Quaternion Discrete Fourier Transform-Based Color Image Watermarking Method Using Quaternion QR Decomposition

Abstract

In this paper, a new Quaternion Discrete Fourier Transform (QDFT)-based digital color image watermarking method is presented. In addition, the Quaternion QR (QQR) decomposition is applied in digital watermarking technology for the first time. First of all, the QDFT and QQR decomposition are performed on the host image, respectively, to acquire the scalar part of the quaternion matrix for watermark information embedding. After that, we divide the scalar part of the quaternion matrix generated by the QQR decomposition into blocks and calculate the entropy. The block with high entropy is selected to embed the watermark information. Then the watermark information is embedded into the extracted block using the quantization index modulation method. We conducted a large number of tests and experimental results indicate that the presented approach obtains excellent robustness against Scaling, Rotation, Median filtering, `Salt & Pepper' noise, and JPEG Compression. Compared with the existing methods, the presented method achieves better performance.

Keywords

• Watermarking technology
• quaternion discrete Fourier transform (QDFT)
• quaternion QR (QQR) decomposition
• quantization index modulation
• scalar part