# Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background

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## Abstract

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## 1. Introduction

## 2. Multiscale Directional Representation of Image Using Shearlet Transform

## 3. Dim Target Detection Using Multiple Feature Fusion and Maximum Kurtosis

#### 3.1. Shearlet Decomposition and Subband Fusion

#### 3.2. Adaptive Threshold with Maximum Contrast Criterion

Algorithm 1 Process of the Proposed Method for Detecting Infrared Targets |

Input: An original infrared image. Output: Detection result. 1: Set the number of scales and directions for the shearlet transform; 2: Use a trous algorithm to implement the nonsubsampled Laplacian pyramid transform; 3: High-frequency subbands ${f}_{d}^{j}[{n}_{1},{n}_{2}]$; 4: 2D Fast Fourier transform (FFT) $\stackrel{\wedge}{{f}_{d}^{j}}({\xi}_{1},{\xi}_{2})$; 5: Use Meyer wavelets as the window function $W({2}^{j}v-l)$; 6: Translate $W$ to obtain the different directional components; 7: Convert to the Cartesian coordinate system to obtain shearing filters ${\widehat{\omega}}_{j,l}[{\xi}_{1},{\xi}_{2}]$; 8: $\stackrel{\wedge}{{f}_{d}^{j}}({\xi}_{1,}{\xi}_{2})\times {\stackrel{\wedge}{w}}_{j,l}({\xi}_{1,}{\xi}_{2})$; 9: 2D inverse FFT to obtain the shearlet coefficients $<f,{\psi}_{j,l,k}>$; 10: High-frequency subbands at n directions of each scale; 11: Fuse the subbands by superposition; 12: Searching the maximum kurtosis and enhance the corresponding columns; 13: Normalization; 14: Fuse the high-frequency subbands at various scales by multiplication; 15: Maximum contrast threshold segmentation; 16: Output results. |

## 4. Experimental Results

#### 4.1. Example of Detection Results

#### 4.2. Performance Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Liu, X.; Chen, Y.; Peng, Z.; Wu, J.; Wang, Z. Infrared image super-resolution reconstruction based on quaternion fractional order total variation with Lp quasinorm. Appl. Sci.
**2018**, 8, 1864. [Google Scholar] [CrossRef] - Lai, R.; Yue, G.; Zhang, G. Total Variation Based Neural Network Regression for Nonuniformity Correction of Infrared Images. Symmetry
**2018**, 10, 157. [Google Scholar] [CrossRef] - Jian, X.; Lv, C.; Wang, R. Nonuniformity Correction of Single Infrared Images Based on Deep Filter Neural Network. Symmetry
**2018**, 10, 612. [Google Scholar] [CrossRef] - Peng, Z.; Zhang, Q.; Wang, J.; Zhang, Q.P. Dim target detection based on nonlinear multi-feature fusion by Karhunen-Loeve transform. Opt. Eng.
**2004**, 43, 2954–2958. [Google Scholar] - Peng, Z.; Zhang, Q.; Guan, A. Extended target tracking using projection curves and matching pel count. Opt. Eng.
**2007**, 46, 066401. [Google Scholar] - Beghdadi, A.; Negrate, A.L.; Lesegno, P.V. Entropic Thresholding Using a Block Soure Model. Comput. Model Image Process
**1995**, 57, 197–205. [Google Scholar] [CrossRef] - Chan, D.S.K.; Langan, D.A.; Stayer, D.A. Spatial processing techniques for the detection of small targets in IR clutter. Proc. SPIE
**1990**, 1305, 53–62. [Google Scholar] - Zhang, B.; Zhang, T.; Cao, Z.; Zhang, K. Fast new small target detection algorithm based on a modified partial differential equation in infrared clutter. SPIE Opt. Eng.
**1990**, 46, 106401–106406. [Google Scholar] [CrossRef] - Zhang, L.; Peng, L.; Zhang, T.; Cao, S.; Peng, Z. Infrared small target detection via non-convex rank approximation minimization joint l2, 1 norm. Remote Sens.
**2018**, 10, 1821. [Google Scholar] [CrossRef] - Zhang, T.; Wu, H.; Liu, Y.; Peng, L. Infrared Small Target Detection Based on Non-Convex Optimization with Lp-Norm Constraint. Remote Sens.
**2019**, 11, 559. [Google Scholar] [CrossRef] - Zhang, L.; Peng, Z. Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm. Remote Sens.
**2019**, 11, 382. [Google Scholar] [CrossRef] - Wang, G.D.; Chen, C.Y.; Shen, X.B. Facet-Based Infrared Small Target Detection Method. Electron. Lett.
**2005**, 41, 1244–1246. [Google Scholar] [CrossRef] - Bosch, I.; Gomez, S.; Vergara, L.; Moragues, J. Infrared image processing and its application to forest fire surveillance. In Proceedings of the IEEE Conference on Advanced Video and Signal Based Surveillance, London, UK, 5–7 September 2007; pp. 283–288. [Google Scholar]
- Rosin, P.L. Training cellular automata for image processing. IEEE Trans. Image Process.
**2006**, 15, 2076–2087. [Google Scholar] [CrossRef] - Li, Y.; Zhang, Y.; Yu, J.G.; Tan, Y.; Tian, J.; Ma, J. A novel spatio-temporal saliency approach for robust dim moving target detection from airborne infrared image sequences. Inf. Sci.
**2016**, 369, 548–563. [Google Scholar] [CrossRef] - Leung, H.; Dubash, N.; Xie, N. Detection of Small Objects in Clutter Using a GA-RBF Neural Network. IEEE Trans. Aerosp. Electron. Syst.
**2002**, 38, 98–118. [Google Scholar] [CrossRef] - DelMarco, S.; Agaian, S. The design of wavelets for image enhancement and target detection. Proc. SPIE
**2009**, 7351. [Google Scholar] [CrossRef] - Tian, L.; Peng, Z. Determining the optimal order of fractional Gabor transform based on kurtosis maximization and its application. J. Appl. Geophys.
**2014**, 108, 152–158. [Google Scholar] [CrossRef] - Kong, D.; Peng, Z.; Fan, H.; He, Y. Seismic random noise attenuation using directional total variation in shearlet domain. J. Seism. Explor.
**2016**, 25, 321–338. [Google Scholar] - Kong, D.; Peng, Z. Seismic random noise attenuation using shearlet and total generalized variation. J. Geophys. Eng.
**2015**, 12, 1024–1035. [Google Scholar] [CrossRef] [Green Version] - Emmanuel, J.S.; Cands, J.; Donoho, D.L. The Curvelet Transform for Image Denoising. IEEE Trans. Image Process.
**2002**, 6, 670–684. [Google Scholar] - Arthur, L.; Zhou, J.; Do, M.N. The Nonsubsampled Contourlet Transform: Theory, Design and Applications. IEEE Trans. Image Process.
**2006**, 15, 3089–3101. [Google Scholar] - Guo, K.; Labate, D. Optimally Sparse Multidimensional Representation using Shearlets. SIAM J. Math. Anal.
**2007**, 39, 298–318. [Google Scholar] [CrossRef] - Easley, G.; Labate, D.; Lim, W. Sparse Directional Image Representation using the Discrete Shearlet Transform. Appl. Comput. Harmon. Anal.
**2008**, 25, 25–46. [Google Scholar] [CrossRef] - Kutyniok, G.; Shahram, M.; Donoho, D.L. Development of a Digital Shearlet Transform Based on Pseudo-Polar FFT. Proc. SPIE
**2009**, 7446. [Google Scholar] [CrossRef] - Kutyniok, G.; Sauer, T. Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis. SIAM J. Math. Anal.
**2009**, 41, 1436–1471. [Google Scholar] [CrossRef] - Lim, W.-Q. The Discrete Shearlet Transform: A New Directional Transform and Compactly Supported Shearlet Frames. IEEE Tran. Image Process.
**2010**, 19, 1166–1180. [Google Scholar] - Shensa, M.J. The discrete wavelet transform: Wedding the àtrous and mallat algorithms. IEEE Trans. Signal Process.
**1992**, 40, 2464–2482. [Google Scholar] [CrossRef]

**Figure 1.**The shearing filters constructed using a Meyer wavelet as the window function; (

**a**) the window function $W$, (

**b**,

**c**) are the shearing filters in two directions.

**Figure 3.**3D display of the shearlet coefficients’ modulus; (

**a**) the original infrared image; (

**b**,

**c**) the shearlet coefficients’ modulus of four directional subbands at the first and second level decomposition, respectively.

**Figure 4.**Clutter suppression performance of the nonsubsampled contourlet transform (NSCT) and shearlet transform method; (

**a**) the original infrared image; (

**b**) the NSCT method; (

**c**) the proposed method.

**Figure 5.**Clutter suppression performance of the NSCT and shearlet transform method; (

**a**) the original infrared image; (

**b**) the NSCT method; (

**c**) the proposed method.

**Table 1.**Performance comparison of different methods. SCR: signal-to-clutter ratio; PSNR: peak signal-to-noise ratio; EST: elapsed time.

Original Images | NSCT | Shearlet Transform | |||||
---|---|---|---|---|---|---|---|

$SC{R}_{\mathrm{in}}$ | $SC{R}_{\mathrm{gain}}$ | PSNR | EST(s) | $SC{R}_{\mathrm{gain}}$ | PSNR | EST(s) | |

Figure 4a | 1.7561 | 11.5748 | 11.9017 | 24.91 | 13.1658 | 11.9112 | 1.41 |

Figure 5a | 0.7972 | 33.2920 | 5.2957 | 25.85 | 30.8466 | 5.4511 | 1.44 |

Method | PR (%) | FAR (%) |
---|---|---|

NSCT | 99.0 | 7.0 |

Shearlet transform | 99.0 | 5.0 |

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## Share and Cite

**MDPI and ACS Style**

Peng, L.; Zhang, T.; Liu, Y.; Li, M.; Peng, Z.
Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background. *Symmetry* **2019**, *11*, 723.
https://doi.org/10.3390/sym11050723

**AMA Style**

Peng L, Zhang T, Liu Y, Li M, Peng Z.
Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background. *Symmetry*. 2019; 11(5):723.
https://doi.org/10.3390/sym11050723

**Chicago/Turabian Style**

Peng, Lingbing, Tianfang Zhang, Yuhan Liu, Meihui Li, and Zhenming Peng.
2019. "Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background" *Symmetry* 11, no. 5: 723.
https://doi.org/10.3390/sym11050723