Tomographic Image Reconstruction Method Combining Exponential Filtering Inverse Projection Reconstruction and Iterative Reconstruction Algorithms

Qianghua Chen; Jinhong Ding; Sheng Zhou; Wenyuan Han; Lü Hongbo; Qiguo Sun; Xiangyue Kong; Huifu Luo

doi:10.3788/LOP202259.2310001

Laser & Optoelectronics Progress, Volume. 59, Issue 23, 2310001(2022)

Tomographic Image Reconstruction Method Combining Exponential Filtering Inverse Projection Reconstruction and Iterative Reconstruction Algorithms

Qianghua Chen^1、*, Jinhong Ding¹, Sheng Zhou¹, Wenyuan Han¹, Lü Hongbo¹, Qiguo Sun¹, Xiangyue Kong², and Huifu Luo³

Author Affiliations

¹School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China

²The 11th Research Institute of China Electronics Technology Corporation, Beijing 100016, China

³School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

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Figures & Tables(10)

Fig. 1. Schematic diagram of two-dimensional Radon transform

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Fig. 2. Schematic diagram of iterative EF inverse projection reconstruction algorithm

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Fig. 3. Schematic diagram of d and r changing with C

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Fig. 4. Comparison of reconstructed images between EF inverse projection and iterative EF inverse projection algorithms.(a) EF inverse projection reconstructed image; (b) grey value comparison of the 128^th line for EF inverse projection algorithm; (c) iterative EF inverse projection reconstructed image; (d) corresponding grey value comparison of the 128^th line for iterative EF inverse projection algorithm

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$Diagram of the refractive index field measurement system based on laser polarization tomography for algorithm verification$

Fig. 5. Diagram of the refractive index field measurement system based on laser polarization tomography for algorithm verification

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$Reconstruction results of 3D refraction field. (a) By EF inverse projection reconstruction algorithm; (b) by iterative EF inverse projection reconstruction algorithm$

Fig. 6. Reconstruction results of 3D refraction field. (a) By EF inverse projection reconstruction algorithm; (b) by iterative EF inverse projection reconstruction algorithm

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$Comparison of refractive index results got by two reconstruction algorithms and calibration results of the instrument$

Fig. 7. Comparison of refractive index results got by two reconstruction algorithms and calibration results of the instrument

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Table 1. Expressions of each filter function

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Table 1. Expressions of each filter function

Filter function	Expression
Ram-Lak^［17］	$H (ω) = \|ω\| r e c t (ω / 2 R)$
Shepp-Logan^［20］	$H (ω) = \|ω\| [2 R s i n (π ω / 2 R) / π ω] r e c t (ω / 2 R)$
Hamming^［17］	$H (ω) = \|ω\| [0.54 + 0.46 c o s (π ω / 2 R)] r e c t (ω / 2 R)$
Hann^［17］	$H (ω) = \|ω\| [0.5 + 0.5 c o s (π ω / 2 R)] r e c t (ω / 2 R)$
Cosine^［15］	$H (ω) = \|ω\| [c o s (π ω / 2 R)] r e c t (ω / 2 R)$
EF^［17］	$H (ω) = \|ω\| e x p (- C {\|ω\|}^{3}) (1 + ω^{2}) r e c t (ω / 2 R)$

Table 2. d and r of reconstruction results by different filter functions
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Table 2. d and r of reconstruction results by different filter functions
Filter function d r
Ram-Lak 0.782835 1.257933
Shepp-Logan 0.689665 1.101311
Hamming 0.429350 0.601243
Hann 0.408654 0.551063
Cosine 0.480448 0.715729
EF 0.388505 0.465358

Table 3. d and r of reconstruction results of EF inverse projection reconstruction algorithm and presented algorithm
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Table 3. d and r of reconstruction results of EF inverse projection reconstruction algorithm and presented algorithm
Reconstruction algorithm d r Time /s
EF inverse projection algorithm 0.388505 0.465358 112
Presented algorithm 0.378190 0.374133 346

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Qianghua Chen, Jinhong Ding, Sheng Zhou, Wenyuan Han, Lü Hongbo, Qiguo Sun, Xiangyue Kong, Huifu Luo. Tomographic Image Reconstruction Method Combining Exponential Filtering Inverse Projection Reconstruction and Iterative Reconstruction Algorithms[J]. Laser & Optoelectronics Progress, 2022, 59(23): 2310001

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