Data Hiding Schemes Based on Singular Value Decomposition

The properties of singular value decomposition (SVD) are used to implement an SVD spatial domain pseudoinverse restoration filter. This type of filter is attractive for poor imaging conditions (low spatial resolution, high image noise) and is thus appealing for nuclear medicine images. The method might offer some advantages over more traditional frequency domain filter techniques since the restoration is performed on a local rather than global basis. High-contrast thyroid phantom images collected at different count densities and low-contrast liver phantom images were processed with the SVD filter. Restored images yielded improved spatial resolution, lesion contrast, and signal-to-noise ratio. The SVD pseudoinverse restoration filter implemented as an interactive process permits the operator to terminate filtering at a stage where the visually "best" image is obtained compared to the original data. Processed images suggest that the technique may have potential for improving lesion detection in nuclear medicine.

We propose a technique for video shot segmentation and classification based on singular value decomposition (SVD). For the input video sequence, we create a feature-frame matrix A, and perform the SVD on it. From this SVD, we are able to not only derive the refined feature space to better segment the video sequence along the time axis, but also define metrics to enable classifications of the detected video shots. Using these SVD properties, we achieve the two goals of accurate video shot segmentation, and visual content-based shot classification at the same time.

In this paper, two new properties of singular value decomposition (SVD) on images are proved. The first property demonstrates the quantitative relationship between singular values and power spectrum. The second one proves that under the condition of losing equal power spectrum, the square-error of the reconstructed image is much smaller when we reduce all singular values proportionally instead of neglect the smaller ones. Based on the two properties, a new data-hiding scheme is proposed. It performs well as for robustness, for it satisfies power-spectrum condition (PSC), and PSC-compliant watermarks are proven to be most robust. Besides, the proposed scheme has a good performance as for capacity and adaptability.

Block-wise reversible data hiding in encrypted domain using SVD

In this article, we have improved the quantitative inversion performance of the cross-correlated contrast source inversion (CC-CSI) method by incorporating the subspace optimization strategy. The proposed method is called the cross-correlated subspace optimization method (CC-SOM). Meanwhile, multifrequency data are used to improve the inversion performance of high-contrast scatterers, where the L-curve method is introduced to select the regularization parameters of each frequency point without relying on experience. Finally, a fast algorithm is implemented by using the property of singular value decomposition (SVD) to simplify the large-scale matrix, and the fast Fourier transform (FFT) to accelerate the calculation. Synthetic and experimental inversion results demonstrate that both CC-SOM and CC-CSI show better robustness than SOM. In comparison to CC-CSI, CC-SOM is superior in terms of inversion accuracy when the regularization parameters have been appropriately selected. However, these advantages come at the cost of higher computational complexity.

Author profiling is a challenging task that consists of identifying a person’s relevant attributes based on the content he/she generates. In this article, we validate a classification method based on the reconstructive classification to identify two demographic attributes, age and gender, for users of social networks based on the text content they publish. For the problem, we consider balanced and unbalanced data, where a gender or age group has a larger presence than the others. The proposed method is based on using the reconstructive property of singular value decomposition (SVD), and its suitability to work with sparse data, to find a matrix with the main latent components to represent the information of specific gender or age classes. Afterward, we use such a matrix to project and reconstruct new users’ information to identify their demographic variables. We test our method with a set of datasets in several languages collected from Twitter and Pinterest users, and we use different evaluation metrics to compare their performance with the ones of several popular classifiers based on traditional machine learning, and on deep learning, and with some relevant works in the literature. The results show that the proposed classifier performs generally well in identifying the age and gender of users in social networks.

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.

Digital Image Watermarking provides a successful method for content authentication and copyright protection. Thus, it has significant scope in today's era due to the rapid growth of internet users. The watermark should be robust and reliable in addition to being imperceptible to the human eye. In this paper, a hybrid singular value decomposition (SVD) and discrete wavelet transform (DWT) based watermarking scheme is presented. The SVD used in this scheme is a variant of the traditional SVD and is called shuffled SVD (SSVD). The cover image is decomposed into four sub-bands (LL, HL, LH, HH) using DWT. The LL subband is further divided into blocks of appropriate size. The principle components of the watermark image obtained after applying SSVD are embedded in various blocks of the LL sub-band. The proposed scheme shows significant robustness in addition to being false positive free.

Efficient video watermarking based on singular value decomposition in the discrete wavelet transform domain

With the advancement of GPU architecture, matrix computation engines such as NVIDIA Tensor Cores now support double-precision (FP64) General matrix multiplications (GEMMs) with the same efficiency as single-precision (FP32) GEMMs. However, the adoption of this enhanced FP64 capability remains limited, primarily restricted to applications that involve multiple FP64 BLAS3 operations. Singular Value Decomposition (SVD), a fundamental decomposition in numerical linear algebra with numerous applications, can greatly benefit from exploiting this hardware feature. In this article, for FP32 SVD, we propose a novel algorithm, FP64 precision eigenvalue decomposition (EVD) based SVD, specifically designed to leverage the latest GPU architectural features. We provide a theoretical analysis demonstrating the feasibility of our approach on emerging GPU architectures and evaluate it from both accuracy and performance perspectives. Moreover, for FP64 SVD, we introduce a double-blocking band reduction technique combined with a GPU-based bulge chasing algorithm to further accelerate the overall SVD process. Experimental results show that, for FP32 SVD, our EVD-based SVD implementation achieves higher numerical accuracy and delivers speedups of up to 6.1× on H100 and 5.0× on A100 over the state-of-the-art cuSOLVER SVD solver. In the case of FP64 SVD, our method also achieves 4.9× and 4.8× speedups on H100 and A100, respectively. These results highlight the potential of our approach as a highly efficient and accurate solution for SVD on modern GPU platforms.

In this paper, we demonstrate the feasibility and efficiency of approximate computing techniques (ACTs) in the embedded Support Vector Machine (SVM) tensorial kernel circuit implementation in tactile sensing systems. Improving the performance of the embedded SVM in terms of power, area, and delay can be achieved by implementing approximate multipliers in the SVD. Singular Value Decomposition (SVD) is the main computational bottleneck of the tensorial kernel approach; since digital multipliers are extensively used in SVD implementation, we aim to optimize the implementation of the multiplier circuit. We present the implementation of the approximate SVD circuit based on the Approximate Baugh-Wooley (Approx-BW) multiplier. The approximate SVD achieves an energy consumption reduction of up to 16% at the cost of a Mean Relative Error decrease (MRE) of less than 5%. We assess the impact of the approximate SVD on the accuracy of the classification; showing that approximate SVD increases the Error rate (Err) within a range of one to eight percent. Besides, we propose a hybrid evaluation test approach that consists of implementing three different approximate SVD circuits having different numbers of approximated Least Significant Bits (LSBs). The results show that energy consumption is reduced by more than five percent with the same accuracy loss.

We present a new image watermarking technique for color images. Tradeoff between imperceptibility, robustness, and security is achieved by this technique. This technique is based on discrete wavelet transform (DWT) and singular valued decomposition (SVD). Advantage of both DWT and SVD has been utilized to achieve more robustness. Differential evolution (DE) is used for optimization of scaling factors. DE is incorporated to find optimal scaling factors to scale down the watermark and increase the visual quality and robustness of watermarked image. Color cover image is split into three color channels using RGB color space. To improve the security, watermark is scrambled before embedding using random Bit-Plane and XOR operation. Experimental results show that the watermarked image is imperceptible and resistant to various geometric attacks and image processing.

Recently Pretrained Convolutional Neural Networks (CNNs) have proven its effectiveness in image extraction and classification. This powerful feature of CNNs in image processing is facilitated by machine learning to train and classify big data. Image capturing and security transformation are considered as a central necessity of remote sensing imagery of unmanned aerial vehicles (UAVs) and drones. This paper presents a novel artificial intelligent drone-based encrypted machine learning of image classification using a pertained CNN and image encryption-decryption by utilizing singular value decomposition (SVD) and XOR-Secret-Key block cipher cryptology. Initially, pretrained convolutional neural networks (CNN) are extensively used to extract and classify image features making advantage of machine learning training tools features. Training of partial set of image data can be performed to test, classify and label the untrained image data. Pretrained CNN can classify images into object categories. Afterward, the CNN the classified image output is transformed into a digital matrix using SVD and identifies its associated eigenvalues. These eigenvalues are then converted into a binary code. The image data encryption is implemented according to suggested keys. The first part applies the exclusive OR (XOR) operation of the eigenvalues with a selected cipher key. Meanwhile, the second part implements the XOR operation of the output of part one with a randomly generated key using Poisson distribution. The last step in the encryption will be obtained by generating a non-real SVD decomposition matrix; according to which a non-readable image will be resulted. The original image-matrix can be constructed by reversing the process using the security key-cipher block (Poisson Distribution Key and Stand-alone Cipher Code). Finally, SVD image processing results are demonstrated to verify the effectiveness and security of the applied approach that can be implemented for different images.

Matrix factorization plays an important role in scientific computation. The widely used one is singular value decomposition (SVD) which approximates the original data matrix with three lower rank matrices with orthogonality constraints. Recently nonnegative matrix factorization (NMF) considering the nonnegativity of data makes the results more interpretable than those of SVD. However NMF finds only two factor matrices and there is no significant index as singular values of SVD which can be used for sorting learned basis vectors. In this paper we take into account the nonnegativity for SVD and propose nonnegative SVD (NNSVD). The preliminary results on the microarray data of spermatogenesis show that NNSVD has advantages of both SVD and NMF.

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.