Detecting double JPEG compression with the same quantization matrix

Detection of double joint photographic experts group (JPEG) compression is of great significance in the field of digital forensics. Some successful approaches have been presented for detecting double JPEG compression when the primary compression and the secondary compression have different quantization matrixes. However, when the primary compression and the secondary compression have the same quantization matrix, no detection method has been reported yet. In this paper, we present a method which can detect double JPEG compression with the same quantization matrix. Our algorithm is based on the observation that in the process of recompressing a JPEG image with the same quantization matrix over and over again, the number of different JPEG coefficients, i.e., the quantized discrete cosine transform coefficients between the sequential two versions will monotonically decrease in general. For example, the number of different JPEG coefficients between the singly and doubly compressed images is generally larger than the number of different JPEG coefficients between the corresponding doubly and triply compressed images. Via a novel random perturbation strategy implemented on the JPEG coefficients of the recompressed test image, we can find a "proper" randomly perturbed ratio. For different images, this universal "proper" ratio will generate a dynamically changed threshold, which can be utilized to discriminate the singly compressed image and doubly compressed image. Furthermore, our method has the potential to detect triple JPEG compression, four times JPEG compression, etc.