Robust optimum detection of transform domain multiplicative watermarks

Qiang Cheng, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review

172 Scopus citations


Digital watermarking is an emerging technique to protect data security and intellectual property right. Identification or verification of watermarking patterns can be achieved by detecting watermarks in received signals. However, one of the biggest challenges in watermarking detection is that the strengths of the watermark signals will change after being distorted by an attacker in a watermarking channel. Meanwhile, the embedding strengths may be adapted to original signals, which are unknown at the receiver end. Further, the original signals are often highly non-Gaussian. Although some work has been done on optimum detection of watermarks, the uncertainty of watermark signal strengths and real statistical behavior of multimedia contents have not been taken into account simultaneously. Much more study is needed to enhance the performance of watermarking systems. Since multiplicative watermarks are robust and well suited for copyright protection, this paper presents our investigation on robust optimum detection of multiplicative watermarks. For sub-band transformed domains such as the discrete cosine transform (DCT), discrete wavelet transform (DWT), and pyramid transform, a class of generalized correlators is constructed based on the generalized Gaussian distributions. Thresholding methods to achieve a given false alarm rate, and the performance analyses are provided. The square-root detector is designed and demonstrated to have near optimal performance for a large set of natural images and can be employed as a "universally optimal" detector or decoder for images and video. The locally most powerful detection method is then extended to DFT domain multiplicative watermarking, with the magnitudes of coefficients modeled by the Weibull distributions. Another class of detectors is built based on this statistical modeling. The robust optimum detection of multiplicative watermarks can be applied to copyright notification, enforcement, and broadcast monitoring. We have applied the robust optimum watermarking detection to combined audio and video watermarking.

Original languageEnglish
Pages (from-to)906-924
Number of pages19
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - Apr 2003

Bibliographical note

Funding Information:
Manuscript received February 4, 2002; revised December 3, 2002. This work was supported in part by the National Science Foundation under Grants CDA 96-24386 and 96-24396. The associate editor coordinating the review of this paper and approving it for publication was Dr. Bede Liu.


  • Digital watermarking
  • Generalized Gaussian distribution
  • Generalized correlation detector
  • Robust optimum detection
  • Square-root detector
  • Weibull distribution

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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