singular value decomposition

In the present era, along with the spread of technology in different fields and the possibility of remotely accomplishing different tasks and using internal networks and the Internet, related problems and challenges have occurred. One of these problems is maintaining the security of information while sending and receiving, to prevent unauthorized access. Watermarking is the science of hiding and covering the information with the highest degree of accuracy in security, in order to securely transfer information between the points of interest, so that even when an unauthorized access happens, there is no access to the watermarked data. There are two important features in watermarking. First, the information embedding should not make significant changes in the host environment, and second, the statistical properties of the cover image and the message should be as close as possible in order to have better cryptography. The main purpose of this paper is to provide a new method based on discrete wavelet transform to achieve a suitable cryptographic method. In this method, based on wavelet transforms, color images are watermarked so that they are not normally visible and their key is needed to view them. Simulation results indicate the efficiency of the proposed method.

Median filtering, as a nonlinear content preserving process that is often employed for smoothing and denoising images, has received significant attention from the forensics and documentation research community. In this paper, a detection scheme for median filtering of compressed images is proposed, based on singular value decomposition of the process matrix. In the proposed method, the process matrix is obtained by linear estimation of the decoding process, implementation of median filtering and recompression of the image. The projections of input data over eigenspaces of this process matrix is then used as features of the image. A small number of such features are utilized to classify the image as either original or processed, thus leading to a fast and effective detection scheme for median filtering. The experimental evaluations show that the proposed scheme outperforms the existing methods, particularly over highly compressed images, and its detection error is 2% to 5% lower in comparison to the errors introduced by other detection schemes. The singular value decomposition of the process matrix introduced in this paper, may also be used in detection of other cases of image content manipulation.