A Robust Zero-Watermark Algorithm Based on Singular Value Decomposition and Discreet Cosine Transform

A Modified DWT-SVD Algorithm for T1-w Brain MR Images Contrast Enhancement

The paper presents a new digital image hiding algorithm based on wavelet packets transform and singular value decomposition. The low-frequency sub-band of wavelet packets transform has strong anti-jamming capacity and the singular value has very strong stability. The presented algorithm implements bit plane decomposition on the secret image and wavelet packet decomposition on the carrier image. Then, it hides the bit planes with important information into the singular value matrix of the low frequency coefficient matrix, and also hides the bit planes with secondary information into the remainder sub-band matrix with higher entropy energy. The hiding location is adaptively determined by the carrier image. The experimental results indicate that, the proposed image hiding algorithm has strong robustness and anti-attack, and it also has good invisibility and big capability.

In this paper, a novel contrast enhancement technique for contrast enhancement of a low-contrast satellite image has been proposed based on the singular value decomposition (SVD) and discrete cosine transform (DCT). The singular value matrix represents the intensity information of the given image and any change on the singular values change the intensity of the input image. The proposed technique converts the image into the SVD-DCT domain and after normalizing the singular value matrix; the enhanced image is reconstructed by using inverse DCT. The visual and quantitative results suggest that the proposed SVD-DCT method clearly shows the increased efficiency and flexibility of the proposed method over the exiting methods such as the histogram equalization, gamma correction and SVD-DWT based techniques.

Robust zero-watermarking is an effective and distortion-free technique for copyright protection and has become a research hotspot in the field of digital watermarking. In the face of weak robustness and security of existing schemes, this paper presents a novel robust and secure color image zero-watermarking algorithm based on majority voting pattern and hyper-chaotic encryption. In the proposed algorithm, firstly an original color image is decomposed by one-level discrete wavelet transform (DWT) and the corresponding low-frequency components of three channels are partitioned into blocks. Then, to resist strong attacks, we construct a distinguishable robust binary feature matrix extracted from all blocks and color components by using a combination of Frobenius norm in the singular value decomposition (SVD) domain and majority voting pattern. To promote security, a binary copyright logo is confused and diffused by hyper-chaotic Lorenz system. Finally, it performs a bitwise exclusive-or operation on the binary feature matrix and the encrypted copyrighted logo to obtain a zero-watermark signal. Experimental results indicate that in addition to the high-level security, the proposed zero-watermarking algorithm also has a stronger robustness against common geometric and non-geometric attacks, including rotation, scaling, filtering, JPEG compression and noise addition, compared with some existing typical zero-watermarking and traditional watermarking methods.

In this paper, a novel image watermarking scheme using an encrypted kinoform in the hybrid nonsubsampled contourlet transform (NSCT) and singular value decomposition (SVD) domain is presented. In the scheme, a watermark is firstly transformed into an encrypted kinoform with fractional Fourier transform and Gerchberg-Saxton algorithm. Then the host image is decomposed with NSCT and the low frequency sub-band is divided into nonoverlapping blocks. SVD is applied to every block. The kinoform is embedded into the low frequency NSCT coefficients by modifying the largest singular value of each block. To withstand geometric attacks, the geometric distortion parameters of the attacked watermarked image are computed first by the Zernike moment-based geometric correction method in the detection process. Then the mark kinoform is extracted from the recovered image. In comparison with other method, the proposed watermarking scheme offers better performances for imperceptibility. Experimental results demonstrate that the proposed image watermarking is not only invisible but also robust against a variety of attacks including scaling, rotation, flipping, noise addition, filtering, JPEG compression, etc.

Cellular automata based color image watermarking using non sub sampled contourlet transform (NSCT) and singular value decomposition (SVD) is presented in this paper. Game of life (GOL) cellular automata is used to scramble binary watermark so that no one can recover the watermark without secret scrambling keys. Because of the salient features like multiscale, multidirection and shift invariance of NSCT, 2-level NSCT is applied to red, green and blue component of RGB cover image. Most of the perceptual content of an image focuses on low frequency subband of NSCT and the singular values taken from low frequency subband have certain stability. So a modest change in the singular values taken from low frequency subband of NSCT is applicable. In this proposed scheme, each singular value of scrambled binary watermark is embedded in fixed location of singular value matrix of low frequency subbands of NSCT of red, green and blue components. The scheme offers security, imperceptibility and robustness against various image processing and geometric attacks like Gaussian white noise, salt and pepper noise, median filtering, JPEG compression, cropping and rotation. The proposed scheme is compared with existing watermarking schemes in terms of Peak Signal to Noise ratio (PSNR), Normalized Correlation (NC)and provides satisfactory performance than other schemes.

This paper concerns accurate computation of the singular value decomposition (SVD) of an $m\times n$ matrix $A$ . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of $A^{\rm T}A$ and take the square roots of the large eigenvalues of it as the large singular values of $A$ ; (b) form the Rayleigh quotient of $A^{\rm T}A$ with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of $A^{\rm T}A$ ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of $A$ . A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff $\epsilon$ . An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm.

Most Discrete Wavelet Transform(DWT)/Singular Value Decomposition(SVD) watermark methods are robust to common attacks, such as loss compression, noise and filtering attacks, but they cannot resist geometrical attacks. As Scale Invariant Feature Transform(SIFT) feature points are invariant to rotation, scaling and translation, a blind DWT-SVD watermark method against geometrical attacks based on SIFT is proposed. The square of the inscribed circle of the host image matrix is chosen as the watermark embedding area. Firstly, the watermark embedding area is decomposed with 1-level DWT and the low-frequency sub-band is divided into non-overlapping blocks; then the SVD is applied to every block. Secondly, the watermark is embedded by quantifying the maximum singular value of each block. Finally, SIFT feature points of the watermarked image are saved to detect and correct possible geometrical attacks. The experimental results show that the proposed method not only has the robustness to any angle of rotation attacks, wide range of scaling attacks and translation attacks, but also can achieve blind extraction.

This contribution applies tools from the information theory and soft computing (SC) paradigms to the embedding and extraction of watermarks in aerial remote sensing (RS) images to protect copyright. By the time 5G came along, Internet usage had already grown exponentially. Regarding copyright protection, the most important responsibility of the digital image watermarking (DIW) approach is to provide authentication and security for digital content. In this paper, our main goal is to provide authentication and security to aerial RS images transmitted over the Internet by the proposal of a hybrid approach using both the redundant discrete wavelet transform (RDWT) and the singular value decomposition (SVD) schemes for DIW. Specifically, SC is adopted in this work for the numerical optimization of critical parameters. Moreover, 1-level RDWT and SVD are applied on digital cover image and singular matrices of LH and HL sub-bands are selected for watermark embedding. Further selected singular matrices SLH and SHL are split into 3×3 non-overlapping blocks, and diagonal positions are used for watermark embedding. Three-level symmetric encryption with low computational cost is used to ensure higher watermark security. A hybrid grasshopper–BAT (G-BAT) SC-based optimization algorithm is also proposed in order to achieve high quality DIW outcomes, and a broad comparison against other methods in the state-of-the-art is provided. The experimental results have demonstrated that our proposal provides high levels of imperceptibility, robustness, embedding capacity and security when dealing with DIW of aerial RS images, even higher than the state-of-the-art methods.

In this paper, a new robust watermarking scheme is proposed using fractional Fourier transform (FrFT) and singular value decomposition. The core idea of the proposed scheme is to decompose an image using FrFT followed by the non-overlapping block segmentation. A new key matrix is then formed by taking maximum singular values of all non-overlapping blocks. For embedding this key matrix is used and is done by modifying singular values with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks.

In this paper, a blind image watermarking scheme based on discrete wavelet transform (DWT) and singular value decomposition (SVD) is proposed. In this scheme, DWT is applied on ROI (region of interest) of the medical image to get different frequency subbands of its wavelet decomposition. On the low frequency subband LL of the ROI, block-SVD is applied to get different singular matrices. A pair of elements with similar values is identified from the left singular value matrix of these selected blocks. The values of these pairs are modified using certain threshold to embed a bit of watermark content. Appropriate threshold is chosen to achieve the imperceptibility and robustness of medical image and watermark contents respectively. For authentication and identification of original medical image, one watermark image (logo) and other text watermark have been used. The watermark image provides authentication whereas the text data represents electronic patient record (EPR) for identification. At receiving end, blind recovery of both watermark contents is performed by a similar comparison scheme used during the embedding process. The proposed algorithm is applied on various groups of medical images like X-ray, CT scan and mammography. This scheme offers better visibility of watermarked image and recovery of watermark content due to DWT-SVD combination. Moreover, use of Hamming error correcting code (ECC) on EPR text bits reduces the BER and thus provides better recovery of EPR. The performance of proposed algorithm with EPR data coding by Hamming code is compared with the BCH error correcting code and it is found that later one perform better. A result analysis shows that imperceptibility of watermarked image is better as PSNR is above 43 dB and WPSNR is above 52 dB for all set of images. In addition, robustness of the scheme is better than existing scheme for similar set of medical images in terms of normalized correlation coefficient (NCC) and bit-error-rate (BER). An analysis is also carried out to verify the performance of the proposed scheme for different size of watermark contents (image and EPR data). It is observed from analysis that the proposed scheme is also appropriate for watermarking of color image. Using proposed scheme, watermark contents are extracted successfully under various noise attacks like JPEG compression, filtering, Gaussian noise, Salt and pepper noise, cropping, filtering and rotation. Performance comparison of proposed scheme with existing schemes shows proposed scheme has better robustness against different types of attacks. Moreover, the proposed scheme is also robust under set of benchmark attacks known as checkmark attacks.

In this article, a new contrast enhancement approach is presented for quality enhancement of low-contrast satellite images. The proposed technique is based on the Artificial Bee Colony (ABC) algorithm using Discrete Wavelet Transform and Singular Value Decomposition (DWT-SVD). The method employs the ABC technique to learn the parameters of the adaptive thresholding function required for optimum enhancement. In this approach, the input image is primarily decomposed into four sub-bands through DWT, and then each sub-band of DWT is optimized through the ABC algorithm. After that, a singular value matrix of the low–low thresholded sub-band image is estimated and, finally, the enhanced image is constructed by applying inverse DWT. The results obtained through this method reveal that the proposed methodology gives better performance in terms of peak signal-to-noise ratio (PSNR), mean square error (MSE), and mean and standard deviation as compared to General Histogram Equalization (GHE), Discrete Cosine Transform and Singular Value Decomposition (DCT-SVD), DWT-SVD, Particle Swarm Optimization (PSO), and modified versions of the PSO-based enhancement approach.

In this paper, we propose a semi-blind, imperceptible, and robust digital audio watermarking algorithm. The proposed algorithm is based on cascading two well-known transforms: the discrete wavelet transform and the singular value decomposition. The two transforms provide different, but complementary, levels of robustness against watermarking attacks. The uniqueness of the proposed algorithm is twofold: the distributed formation of the wavelet coefficient matrix and the selection of the off-diagonal positions of the singular value matrix for embedding watermark bits. Imperceptibility, robustness, and high data payload of the proposed algorithm are demonstrated using different musical clips.

Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.

The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible due to the decomposition of the basic matrix with the use of Singular Value Decomposition (SVD). There are three matrices used in the process of decomposition: right singular vectors, left singular vectors, and a singular value diagonal matrix. The aim of this paper is to compare four different approaches and algorithms of SVD methods used in a correspondence analysis. In the literature, four approaches are known to singular value decomposition, defined by: R.A. Fisher (1940), M.J. Greenacre (1984), E.B. Anderson (1991), and J.D. Jobson (1992). Those computational procedures will be presented and compared in this paper. Also, methods of determining the coordinates of the category column and line matrix, as well as the values of inertia will be defined for these approaches. A key problem is to compare the well-known approaches, since in the literature only one approach ‒ proposed by Greenacre ‒ is used for singular value decomposition. The reason of the superiority of this algorithm over the others may be the simplicity and ease of the mathematical calculations. Greenacre’s algorithm is also used in R statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.