# Reflective Tomography Lidar Image Reconstruction for Long Distance Non-Cooperative Target

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## Abstract

**:**

## 1. Introduction

## 2. LRT Model and Experimental Design

#### 2.1. Laser Reflection Tomography Model

#### 2.2. Experimental System

## 3. LRT Image Reconstruction

#### 3.1. LRT Data Processing Framework

#### 3.2. Tomographic Imaging of Lidar Projection Data

#### 3.2.1. ART for Lidar Image Reconstruction

#### 3.2.2. Sparse Reconstruction with ART Model

#### 3.2.3. TV Sparse Reconstruction with ART Model

Algorithm 1: Implementation of TV sparse reconstruction with ART model. |

Given $p,A,N$, maxiter, $\alpha $ |

Initialization: ${u}_{0}=0$ |

for k = 1,2,3... maxiter do |

ART Updating: |

for j = 1,2,3..., N do |

${u}_{j}^{k}={u}_{j}^{k-1}+\lambda \frac{{p}_{i}-{\displaystyle {\sum}_{j=1}^{N}{\omega}_{in}{u}_{n}^{k-1}}}{{\displaystyle {\sum}_{n=1}^{N}{\omega}_{in}^{2}}}{\omega}_{ij}$ |

${u}_{j}^{k}=\{\begin{array}{c}{u}_{j}^{k}\begin{array}{cc}& \end{array}{u}_{j}^{k}\ge 0\\ {0}_{}^{}\begin{array}{cc}& \end{array}{u}_{j}^{k}<0\end{array}$ |

end |

TV Minimization: |

${t}^{k-1}={u}^{k}$ |

$v=\partial {\Vert {t}^{k-1}\Vert}_{TV}/\partial {t}^{k-1}$ |

${t}^{k}={t}^{k-1}-\alpha \cdot v$ |

${u}^{k}={t}^{k}$ |

$k=k+1$ |

End |

## 4. Experiments

#### 4.1. Near-Field Experiment

#### 4.2. Far-Field Experiment

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

APD | Avalanche Photodiode |

ART | Algebraic Reconstruction Technique |

CC | Correlation Coefficient |

CT | Computed Tomography |

DCT | Discrete Cosine Transform |

FBP | Filtered Back Projection |

FFT | Fast Fourier Transform |

IE | Information Entropy |

IPC | Industrial Personal Computer |

LRT | Laser Reflection Tomography |

MC Laser | Microchip Laser |

NLTV | Non-local Total Variation |

NRSNR | No-reference Signal-noise Ratio |

NPBS | Non-polarizing Beam Splitter |

OMP | Orthogonal Matching Pursuit |

PIN | Positive Intrinsic Negative |

SMF | Single Mode Fiber |

SNR | Signal-noise Ratio |

TV | Total Variation |

TVS-POCS | Total variation-strokes-projection Onto Convex Sets |

Var | Variance |

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**Figure 2.**Experimental platform. (

**a**) The laser transmitter and (

**b**) the outfield experiment environment.

**Figure 3.**Schematic diagram of LRT radar prototype: R, reflector; NPBS, Non-polarizing beam splitter; APD, avalanche photodiode; Pin, positive intrinsic negative; SMF, single mode fiber; MC Laser, microchip laser.

**Figure 6.**(

**a**) Laser reflection projection data after registration; (

**b**) converted projection data in complete angle.

**Figure 7.**Near-field experimental imaging results with uniformly sampled views of projections (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) Complete view data (

**a1**–

**a5**); (

**b**) sampled data at 5° intervals (

**b1**–

**b5**); (

**c**) sampled data at 10° intervals (

**c1**–

**c5**); (

**d**) sampled data at 20° intervals (

**d1**–

**d5**).

**Figure 8.**Second near-field experimental imaging results (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) Complete view data with noise (

**a1**–

**a5**); (

**b**) sampled data at 10°intervals with noise (

**b1**–

**b5**); (

**c**) random sampled data at 10° intervals (

**c1**–

**c5**).

**Figure 9.**Near-field experimental imaging results under limited view of projections (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) 0–60° sampled data (

**a1**–

**a5**); (

**b**) 0–90° sampled data (

**b1**–

**b5**); (

**c**) 0–120° sampled data (

**c1**–

**c5**); (

**d**) 0–150° sampled data (

**d1**–

**d5**).

**Figure 11.**Far-field experimental imaging results with uniformly sampled views of projections (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) Complete view data (

**a1**–

**a5**); (

**b**) sampled data at 5° intervals (

**b1**–

**b5**); (

**c**) sampled data at 10° intervals (

**c1**–

**c5**); (

**d**) sampled data at 20° intervals (

**d1**–

**d5**).

**Figure 12.**Far-field experimental imaging results (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) Complete view data with noise (

**a1**–

**a5**); (

**b**) sampled data at 10° intervals with noise (

**b1**–

**b5**); (

**c**) random sampled data at 10° intervals (

**c1**–

**c5**).

**Figure 13.**Far-field experimental imaging results under a limited view of projections (

**Far left**) iRadon; (

**Left**) FBP; (

**Middle**) ART; (

**Right**) sparse ART with OMP; (

**Far right**) TV sparse reconstruction with ART. (

**a**) 0–60° sampled data (

**a1**–

**a5**); (

**b**) 0–90° sampled data (

**b1**–

**b5**); (

**c**) 0–120° sampled data (

**c1**–

**c5**); (

**d**) 0–150° sampled data (

**d1**–

**d5**).

**Figure 14.**(

**a**) Far-field target; (

**b**) laser reflection projection data after registration; (

**c**) converted projection data in complete angle.

**Figure 15.**Far field experimental imaging results with uniformly sampled view of projections (

**Far left**) iRadon; (

**Left**) FBP; (

**Right**) ART; (

**Far right**) TV sparse reconstruction with ART. (

**a**) Complete view data (a1:a4); (

**b**) sampled data at 5° intervals (b1:b4); (

**c**) sampled data at 10° intervals (c1:c4); (

**d**) sampled data at 20° intervals (d1:d4).

IE | NRSNR (dB) | Var | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | |

complete view | 5.1485 | 6.2253 | 6.1133 | 9.6305 | 1.5081 | 2.0758 | 2.6317 | 3.2437 | 0.0463 | 0.2478 | 0.1318 | 0.3428 |

5° intervals | 5.2353 | 5.2453 | 6.197 | 9.6313 | 1.5746 | 1.9728 | 2.3742 | 3.1592 | 0.0470 | 0.0423 | 0.0881 | 0.1572 |

10° intervals | 5.3875 | 5.1411 | 6.0973 | 9.6319 | 1.7853 | 1.8311 | 2.4937 | 3.4724 | 0.0481 | 0.109 | 0.0649 | 0.1776 |

20° intervals | 5.4357 | 4.6286 | 5.7298 | 9.6313 | 1.9615 | 1.574 | 2.623 | 3.2858 | 0.0461 | 0.0618 | 0.031 | 0.0912 |

IE | NRSNR (dB) | Var | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | |

complete view with noise | 5.3208 | 5.4121 | 6.1208 | 9.6315 | 1.9989 | 1.9855 | 1.6487 | 2.2245 | 0.0298 | 0.0563 | 0.1359 | 0.2552 |

10° intervals with noise | 5.4262 | 4.6257 | 6.1078 | 9.6305 | 2.0265 | 1.6557 | 1.3547 | 2.5897 | 0.0137 | 0.0379 | 0.0641 | 0.1966 |

10° intervals random sample | 5.2839 | 4.7442 | 6.5712 | 9.6314 | 2.0345 | 1.5427 | 1.3827 | 2.3098 | 0.0418 | 0.0375 | 0.0651 | 0.0982 |

CC | ||||
---|---|---|---|---|

FBP | ART | OMP | TV-ART | |

0–60° sampled | 0.4443 | 0.5061 | 0.4562 | 0.5380 |

0–90° sampled | 0.4934 | 0.4848 | 0.5178 | 0.5789 |

0–120° sampled | 0.6348 | 0.6538 | 0.6048 | 0.6919 |

0–150° sampled | 0.8480 | 0.8612 | 0.6916 | 0.9319 |

IE | NRSNR (dB) | Var | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | |

complete view | 4.5046 | 2.2764 | 3.9911 | 9.6317 | 4.251 | 1.5794 | 3.3193 | 5.7955 | 0.0781 | 0.0101 | 0.0563 | 0.1015 |

5° intervals | 4.4616 | 1.9777 | 4.0875 | 9.6308 | 3.734 | 1.4916 | 4.0301 | 4.6043 | 0.0933 | 0.0187 | 0.0227 | 0.098 |

10° intervals | 4.6289 | 1.764 | 4.4602 | 9.6312 | 3.3437 | 1.4779 | 3.9256 | 4.5962 | 0.0526 | 0.039 | 0.0545 | 0.0559 |

20° intervals | 4.5152 | 1.7045 | 4.6932 | 9.6316 | 4.1645 | 1.5371 | 3.8309 | 4.7132 | 0.0319 | 0.0446 | 0.0452 | 0.0503 |

IE | NRSNR (dB) | Var | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | FBP | ART | OMP | TV-ART | |

complete view with noise | 5.0696 | 2.1788 | 4.0617 | 9.6315 | 6.978 | 2.1002 | 4.8256 | 11.8431 | 0.0084 | 0.0086 | 0.0164 | 0.01672 |

10° intervals with noise | 5.154 | 1.9383 | 4.2768 | 9.6314 | 7.3181 | 1.974 | 5.2402 | 9.1245 | 0.0022 | 0.0044 | 0.0553 | 0.0479 |

10° intervals random sample | 4.373 | 1.8787 | 4.491 | 9.6313 | 4.9049 | 1.8302 | 2.4533 | 6.9627 | 0.0219 | 0.005 | 0.0297 | 0.0411 |

CC | ||||
---|---|---|---|---|

FBP | ART | OMP | TV-ART | |

0–60° sampled | 0.3978 | 0.3687 | 0.1975 | 0.4913 |

0–90° sampled | 0.471 | 0.4134 | 0.3701 | 0.4925 |

0–120° sampled | 0.4353 | 0.4269 | 0.4066 | 0.4727 |

0–150° sampled | 0.7586 | 0.7499 | 0.6805 | 0.7979 |

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## Share and Cite

**MDPI and ACS Style**

Guo, R.; Jiang, Z.; Jin, Z.; Zhang, Z.; Zhang, X.; Guo, L.; Hu, Y.
Reflective Tomography Lidar Image Reconstruction for Long Distance Non-Cooperative Target. *Remote Sens.* **2022**, *14*, 3310.
https://doi.org/10.3390/rs14143310

**AMA Style**

Guo R, Jiang Z, Jin Z, Zhang Z, Zhang X, Guo L, Hu Y.
Reflective Tomography Lidar Image Reconstruction for Long Distance Non-Cooperative Target. *Remote Sensing*. 2022; 14(14):3310.
https://doi.org/10.3390/rs14143310

**Chicago/Turabian Style**

Guo, Rui, Zheyi Jiang, Zhihan Jin, Zhao Zhang, Xinyuan Zhang, Liang Guo, and Yihua Hu.
2022. "Reflective Tomography Lidar Image Reconstruction for Long Distance Non-Cooperative Target" *Remote Sensing* 14, no. 14: 3310.
https://doi.org/10.3390/rs14143310