# Parameter Estimation of Signal-Dependent Random Noise in CMOS/CCD Image Sensor Based on Numerical Characteristic of Mixed Poisson Noise Samples

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## Abstract

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## 1. Introduction

## 2. Proposed Method

_{Si}, i = 1~16.

_{Si}[7] as shown in (4).

_{Si}in every block, Median(●) is the MAD value and $W\left\{HH\right\}$ is the HH sub-band wavelet coefficient of the stitched image in every block shown in Figure 4. It can be determined from (1) that ${b}_{i}={\widehat{\sigma}}_{g-{S}_{i}}^{2}$, i = 1~16.

_{i}, i = 1~16.

_{i}is denoted as ${n}_{P-G-{S}_{i}}$ (i = 1~16); the mixed Poisson noise corresponding to the noiseless stitched region S

_{i}is denoted as ${\eta}_{p-{S}_{i}}$ (i = 1~16); and the Gaussian noise corresponding to the noiseless stitched region S

_{i}is denoted as ${\eta}_{g-{S}_{i}}$ (i = 1~16). The forming process of the mixed Poisson noise ${\eta}_{p-{S}_{i}}$ (i = 1~16) corresponding to the noiseless stitched image S

_{i}is shown in Figure 5.

_{i}(x) (i = 1~16, x = 0~255)) of every noiseless stitched image (denoted as S

_{i}(i = 1~16)). Because the parasitic Poisson noise is signal-dependent and ${\eta}_{p}\left(x\right)~P\left(ax\right)$, as shown in (1), the Poisson noise samples ${\eta}_{pi}\left(x\right)$ (i = 1~16, x = 0~255) and the corresponding sample size n

_{i}(x) (i = 1~16, x = 0~255) can be obtained according to histogram analysis. All the noise samples ${\eta}_{pi}\left(x\right)$ constitute the mixed Poisson noise sample ${\eta}_{p-{S}_{i}}=\left\{{\eta}_{pi}\left(0\right),{\eta}_{pi}\left(1\right),{\eta}_{pi}\left(2\right)\dots \dots {\eta}_{pi}\left(255\right)\right\}$ (i = 1~16) corresponding to S

_{i}(i = 1~16) and the sample size of ${\eta}_{p-{S}_{i}}$ can be represented as N

_{i}(i = 1~16). As a result, ${N}_{i}={\displaystyle \sum _{x=0}^{255}{n}_{i}\left(x\right)}$ (i = 1~16) and the unbiased estimations of the mean of ${\eta}_{p-{S}_{i}}$ (i = 1~16) can be obtained as (6).

_{Si}and the noiseless stitched image S

_{i}, i = 1~16. The unbiased estimation of variance of ${n}_{P-G-{S}_{i}}$ (i = 1~16) can be calculated by (9).

_{i}in every block can be acquired from (12).

_{i}(i = 1~16) are positive.

## 3. Simulation Results and Comparison

#### 3.1. Simulation and Comparison Results with Kodak Test Image

#### 3.2. Simulation and Comparison Results with Actual Image of CMOS Image Sensor

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**The average values of estimated noise parameters in R, G, B channels of the ten Kodak testing images, by using different estimation methods.

**Figure 8.**The average values of estimated noise parameters of the ten Kodak testing images, by using different estimation methods.

**Figure 10.**The average MAE values of estimated noise parameters of the six actual testing images from CMOS image sensor, by using different estimation methods.

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/s18072276

**AMA Style**

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(7):2276.
https://doi.org/10.3390/s18072276

**Chicago/Turabian Style**

Zhang, Yu, Guangyi Wang, and Jiangtao Xu.
2018. "Parameter Estimation of Signal-Dependent Random Noise in CMOS/CCD Image Sensor Based on Numerical Characteristic of Mixed Poisson Noise Samples" *Sensors* 18, no. 7: 2276.
https://doi.org/10.3390/s18072276