# Parameter Estimation of Poisson–Gaussian Signal-Dependent Noise from Single Image of CMOS/CCD Image Sensor Using Local Binary Cyclic Jumping

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Poisson–Gaussian Signal-Dependent Noise Model

#### 3.2. Proposed Noise Parameter Estimation Model

^{−6}as in [18]. F

^{−1}represents an inverse binomial cumulative function. The image blocks where the texture strengths are less than $\tau $, are defined as weakly textured image blocks.

## 4. Experimental Results

## 5. Computational Complexity

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Li, Z.P.; Jiang, M.; Zhang, X.N.; Chen, X.Y.; Hou, W.K. Space-time-multiplexed multi-image visible light positioning system exploiting pseudo-miller-coding for smart phones. IEEE Trans. Wirel. Commun.
**2017**, 16, 8261–8274. [Google Scholar] [CrossRef] - Cao, C.; Shirakawa, Y.; Tan, L.; Seo, M.W. A time-resolved NIR lock-in pixel CMOS image sensor with background cancelling capability for remote heart rate detection. IEEE J. Solid-State Circ.
**2019**, 54, 978–991. [Google Scholar] [CrossRef] - Hasan, A.M.; Melli, A.; Wahid, K.A. Denoising low-dose CT images using multiframe blind source separation and block matching filter. IEEE Trans. Radiat. Plasma Med. Sci.
**2018**, 27, 279–287. [Google Scholar] [CrossRef] - Ma, X.L.; Hu, S.H.; Yang, D.S. SAR Image De-noising Based on Residual Image Fusion and Sparse Representation. KSII Trans. Internet Inf. Syst.
**2019**, 13, 3620–3637. [Google Scholar] [CrossRef] [Green Version] - Xu, J.T.; Nie, H.F.; Nie, K.M.; Jin, W.M. Fixed-pattern noise correction method based on improved moment matching for a TDI CMOS image sensor. J. Opt. Soc. Am. A
**2017**, 34, 1500–1510. [Google Scholar] [CrossRef] [PubMed] - Han, L.Q.; Xu, J.T. Long exposure time noise in pinned photodiode CMOS image sensors. IEEE Electr. Device Lett.
**2018**, 39, 979–982. [Google Scholar] [CrossRef] - Ding, L.; Zhang, H.Y.; Xiao, J.S.; Lei, J.F.; Xu, F.; Lu, S.J. Mixed Noise Parameter Estimation Based on Variance Stable Transform. CMES-Comput. Model. Eng. Sci.
**2020**, 122, 675–690. [Google Scholar] [CrossRef] - Ehret, T.; Davy, A.; Morel, J.M. Model-blind video denoising via frame-to-frame training. Comput. Vis. Pattern Recognit.
**2019**, 11, 11369–11378. [Google Scholar] [CrossRef] [Green Version] - Yi, W.; Qiang, C.Q.; Yan, Y. Robust impulse noise variance estimation based on image histogram. IEEE Signal. Proc. Lett.
**2010**, 17, 485–488. [Google Scholar] [CrossRef] - Foi, A.; Trimeche, M.; Katkovnik, V.; Egiazarian, K. Practical Poissonian–Gaussian noise modeling and fitting for single-image raw-data. IEEE Trans. Image Process.
**2008**, 17, 1737–1754. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pham, T.D. Estimating parameters of optimal average and adaptive wiener filters for image restoration with sequential Gaussian simulation. IEEE Signal. Proc. Lett.
**2015**, 11, 1950–1954. [Google Scholar] [CrossRef] [Green Version] - Pyatykh, S.; Hesser, J. Image sensor noise parameter estimation by variance stabilization and normality assessment. IEEE Trans. Image Process.
**2014**, 23, 3990–3998. [Google Scholar] [CrossRef] [PubMed] - Mäkitalo, M.; Foi, A. Noise parameter mismatch in variance stabilization with an application to Poisson–Gaussian noise estimation. IEEE Trans. Image Process.
**2014**, 23, 5348–5359. [Google Scholar] [CrossRef] - Huang, X.T.; Chen, L.; Tian, J.; Zhang, X.L. Blind image noise level estimation using texture-based eigenvalue analysis. Multimed. Tools Appl.
**2015**, 75, 2713–2714. [Google Scholar] [CrossRef] - Jeong, B.G.; Kim, B.C.; Moon, Y.H.; Eom, I.K. Simplified noise model parameter estimation for signal-dependent noise. Signal. Process.
**2014**, 96, 266–273. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, G.; Xu, J. Parameter estimation of signal-dependent random noise in CMOS/CCD image sensor based on numerical characteristic of mixed Poisson noise samples. Sensors
**2018**, 18, 2276. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Wang, G.; Xu, J. The modified gradient edge detection method for the color filter array image of the CMOS image sensor. Opt. Laser Technol.
**2014**, 62, 73–81. [Google Scholar] [CrossRef] - Liu, X.; Tanaka, M.; Okutomi, M. Practical signal-dependent noise parameter estimation from a single noisy image. IEEE Trans. Image Process.
**2014**, 23, 4361–4371. [Google Scholar] [CrossRef] [PubMed] - Dong, L.; Zhou, J.; Tang, Y.Y. Effective and fast estimation for image sensor noise via constrained weighted least squares. IEEE Trans. Image Process.
**2018**, 27, 2715–2730. [Google Scholar] [CrossRef] [PubMed] - Li, Y.; Li, Z.; Wei, K. Noise estimation for image sensor based on local entropy and median absolute deviation. Sensors
**2019**, 19, 339. [Google Scholar] [CrossRef] [Green Version] - Chen, J.; Chen, J.; Chao, H. Image blind denoising with generative adversarial network based noise modelling. Comput. Vis. Pattern Recognit.
**2018**, 11, 3155–3164. [Google Scholar] [CrossRef] - Guo, S.; Yan, Z.; Zhang, K. Toward convolutional blind denoising of real photographs. Comput. Vis. Pattern Recognit.
**2019**, 11, 1712–1722. [Google Scholar] [CrossRef] [Green Version] - Zhu, S.; Xu, G.; Cheng, Y. BDGAN: Image blind denoising using generative adversarial networks. Pattern Recognit. Comput. Vis.
**2019**, 12, 241–252. [Google Scholar] [CrossRef] - Tan, Z.; Li, K.; Wang, Y. Differential evolution with adaptive mutation strategy based on fitness landscape analysis. Inf. Sci.
**2021**, 549, 142–163. [Google Scholar] [CrossRef] - Tan, Z.; Li, K. Differential evolution with mixed mutation strategy based on deep reinforcement learning. Appl. Soft Comput.
**2021**, 11, 107678. [Google Scholar] [CrossRef] - Standard Kodak PCD0992 Test Images. Available online: http://r0k.us/graphics/kodak/ (accessed on 1 March 2018).
- Xu, J.; Zhang, L.; Zhang, D. Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising. IEEE Comput. Soc.
**2017**, 11, 1105–1113. [Google Scholar] [CrossRef] [Green Version] - Mafi, M. Deep convolutional neural network for mixed random impulse and Gaussian noise reduction in digital images. IET Image Process.
**2020**, 14, 3791–3801. [Google Scholar] [CrossRef]

**Figure 1.**Principle of local binary cyclic jumping of central pixel ${I}_{k}(m,n)$. (

**a**) N × N-sized image block ${I}_{k}$; (

**b**) central point ${I}_{k}(m,n)$ and adjacent pixels in eight-neighbor connected domain; (

**c**) pixel values of ${I}_{k}(m,n)$ and adjacent pixels in eight-neighbor connected domain; (

**d**) absolute difference between central pixel and those in eight-neighbor connected domain; (

**e**) binary values of corresponding pixels in eight-neighbor connected domain; (

**f**) calculating the number of cyclic jumps of central pixel.

**Figure 3.**MSE comparison results of different parameter estimation methods. (

**a**) Comparison results of MSE (a); (

**b**) comparison results of MSE (b).

**Figure 4.**Weakly textured blocks selected by different methods. (

**a**) Original image; (

**b**) selection results based on LBCJ; (

**c**) selection results based on grey entropy; (

**d**) selection results based on gradient matrix; and (

**e**) selection results based on histogram.

Noise Parameters | Time (s) | ||||
---|---|---|---|---|---|

a | b | Image Gradient Matrix | Local Grey Entropy | Image Histogram | LBCJ |

0.005 | 0.0016 | 12.72 | 19.56 | 19.22 | 11.66 |

0.005 | 0.0036 | 12.86 | 19.59 | 18.56 | 11.45 |

0.005 | 0.0064 | 12.71 | 19.55 | 18.67 | 11.51 |

0.005 | 0.0100 | 12.69 | 19.55 | 18.56 | 11.25 |

0.010 | 0.0016 | 15.87 | 19.45 | 18.89 | 11.40 |

0.010 | 0.0036 | 15.53 | 19.56 | 18.52 | 11.39 |

0.010 | 0.0064 | 16.48 | 19.66 | 18.52 | 12.17 |

0.010 | 0.0100 | 16.14 | 19.59 | 18.55 | 12.46 |

0.015 | 0.0016 | 15.54 | 19.68 | 18.64 | 13.17 |

0.015 | 0.0036 | 15.97 | 19.52 | 19.03 | 13.51 |

0.015 | 0.0064 | 15.61 | 19.56 | 18.88 | 11.87 |

0.015 | 0.0100 | 15.33 | 19.57 | 19.04 | 12.01 |

0.020 | 0.0016 | 22.52 | 30.56 | 20.52 | 12.36 |

0.020 | 0.0036 | 22.18 | 30.59 | 20.52 | 12.06 |

0.020 | 0.0064 | 22.45 | 30.52 | 20.62 | 12.68 |

0.020 | 0.0100 | 21.60 | 30.61 | 20.83 | 12.33 |

Noise Parameters | Memory Consumption (MB) | ||||
---|---|---|---|---|---|

a | b | Image Gradient Matrix | Local Grey Entropy | Image Histogram | LBCJ |

0.005 | 0.0016 | 3738 | 3721 | 3507 | 3513 |

0.005 | 0.0036 | 3741 | 3719 | 3500 | 3518 |

0.005 | 0.0064 | 3799 | 3716 | 3515 | 3511 |

0.005 | 0.0100 | 3797 | 3715 | 3512 | 3500 |

0.010 | 0.0016 | 3775 | 3730 | 3500 | 3499 |

0.010 | 0.0036 | 3770 | 3722 | 3488 | 3512 |

0.010 | 0.0064 | 3749 | 3729 | 3487 | 3510 |

0.010 | 0.0100 | 3744 | 3743 | 3525 | 3517 |

0.015 | 0.0016 | 3775 | 3728 | 3446 | 3340 |

0.015 | 0.0036 | 3769 | 3727 | 3453 | 3354 |

0.015 | 0.0064 | 3762 | 3721 | 3452 | 3428 |

0.015 | 0.0100 | 3753 | 3720 | 3463 | 3462 |

0.020 | 0.0016 | 3733 | 3731 | 3472 | 3469 |

0.020 | 0.0036 | 3733 | 3733 | 3470 | 3463 |

0.020 | 0.0064 | 3731 | 3731 | 3469 | 3464 |

0.020 | 0.0100 | 3742 | 3732 | 3452 | 3500 |

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**MDPI and ACS Style**

Li, J.; Wu, Y.; Zhang, Y.; Zhao, J.; Si, Y.
Parameter Estimation of Poisson–Gaussian Signal-Dependent Noise from Single Image of CMOS/CCD Image Sensor Using Local Binary Cyclic Jumping. *Sensors* **2021**, *21*, 8330.
https://doi.org/10.3390/s21248330

**AMA Style**

Li J, Wu Y, Zhang Y, Zhao J, Si Y.
Parameter Estimation of Poisson–Gaussian Signal-Dependent Noise from Single Image of CMOS/CCD Image Sensor Using Local Binary Cyclic Jumping. *Sensors*. 2021; 21(24):8330.
https://doi.org/10.3390/s21248330

**Chicago/Turabian Style**

Li, Jinyu, Yuqian Wu, Yu Zhang, Jufeng Zhao, and Yingsong Si.
2021. "Parameter Estimation of Poisson–Gaussian Signal-Dependent Noise from Single Image of CMOS/CCD Image Sensor Using Local Binary Cyclic Jumping" *Sensors* 21, no. 24: 8330.
https://doi.org/10.3390/s21248330