This paper proposes a novel Gauss–Jordan elimination-based image tampering detection and self-recovery scheme, aiming at dealing with the problem of malicious tampering on digital images. To deal with the copy–move tampering which is challenging because the tampered region may contain the watermark information, we propose the Improved Check Bits Generation algorithm during watermark generation, to generate the check bits for tampering detection. Meanwhile, the recovery bits are reconstructed according to the fundamental of Gauss–Jordan Elimination, for purpose of image contents self-recovery. To improve the accuracy of detection and the quality of recovered images, we propose the Morphological Processing-Based Enhancement method and the Edge Extension preprocessing respectively during and after the tampering detection Finally, the Gauss–JordanElimination-Based Self-Recovery method is proposed to recover the damaged content mathematically on basis of the detected results. By employing the unchanged recovery bits which are embedded in the non-tampered region, the failure in recovery caused by the damaged recovery bits can be completely avoided. A large number of experiments have been conducted to show the very good performance of the proposed scheme. The precision, recall, and F1 score are calculated for evaluation of tampering detection, while the PSNR values are calculated for evaluation of image recovery. The comparisons with the state-of-the-art methods show that the proposed scheme shows the superiorities in terms of imperceptibility, security and recovery capability. The experimental result indicates the average PSNR of recovered image is 44.415dB.

本文针对基于数字图像的恶意篡改问题，提出了一种基于高斯-乔丹消去法的图像篡改检测和自恢复方案。为了应对由于复制区域可能包含水印信息而造成的复制移动篡改的挑战，我们提出了在水印生成过程中使用改进的校验位生成算法，以生成用于篡改检测的校验位。同时，根据高斯-乔丹消除法的基本原理重建恢复位，以实现图像内容的自我恢复。为了提高检测的准确性和恢复图像的质量，我们分别提出了基于形态学处理的增强方法和篡改检测前后的边缘扩展预处理。提出了基于高斯-乔丹消除法的自我修复方法，可以根据检测到的结果以数学方式修复损坏的内容。通过使用嵌入在非篡改区域中的未改变的恢复位，可以完全避免由损坏的恢复位引起的恢复失败。已经进行了大量的实验以显示所提出的方案的非常好的性能。的计算精度，查全率和F1分数以评估篡改检测，同时计算PSNR值以评估图像恢复。与最新方法的比较表明，所提出的方案在不可感知性，安全性和恢复能力方面显示出优势。实验结果表明，恢复图像的平均PSNR为44.415dB。