## Simultaneous fusion, compression, and encryption of multiple images |

Optics Express, Vol. 19, Issue 24, pp. 24023-24029 (2011)

http://dx.doi.org/10.1364/OE.19.024023

Acrobat PDF (1819 KB)

### Abstract

We report a new spectral multiple image fusion analysis based on the discrete cosine transform (DCT) and a specific spectral filtering method. In order to decrease the size of the multiplexed file, we suggest a procedure of compression which is based on an adapted spectral quantization. Each frequency is encoded with an optimized number of bits according its importance and its position in the DC domain. This fusion and compression scheme constitutes a first level of encryption. A supplementary level of encryption is realized by making use of biometric information. We consider several implementations of this analysis by experimenting with sequences of gray scale images. To quantify the performance of our method we calculate the MSE (mean squared error) and the PSNR *(*peak signal to noise ratio). Our results consistently improve performances compared to the well-known JPEG image compression standard and provide a viable solution for simultaneous compression and encryption of multiple images.

© 2011 OSA

## 1. Introduction

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. **1**(3), 589–636 (2009). [CrossRef]

7. B. Javidi, C. M. Do, S.-H. Hong, and T. Nomura, “Multi-spectral holographic three-dimensional image fusion using discrete wavelet transform,” J. Disp. Technol. **2**(4), 411–417 (2006). [CrossRef]

2. M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process. **52**(10), 2992–3006 (2004). [CrossRef]

4. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. **35**(11), 1914–1916 (2010). [CrossRef] [PubMed]

*et al*. [5

5. T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. **42**(23), 4758–4764 (2003). [CrossRef] [PubMed]

6. P. Refrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. **20**(7), 767–769 (1995). [CrossRef] [PubMed]

## 2. Spectrally multiplexing multiple images

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. **1**(3), 589–636 (2009). [CrossRef]

8. See, e.g. K. R. Rao and P. Yip, *Discrete Cosine Transform: Algorithms, Advantages, Applications,* (Academic Press, 1990), and http://www.jpeg.org/.

*x*and

*y*can now be expressed as a properly scaled function of the target image size (in pixels)

*n*denotes the number of target images. Next, well defined rotation and shift operations are applied to each filtered part for grouping 4 DCTs as shown in Fig. 1. Such a grouping of the DCTs results in a first level of encryption. Special attention is called to the fact that the result of this grouping is similar to a Fourier transform. In addition, the reconstructed images overlap each other after these transformations.

5. T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. **42**(23), 4758–4764 (2003). [CrossRef] [PubMed]

## 3. Compressing images

*m*is the number of bits used for encoding these real-valued frequencies, and

*round*(…) is the integer part function. An example of a filtered and quantized DCT is shown in Fig. 2(e) illustrating the changes in the frequencies values for a given

*n*target 8-bit encoded gray-level images of size

*T*

_{c}can be done by choosing a number of bits relevant to each area (Fig. 2(e)) as

*T*

_{c}and reconstruction results. The integer in the first row considers the number of target images at the input of the system. The second row shows the reconstructed images at the output of the system by encoding the filtered and multiplexed DCTs with

*m*= 15 bits (Fig. 2(e)). The third, fourth, and fifth rows show the results for

*m*= 8, 5, and 3 bits, respectively. For each n and

*m*values we show the reconstructed image at the output of the system.

*m*the lesser is the quality of the reconstructed image and the larger is the compression rate. As also seen in Table 1, good results can be achieved when

*m*= 5, while maintaining a significant compression rate.

## 4. Comparing with the JPEG image compression encoder

8. See, e.g. K. R. Rao and P. Yip, *Discrete Cosine Transform: Algorithms, Advantages, Applications,* (Academic Press, 1990), and http://www.jpeg.org/.

*T*

_{c}and found that our scheme renders higher PSNR than its JPEG compressed counterpart.

## 5. Encrypting images

### 5.1. Optimized encryption level

### 5.2. Resistance of the encryption scheme against attack

10. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express **15**(16), 10253–10265 (2007). [CrossRef] [PubMed]

## 6. Concluding section

## Acknowledgment

## References and links

1. | A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. |

2. | M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process. |

3. | A. Alfalou, A. Loussert, A. Alkholidi, and R. El Sawda, “System for image compression and encryption by spectrum fusion in order to optimise image transmission,” FGCN 2007, IEEE Proceeding, ISBN: 0–7695–3048–6, Vol. 2, 2007, pp. 593–596. |

4. | A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. |

5. | T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. |

6. | P. Refrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. |

7. | B. Javidi, C. M. Do, S.-H. Hong, and T. Nomura, “Multi-spectral holographic three-dimensional image fusion using discrete wavelet transform,” J. Disp. Technol. |

8. | See, e.g. K. R. Rao and P. Yip, |

9. | B. Javidi, ed., |

10. | Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(100.0100) Image processing : Image processing

(200.4560) Optics in computing : Optical data processing

**ToC Category:**

Image Processing

**History**

Original Manuscript: August 25, 2011

Manuscript Accepted: October 19, 2011

Published: November 10, 2011

**Citation**

A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, "Simultaneous fusion, compression, and encryption of multiple images," Opt. Express **19**, 24023-24029 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24023

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### References

- A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon.1(3), 589–636 (2009). [CrossRef]
- M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004). [CrossRef]
- A. Alfalou, A. Loussert, A. Alkholidi, and R. El Sawda, “System for image compression and encryption by spectrum fusion in order to optimise image transmission,” FGCN 2007, IEEE Proceeding, ISBN: 0–7695–3048–6, Vol. 2, 2007, pp. 593–596.
- A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett.35(11), 1914–1916 (2010). [CrossRef] [PubMed]
- T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt.42(23), 4758–4764 (2003). [CrossRef] [PubMed]
- P. Refrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett.20(7), 767–769 (1995). [CrossRef] [PubMed]
- B. Javidi, C. M. Do, S.-H. Hong, and T. Nomura, “Multi-spectral holographic three-dimensional image fusion using discrete wavelet transform,” J. Disp. Technol.2(4), 411–417 (2006). [CrossRef]
- See, e.g. K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications, (Academic Press, 1990), and http://www.jpeg.org/ .
- B. Javidi, ed., Optical and Digital Techniques for Information Security, (Springer Verlag, New York, 2005).
- Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express15(16), 10253–10265 (2007). [CrossRef] [PubMed]

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