# Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Introduction to CS Theory

_{0}.

## 3. Design of Pseudo-Random Circulant Measurement Matrix Based on Chaotic Sequence

#### 3.1. Design of Measurement Matrix Based on Chaotic Sequence

#### 3.2. Design of Pseudo-Random Circulant Measurement Matrix Based on Chaotic Sequence

## 4. Experimental Results and Analysis

#### 4.1. Design of Single-Pixel Color Imaging System

#### 4.2. Performance Comparison of Measurement Matrices

_{10}((2

^{k}− 1)

^{2}/MSE),

_{x}μ

_{y}+ c

_{1})/(μ

_{x}

^{2}+ μ

_{y}

^{2}+ c

_{1}),

_{x}σ

_{y}+ c

_{2})/(σ

_{x}

^{2}+ σ

_{y}

^{2}+ c

_{2}),

_{xy}+ c

_{3})/(σ

_{x}σ

_{y}+ c

_{3}),

_{x}and μ

_{y}represent the mean value of images x and y respectively, σ

_{x}and σ

_{y}represent the variance of images x and y respectively, σ

_{xy}is the covariance of images x and y, and c

_{1}, c

_{2}, and c

_{3}are constants as shown in Formula (15). To avoid the case where the denominator is 0, K

_{1}= 0.01, K

_{2}= 0.03, and L = 255 are generally used. The SSIM value range is [0, 1], and the larger the value is, the smaller the image distortion becomes.

_{1}= (K

_{1}× L)

^{2}, c

_{2}= (K

_{2}× L)

^{2}, c

_{3}= c

_{2}/2,

#### 4.3. Color Camera Imaging Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of reconstruction of the target image with the TVAL3 recovery algorithm under different measurement matrices: (

**a**) analysis of reconstruction results by using peak signal-to-noise ratio (PSNR), (

**b**) analysis on reconstruction results by using structural similarity (SSIM), and (

**c**) target image.

**Figure 4.**Comparison of the reconstruction of the target image with the TVAL3 recovery algorithm under different measurement matrices: (

**a**) analysis of reconstruction results by using PSNR, (

**b**) analysis of reconstruction results by using SSIM, and (

**c**) target image.

**Figure 5.**Results obtained by the single-pixel camera: (

**a**) target image; (

**b**) recovered images using logistic chaotic sequence (LCS-MM), PSNR = 10.60 dB, SSIM = 0.10; (

**c**) recovered images using LCS-CMM, PSNR = 9.07 dB, SSIM = 0.06; (

**d**) recovered images using LCS-PRC-MM, PSNR = 12.98 dB, SSIM = 0.11.

**Figure 6.**Results obtained by the single-pixel camera: (

**a**) target image; (

**b**) recovered images using LCS-MM, PSNR = 13.13 dB, SSIM = 0.11; (

**c**) recovered images using LCS-CMM, PSNR = 11.59 dB, SSIM = 0.08; (

**d**) recovered images using LCS-PRC-MM, PSNR = 14.72 dB, SSIM = 0.13.

**Figure 7.**Results obtained by the single-pixel color camera, and the target image is color letter N: (

**a**) recovered images using LCS-MM, PSNR = 19.80 dB, SSIM = 0.19; (

**b**) recovered images using LCS-CMM, PSNR = 18.18 dB, SSIM = 0.08; (

**c**) recovered images using LCS-PRC-MM, PSNR = 20.17 dB, SSIM = 0.20.

**Figure 8.**Results obtained by single-pixel color camera, and the target image is colored Wi-Fi logo: (

**a**) recovered images using LCS-MM, PSNR = 23.40 dB, SSIM = 0.13; (

**b**) recovered images using LCS-CMM, PSNR = 20.52 dB, SSIM = 0.07; (

**c**) recovered images using LCS-PRC-MM, PSNR = 23.81 dB, SSIM = 0.14.

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**MDPI and ACS Style**

Jia, T.; Chen, D.; Wang, J.; Xu, D.
Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix. *Appl. Sci.* **2018**, *8*, 1293.
https://doi.org/10.3390/app8081293

**AMA Style**

Jia T, Chen D, Wang J, Xu D.
Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix. *Applied Sciences*. 2018; 8(8):1293.
https://doi.org/10.3390/app8081293

**Chicago/Turabian Style**

Jia, Tong, Dongyue Chen, Ji Wang, and Dong Xu.
2018. "Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix" *Applied Sciences* 8, no. 8: 1293.
https://doi.org/10.3390/app8081293