Using Matrix Decomposition and Frequency Transforms to Detect Forgeries in Digital Images

Digital images are very popular, but they are quite easy to manipulate. This may have bad consequences, especially when the editing changes important content in the images. Therefore, detecting traces of modifications in digital images is an urgent need. There are various techniques have been proposed, mainly based on finding specific features on the spatial domain or on the frequency domain of the images. In this paper, we study some matrix decomposition methods, which apply for detection of image manipulations. Next, we employ QR matrix factorization for design a new image forgery detection scheme. We also compare the proposed scheme with some other widely-used schemes based on frequency transforms and matrix decomposition methods. The experimental results on hundreds of images in different types show that the matrix decomposition based schemes accurately detect the copy-paste forgeries with rather low false positive rates. The schemes are robust against some common attacks. Moreover, the QR based scheme is much faster than the others. This characteristic is very useful when working with a large scale image dataset in practice.