A fragile zero-watermarking method based on dual quaternion matrix decomposition

TL;DR

The paper addresses copyright protection and content tampering detection for medical images without modifying the original data. It proposes a fragile zero-watermarking framework based on dual quaternion matrix decomposition, formulating the carrier-watermark pair as a dual quaternion matrix $A=A_s+A_i \epsilon$ and deriving watermark information from dual parts using dual quaternion LU, QR, and SVD decompositions (e.g., $A=(L_s+L_i\epsilon)(U_s+U_i\epsilon)$ or $A=(U_s+U_i\epsilon)(\Sigma_t+\Sigma_i\epsilon)(V_s^H+V_i^H\epsilon)$). The method preprocesses the watermark with Arnold transformation and extracts carrier features via a 2D FFT, then binds them through the dual-quaternion color image model $F=F_1^{(1)} i + F_1^{(2)} j + F_1^{(3)} k + (F_2^{(1)} i + F_2^{(2)} j + F_2^{(3)} k) \epsilon$ to generate zero-watermarking information. Verification reconstructs the watermark from a verified carrier and the stored dual-part data, quantified by PSNR, SSIM, BER, and NC, with experiments on medical images showing intact watermark recovery under no attack and effective tampering detection under various attacks. The work offers a non-invasive, cryptographically secure mechanism for medical image copyright and integrity checks, facilitating safer sharing of sensitive clinical data.

Abstract

Medical images play a crucial role in assisting diagnosis, remote consultation, and academic research. However, during the transmission and sharing process, they face serious risks of copyright ownership and content tampering. Therefore, protecting medical images is of great importance. As an effective means of image copyright protection, zero-watermarking technology focuses on constructing watermarks without modifying the original carrier by extracting its stable features, which provides an ideal approach for protecting medical images. This paper aims to propose a fragile zero-watermarking model based on dual quaternion matrix decomposition, which utilizes the operational relationship between the standard part and the dual part of dual quaternions to correlate the original carrier image with the watermark image, and generates zero-watermarking information based on the characteristics of dual quaternion matrix decomposition, ultimately achieving copyright protection and content tampering detection for medical images.

Figures (6)

• Figure 1: Zero-watermarking process.
• Figure 2: Arnold scrambling process.
• Figure 3: Zero-watermarking generation process.
• Figure 4: Watermark verification process.
• Figure 5: $512\times 512$ medical images.