# Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation

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## Abstract

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## 1. Introduction

## 2. The Gyrator Transform (GT) Operator

## 3. Generalized Shift Operator

## 4. Convolution Operator in the GD

## 5. Correlation Operator in the GD

## 6. Sampling Theorem in the GD

## 7. Optical Image Encryption System Using a Nonlinear Joint Transform Correlator (JTC) in the GD

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the optical system. The encryption system is a nonlinear joint transform correlator (JTC) architecture that uses a gyrator transform (GT) and the decryption system performs two successive GTs [19].

**Figure 2.**(

**a**) Original image to encrypt $z(x,y)$. (

**b**) Random distribution code $m(x,y)$ of the random phase mask (RPM) $k(x,y)$. (

**c**) Encrypted image ${e}_{\alpha}(u,v)$ for the security keys $\alpha =0.727\pi $ and the RPM $h(x,y)$. (

**d**) Right decrypted image $\tilde{z}(x,y)$.

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**MDPI and ACS Style**

Perez, R.A.; Vilardy O., J.M.; Torres M., C.O. Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation. *Photonics* **2019**, *6*, 120.
https://doi.org/10.3390/photonics6040120

**AMA Style**

Perez RA, Vilardy O. JM, Torres M. CO. Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation. *Photonics*. 2019; 6(4):120.
https://doi.org/10.3390/photonics6040120

**Chicago/Turabian Style**

Perez, Ronal A., Juan M. Vilardy O., and Cesar O. Torres M. 2019. "Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation" *Photonics* 6, no. 4: 120.
https://doi.org/10.3390/photonics6040120