To deal with the problem of image forgery detection, many forensic tools have been proposed. Most existing tools perform efficiently in a supervised scenario with a large training set while their statistical performances cannot be analytically established. Also, limited research proposes statistical model-based detectors for image forensics, especially for image splicing forgery detection. Therefore, in this paper, we propose a training-free forensic detector with analytically statistical performance for splicing forgery detection. The detector is designed based on a simplified noise model of JPEG image which assumes the variance of pixels as a quadratic function of the expectation of pixels. The proposed simplified noise model is characterized by two parameters which can serve as camera fingerprints for image forgery detection. By employing the framework of hypothesis testing theory, a training-free Generalized Likelihood Ratio Test (GLRT) is designed, which ensures the high detection performance for a prescribed false alarm rate. Besides, detection threshold can be configured in the fashion independent of image content. Numerical results validate the accuracy of the simplified noise model and the effectiveness of the proposed detector.

为了处理图像伪造检测的问题，已经提出了许多取证工具。大多数现有工具在具有大型训练集的受监督场景中高效执行，而无法通过分析确定其统计性能。此外，有限的研究提出了基于统计模型的图像取证检测器，特别是用于图像拼接伪造检测。因此，在本文中，我们提出了一种具有分析统计性能的免训练法医检测器，用于拼接伪造检测。该检测器是基于JPEG图像的简化噪声模型设计的，该模型假设像素的方差是像素期望的二次函数。所提出的简化噪声模型具有两个参数，可以作为图像伪造检测的相机指纹。采用假设检验理论框架，设计了一种免训练的广义似然比检验（GLRT），保证了在规定的误报率下的高检测性能。此外，检测阈值可以独立于图像内容的方式进行配置。数值结果验证了简化噪声模型的准确性和所提出检测器的有效性。