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Recovering Missing Coefficients in DCT-Transformed Images

Shujun Li1, Andreas Karrenbauer1, Dietmar Saupe1 and C.-C. Jay Kuo2

1 University of Konstanz, Germany
2 University of Southern California, USA

In Proceedings of 2011 18th IEEE International Conference on Image Processing (ICIP 2011, Brussels, Belgium, September 11-14, 2011), pp. 1569-1572, 2011.

Copyright 2011 IEEE. Published in the 2011 IEEE International Conference on Image Processing (ICIP 2011), September 11-14, 2011, Brussels, Belgium. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works, must be obtained from the IEEE. Contact: Manager, Copyrights and Permissions / IEEE Service Center / 445 Hoes Lane / P.O. Box 1331 / Piscataway, NJ 08855-1331, USA. Telephone: + Intl. 908-562-3966.

Abstract

A general method for recovering missing DCT coefficients in DCT-transformed images is presented in this work. We model the DCT coefficients recovery problem as an optimization problem and recover all missing DCT coefficients via linear programming. The visual quality of the recovered image gradually decreases as the number of missing DCT coefficients increases. For some images, the quality is surprisingly good even when more than 10 most significant DCT coefficients are missing. When only the DC coefficient is missing, the proposed algorithm outperforms existing methods according to experimental results conducted on 200 test images. The proposed recovery method can be used for cryptanalysis of DCT based selective encryption schemes and other applications.

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Previous Methods

Previous methods can only recover DC coefficients from AC ones. There are only two known methods, which are both based on local propagation and the following two properties. In the following, we will only show how different the results of the two methods are. To get more ideas about the two methods, please click here.

USO

HK_shop (Original) emotion icon HK_shop (DC-free) emotion icon HK_shop (USO)

FRM

HK_shop (Original) emotion icon HK_shop (DC-free) emotion icon HK_shop (FRM)

Our Optimization Model

FRM is still not good enough!

cameraman (Original) emotion icon cameraman (DC-free) emotion icon cameraman (FRM)

We need global optimization!

The recovery problem of any missing DCT coefficients from known ones can be modeled as a linear program, thus allowing global optimization towards an objective.

Experimental Results

AC2DC

cameraman (Original) emotion icon cameraman (DC-free) emotion icon cameraman (LP)

We also compared the linear program based approach with FRM, and found out that the former achieves an overall better performance as expected. In the following figure, we show the difference between the visual quality of the images recoverd via linear program and that via FRM. A positive value suggests that the linear program based approach is better. The red lines show the average difference over all the 200 test images.

LP vs. FRM (1) LP vs. FRM (2)

DCT2DCT

cameraman (2 DCT coefficients are missing) cameraman (4 DCT coefficients are missing) cameraman (6 DCT coefficients are missing) cameraman (8 DCT coefficients are missing) cameraman (10 DCT coefficients are missing) cameraman (12 DCT coefficients are missing) cameraman (15 DCT coefficients are missing)

cameraman (2 DCT coefficients are missing) cameraman (4 DCT coefficients are missing) cameraman (6 DCT coefficients are missing) cameraman (8 DCT coefficients are missing) cameraman (10 DCT coefficients are missing) cameraman (12 DCT coefficients are missing) cameraman (15 DCT coefficients are missing)

Key References

[1]  Takeyuki Uehara, Reihaneh Safavi-Naini, and Philip Ogunbona, "Recovering DC coefficients in block-based DCT," IEEE Transactions on Image Processing, vol. 15, no. 11, pp. 3592-3596, IEEE, 2006

[2]  Shujun Li, Junaid Jameel Ahmad, Dietmar Saupe and C.-C. Jay Kuo, "An Improved DC Recovery Method from AC Coefficients of DCT-Transformed Images," In Proceedings of 17th IEEE International Conference on Image Processing (ICIP 2010, Hong Kong, China, September 26-29, 2010), pp. 2085-2088, IEEE, 2010 Companion Web Page

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