table 3. Running time of OR1MP algorithm and relative errors of the boundary observation vectors before and after denoising operation
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Table 3. Running time of OR1MP algorithm and relative errors of the boundary observation vectors before and after denoising operation
NL 0.06/50 0.06/60 0.06/70 0.06/80 0.06/90 0.06/100
Time /s 0.0052 0.0052 0.0058 0.0062 0.0056 0.0054
e_LR 1.0172 0.8858 0.7965 0.7331 0.6863 0.6508
e_NO 1.4944 1.2453 1.0674 0.9340 0.8302 0.7472

Table 4. Reconstruction using two methods at different noise levels

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Table 4. Reconstruction using two methods at different noise levels

Method	NL	(τ,ε)	LE /mm	CNR	Time /s
IVTCG-LR	0.06/50	(10^-14,10^-13)	0.8234±1.9×10^-3	18.8590±6.1×10^-2	148.0212±4.4
IVTCG-NO	0.06/50	(10^-16,10^-12)	2.7076±0	13.5230±0	43.6608±1.4
IVTCG-LR	0.06/60	(10^-14,10^-13)	0.8443±8.6×10^-4	18.6281±4.6×10^-2	146.4514±3.2
IVTCG-NO	0.06/60	(10^-15,10^-12)	2.7227±0	13.2980±0	48.4676±2.2
IVTCG-LR	0.06/70	(10^-14,10^-13)	0.8650±2.4×10^-3	18.2852±6.9×10^-2	146.5268±2.1
IVTCG-NO	0.06/70	(10^-15,10^-12)	2.7368±0	13.2485±0	47.4714±1.1
IVTCG-LR	0.06/80	(10^-14,10^-13)	0.8837±1.8×10^-3	18.1829±9.2×10^-2	151.7274±1.3
IVTCG-NO	0.06/80	(10^-16,10^-12)	2.7259±0	13.3588±0	51.4532±1.3
IVTCG-LR	0.06/90	(10^-14,10^-13)	0.9003±3.1×10^-3	17.8455±1.9×10^-1	147.2034±3.8
IVTCG-NO	0.06/90	(10^-16,10^-12)	2.7150±0	13.5971±0	50.9520±0.3
IVTCG-LR	0.06/100	(10^-15,10^-12)	0.9110±2.8×10^-3	18.6627±1.6×10^-1	70.1896±11
IVTCG-NO	0.06/100	(10^-17,10^-12)	2.7343±0	13.1110±0	48.5222±7.2

Table 5. LE of light source 1 and light source 2 mm

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Table 5. LE of light source 1 and light source 2 mm

NL	0.06/50	0.06/60	0.06/70	0.06/80	0.06/90	0.06/100
IVTCG-LR(LE1)	0.4862±1.0×10^-3	0.5057±8.1×10^-4	0.5247±1.0×10^-3	0.5423±9.4×10^-4	0.5579±2.4×10^-3	0.5787±3.1×10^-3
IVTCG-LR(LE2)	0.3372±1.5×10^-3	0.3386±8.4×10^-4	0.3403±1.5×10^-3	0.3414±9.2×10^-4	0.3424±9.9×10^-4	0.3224±2.1×10^-3
IVTCG-NO(LE1)	1.8779±0	1.8957±0	1.9109±0	1.8988±0	1.8767±0	1.9088±0
IVTCG-NO(LE2)	0.8297±0	0.8270±0	0.8259±0	0.8271±0	0.8383±0	0.8255±0

Table 6. Running time of OR1MP algorithm and relative errors of the boundary observation vectors before and after denoising operation
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Table 6. Running time of OR1MP algorithm and relative errors of the boundary observation vectors before and after denoising operation
NL 0.06/50 0.06/60 0.06/70 0.06/80 0.06/90 0.06/100
Time /s 0.0046 0.0056 0.0050 0.0046 0.0054 0.0056
e_LR 1.3504 1.1595 1.0280 0.9332 0.8625 0.8082
e_NO 2.0465 1.7054 1.4618 1.2790 1.1369 1.0232

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Xiaodong Wang, Guohua Geng, Huangjian Yi, Xuelei He, Xiaowei He. Low-Rank-Matrix-Completion-Based Method for Suppressing Background Fluorescence[J]. Acta Optica Sinica, 2018, 38(10): 1017003

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