基于低秩矩阵填充的背景荧光噪声抑制方法 
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Low-Rank-Matrix-Completion-Based Method for Suppressing Background Fluorescence
西北大学信息科学与技术学院, 陕西 西安 710127
图 & 表
图 1. 2D仿真模型
Fig. 1. 2D simulation model
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图 2. 可视域示意图
Fig. 2. Sketch of FOV
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图 3. 算法1的流程图
Fig. 3. Flow chart of algorithm 1
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图 4. 单光源实验中,0.06/50噪声级别下两种方法的2D和3D重建结果。(a) IVTCG-NO方法的2D重建结果;(b) IVTCG-LR方法的2D重建结果; (c) IVTCG-NO方法的3D重建结果; (d) IVTCG-LR方法的3D重建结果
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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图 5. 双光源实验中,0.06/50噪声级别下两种方法的重建结果。(a) IVTCG-NO方法的2D重建结果; (b) IVTCG-LR方法的2D重建结果; (c) IVTCG-NO方法的2D重建结果; (d) IVTCG-LR方法的3D重建结果
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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表 1数字鼠器官光学参数
Table1. Optical parameters of the organs of digital mouse
| Organ | /mm-1 | μ' /mm-1 | /mm-1 | μ' /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 |
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表 2不同噪声级别下两种方法的重建结果
Table2. 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 |
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表 3OR1MP算法的运行时间和去噪前后外表面观测的相对误差
Table3. 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 |
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| Time /s | 0.0052 | 0.0052 | 0.0058 | 0.0062 | 0.0056 | 0.0054 | | eLR | 1.0172 | 0.8858 | 0.7965 | 0.7331 | 0.6863 | 0.6508 | | eNO | 1.4944 | 1.2453 | 1.0674 | 0.9340 | 0.8302 | 0.7472 |
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表 4不同噪声级别条件下两种方法的重建结果
Table4. 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 |
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表 5光源1和光源2的LE
Table5. 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 |
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表 6OR1MP算法的运行时间和去噪前后外表面观测的相对误差
Table6. 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 |
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| Time /s | 0.0046 | 0.0056 | 0.0050 | 0.0046 | 0.0054 | 0.0056 | | eLR | 1.3504 | 1.1595 | 1.0280 | 0.9332 | 0.8625 | 0.8082 | | eNO | 2.0465 | 1.7054 | 1.4618 | 1.2790 | 1.1369 | 1.0232 |
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王晓东, 耿国华, 易黄建, 何雪磊, 贺小伟. 基于低秩矩阵填充的背景荧光噪声抑制方法[J]. 光学学报, 2018, 38(10): 1017003. 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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