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Showing papers on "QR decomposition published in 2021"


Journal ArticleDOI
TL;DR: In this paper, the authors provide insights on linear precoding algorithms for massive MIMO systems and discuss the performance and energy efficiency of the precoders. And they also present potential future directions of linear precoder algorithms.
Abstract: Massive multiple-input multiple-output (MIMO) is playing a crucial role in the fifth generation (5G) and beyond 5G (B5G) communication systems. Unfortunately, the complexity of massive MIMO systems is tremendously increased when a large number of antennas and radio frequency chains (RF) are utilized. Therefore, a plethora of research efforts has been conducted to find the optimal precoding algorithm with lowest complexity. The main aim of this paper is to provide insights on such precoding algorithms to a generalist of wireless communications. The added value of this paper is that the classification of massive MIMO precoding algorithms is provided with easily distinguishable classes of precoding solutions. This paper covers linear precoding algorithms starting with precoders based on approximate matrix inversion methods such as the truncated polynomial expansion (TPE), the Neumann series approximation (NSA), the Newton iteration (NI), and the Chebyshev iteration (CI) algorithms. The paper also presents the fixed-point iteration-based linear precoding algorithms such as the Gauss-Seidel (GS) algorithm, the successive over relaxation (SOR) algorithm, the conjugate gradient (CG) algorithm, and the Jacobi iteration (JI) algorithm. In addition, the paper reviews the direct matrix decomposition based linear precoding algorithms such as the QR decomposition and Cholesky decomposition (CD). The non-linear precoders are also presented which include the dirty-paper coding (DPC), Tomlinson-Harashima (TH), vector perturbation (VP), and lattice reduction aided (LR) algorithms. Due to the necessity to deal with a high consuming power by the base station (BS) with a large number of antennas in massive MIMO systems, a special subsection is included to describe the characteristics of the peak-to-average power ratio precoding (PAPR) algorithms such as the constant envelope (CE) algorithm, approximate message passing (AMP), and quantized precoding (QP) algorithms. This paper also reviews the machine learning role in precoding techniques. Although many precoding techniques are essentially proposed for a small-scale MIMO, they have been exploited in massive MIMO networks. Therefore, this paper presents the application of small-scale MIMO precoding techniques for massive MIMO. This paper demonstrates the precoding schemes in promising multiple antenna technologies such as the cell-free massive MIMO (CF-M-MIMO), beamspace massive MIMO, and intelligent reflecting surfaces (IRSs). In-depth discussion on the pros and cons, performance-complexity profile, and implementation solidity is provided. This paper also provides a discussion on the channel estimation and energy efficiency. This paper also presents potential future directions in massive MIMO precoding algorithms.

64 citations


Journal ArticleDOI
TL;DR: In this article, a CVTVQR decomposition-based linear matrix equation model was proposed to solve the complex-valued time-varying linear equation (CVTV-LME) problem.
Abstract: The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.

40 citations


Journal ArticleDOI
TL;DR: A robust blind watermarking scheme based on quaternion QR decomposition (QQRD) for color image copyright protection, while using algebraic structure-preserving method to release its computational complexity.

29 citations


Journal ArticleDOI
TL;DR: By using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time by using time derivative information from a known real or complex matrix.
Abstract: QR decomposition (QRD) is of fundamental importance for matrix factorization in both real and complex cases. In this paper, by using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time. The proposed dynamics use time derivative information from a known real or complex matrix. Furthermore, its theoretical analysis is provided to substantiate the convergence and effectiveness of solving the time-varying QRD problem. In addition, numerical experiments in four different-dimensional time-varying matrices show that the proposed model is effective for solving the time-varying QRD problem both in the case of a real or a complex matrix as input.

24 citations


Proceedings ArticleDOI
26 Oct 2021
TL;DR: In this article, the authors proposed a Random RangE FInder based Network Embedding (this articleINE) algorithm, which can perform embedding on one million of nodes (YouTube) within 30 seconds in a single thread.
Abstract: Network embedding approaches have recently attracted considerable interest as they learn low-dimensional vector representations of nodes. Embeddings based on the matrix factorization are effective but they are usually computationally expensive due to the eigen-decomposition step. In this paper, we propose a Random RangE FInder based Network Embedding (REFINE) algorithm, which can perform embedding on one million of nodes (YouTube) within 30 seconds in a single thread. REFINE is 10x faster than ProNE, which is 10-400x faster than other methods such as LINE, DeepWalk, Node2Vec, GraRep, and Hope. Firstly, we formulate our network embedding approach as a skip-gram model, but with an orthogonal constraint, and we reformulate it into the matrix factorization problem. Instead of using randomized tSVD (truncated SVD) as other methods, we employ the Randomized Blocked QR decomposition to obtain the node representation fast. Moreover, we design a simple but efficient spectral filter for network enhancement to obtain higher-order information for node representation. Experimental results prove that REFINE is very efficient on datasets of different sizes (from thousand to million of nodes and edges) for node classification, while enjoying a good performance.

20 citations


Journal ArticleDOI
TL;DR: This work proposes to solve elliptic interface problems by a meshless finite difference method, where the second order elliptic operator and jump conditions are discretized with the help of the QR decomposition of an appropriately rescaled multivariate Vandermonde matrix with partial pivoting.

16 citations


Journal ArticleDOI
23 Mar 2021
TL;DR: In this paper, a balance controller for overhead manipulation tasks with the assistance of the SuperLimb via tunable interaction force and supporting force regulation is proposed, where the critical horizontal push force is learned through experiment to guide the balance controller, and a dynamics control method based on QR decomposition is adopted to decouple joint torques of the superLimb and the interaction forces.
Abstract: Overhead manipulation tasks often require collaborations between two operators, which becomes challenging in confined spaces such as in a compartment. Supernumerary Robotic Limb (SuperLimb), as a promising wearable robotic solution, can provide assistance in terms of broader workspace, wider manipulation functionalities and safer working conditions. However, the safety concerns of human-centered SuperLimb interaction mechanisms are rarely studied to date, particularly regarding human standing balance. This study proposes a balance controller by which one individual operator can accomplish overhead tasks with the assistance of SuperLimb via tunable interaction force and supporting force regulation. The SuperLimb-human interaction is modeled and a dynamics control method based on QR decomposition (also known as QR factorization, in which a matrix is factorized into an orthogonal matrix and an upper triangular matrix) is adopted to decouple joint torques of the SuperLimb and the interaction forces. Therefore, the supporting forces can be regulated independently to guarantee the operator-SuperLimb interaction forces in a safe region. Force plate is used for measuring the CoP position as an evaluation method of the standing balance. The critical horizontal push force is learned through experiment to guide the balance controller. This method is implemented on a SuperLimb prototype worn on the operator's back, to provide necessary supporting forces on overhead object while allowing the operator to move freely underneath.

15 citations


Journal ArticleDOI
TL;DR: By combining the thin QR decomposition and the subsampled randomized Fourier transform (SRFT), an efficient randomized algorithm for computing the approximate Tucker decomposition with a given target multilinear rank is obtained.
Abstract: By combining the thin QR decomposition and the subsampled randomized Fourier transform (SRFT), we obtain an efficient randomized algorithm for computing the approximate Tucker decomposition with a given target multilinear rank. We also combine this randomized algorithm with the power iteration technique to improve the efficiency of the algorithm. By using the results about the singular values of the product of orthonormal matrices with the Kronecker product of SRFT matrices, we obtain the error bounds of these two algorithms. Finally, the efficiency of these algorithms is illustrated by several numerical examples.

13 citations


Proceedings ArticleDOI
01 Jun 2021
TL;DR: The square root bundle adjustment (SBO) solver proposed in this paper relies on nullspace marginalization of landmark variables by QR decomposition, which is algebraically equivalent to the Schur complement trick, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers.
Abstract: We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.

12 citations


Posted ContentDOI
TL;DR: In this article, the authors proposed a Random RangE FInder based Network Embedding (this articleINE) algorithm, which can perform embedding on one million of nodes (YouTube) within 30 seconds in a single thread.
Abstract: Network embedding approaches have recently attracted considerable interest as they learn low-dimensional vector representations of nodes. Embeddings based on the matrix factorization are effective but they are usually computationally expensive due to the eigen-decomposition step. In this paper, we propose a Random RangE FInder based Network Embedding (REFINE) algorithm, which can perform embedding on one million of nodes (YouTube) within 30 seconds in a single thread. REFINE is 10x faster than ProNE, which is 10-400x faster than other methods such as LINE, DeepWalk, Node2Vec, GraRep, and Hope. Firstly, we formulate our network embedding approach as a skip-gram model, but with an orthogonal constraint, and we reformulate it into the matrix factorization problem. Instead of using randomized tSVD (truncated SVD) as other methods, we employ the Randomized Blocked QR decomposition to obtain the node representation fast. Moreover, we design a simple but efficient spectral filter for network enhancement to obtain higher-order information for node representation. Experimental results prove that REFINE is very efficient on datasets of different sizes (from thousand to million of nodes/edges) for node classification, while enjoying a good performance.

11 citations


Journal ArticleDOI
TL;DR: A novel biometric inspired medical encryption technique is proposed based on newly introduced parameterized all phase orthogonal transformation (PR-APBST), singular value, and QR decomposition, which utilizes the biometrics of the patient/owner to generate a key management system to obtain parameters involved in the proposed technique.
Abstract: The protection of sensitive and confidential data become a challenging task in the present scenario as more and more digital data is stored and transmitted between the end users. The privacy is vitally necessary in case of medical data, which contains the important information of the patients. In this article, a novel biometric inspired medical encryption technique is proposed based on newly introduced parameterized all phase orthogonal transformation (PR-APBST), singular value, and QR decomposition. The proposed technique utilizes the biometrics of the patient/owner to generate a key management system to obtain the parameters involved in the proposed technique. The medical image is then encrypted employing PR-APBST, QR and singular value decomposition and is ready for secure transmission or storage. Finally, a reliable decryption process is employed to reconstruct the original medical image from the encrypted image. The validity and feasibility of the proposed framework have been demonstrated using an extensive experiments on various medical images and security analysis.

Journal ArticleDOI
TL;DR: A careful design exploration of core mathematical operations of the tracking algorithm is performed to improve their hardware utilization and timing performance and among the core functional units optimized in this work the discrete Fourier transform achieves a computational time improvement relative to existing works.
Abstract: Real-time object tracking is an important step of many modern image processing applications. The efficient hardware design of real-time object tracker must achieve the desired accuracy while satisfying the frame rate requirements for a variety of image sizes. The existing methods of visual tracking employ sophisticated algorithms and challenge the capabilities of most embedded architectures. Discriminative scale space tracking is one algorithm that is capable of demonstrating good performance with affordable complexity. It has a high degree of parallelism which can be exploited for efficient implementation of reconfigurable hardware architectures. This paper proposes a real-time implementation of the discriminative scale-space tracker on FPGA for the major blocks. A careful design exploration of core mathematical operations of the tracking algorithm is performed to improve their hardware utilization and timing performance. Among the core functional units optimized in this work, the discrete Fourier transform achieves a computational time improvement of 92% relative to existing works, QR factorization achieves a 2.3 $$\times$$ reduction in resource utilization, and singular value decomposition yields a 3.8 $$\times$$ improvement in processing time. The proposed data path architecture is designed using Vivado HLS tool set and implemented for Zync Zed Board (xc7z020clg484-1). For an input image size of 320 $$\times$$ 240, the proposed architecture achieves a mean 25.38 fps.

Journal ArticleDOI
TL;DR: Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appr... as mentioned in this paper, and
Abstract: Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appr...

Journal ArticleDOI
TL;DR: In this paper, a hierarchical multilevel medical image watermarking framework is introduced to improve the payload capacity, imperceptibility and low computational QR transform is used to make watermark scheme free from the false positive problem.

Journal ArticleDOI
TL;DR: A continuous-time QR decomposition model is proposed by applying zeroing neural network method, equivalent transformations, Kronecker product, and vectorization techniques, and a high-precision ten-instant Zhang et al discretization (ZeaD) formula is proposed.

Journal ArticleDOI
TL;DR: Zhang et al. as mentioned in this paper designed a lightweight convolutional neural network (LW-CNN) which adopts a separable convolution structure, which can extract more accurate features with fewer parameters and can extract 3D feature points of a human face.
Abstract: Through the analysis of facial feature extraction technology, this paper designs a lightweight convolutional neural network (LW-CNN). The LW-CNN model adopts a separable convolution structure, which can propose more accurate features with fewer parameters and can extract 3D feature points of a human face. In order to enhance the accuracy of feature extraction, a face detection method based on the inverted triangle structure is used to detect the face frame of the images in the training set before the model extracts the features. Aiming at the problem that the feature extraction algorithm based on the difference criterion cannot effectively extract the discriminative information, the Generalized Multiple Maximum Dispersion Difference Criterion (GMMSD) and the corresponding feature extraction algorithm are proposed. The algorithm uses the difference criterion instead of the entropy criterion to avoid the “small sample” problem, and the use of QR decomposition can extract more effective discriminative features for facial recognition, while also reducing the computational complexity of feature extraction. Compared with traditional feature extraction methods, GMMSD avoids the problem of “small samples” and does not require preprocessing steps on the samples; it uses QR decomposition to extract features from the original samples and retains the distribution characteristics of the original samples. According to different change matrices, GMMSD can evolve into different feature extraction algorithms, which shows the generalized characteristics of GMMSD. Experiments show that GMMSD can effectively extract facial identification features and improve the accuracy of facial recognition.

Journal ArticleDOI
TL;DR: New randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization are proposed, motivated by applications in hyper‐differential sensitivity analysis (HDSA).
Abstract: The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

Journal ArticleDOI
TL;DR: In this article, a tensor completion method based on the L 2, 1 -norm minimization and Qatar Riyal decomposition (LNM-QR) was proposed to solve the tensor matrix completion problem.

Journal ArticleDOI
TL;DR: Two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction are introduced that proved the global convergence for these schemes.
Abstract: This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction. These iterative algorithms use a projection operator based on the QR factorization to preserve the feasibility in each iteration. However, for some particular cases, the proposals do not require the use of any projection operator. In addition, we consider a Barzilai and Borwein-like step-size combined with the Zhang–Hager nonmonotone line-search technique in order to accelerate the convergence of the proposed procedures. We proved the global convergence for these schemes, and we evaluate their effectiveness and efficiency through an extensive computational study, comparing our approaches with other state-of-the-art gradient-type algorithms.

Journal ArticleDOI
TL;DR: A fragile watermarking technique is introduced for verifying images based on QR decomposition and Fourier Transform and it helps to understand whether an image is manipulated or not.
Abstract: In this study, a fragile watermarking technique is introduced for verifying images based on QR decomposition and Fourier Transform (FT). At first, we apply the FT to the host image to achieve the frequency domain, yielding a high-quality image. Then the resulting image is decomposed using QR factorization. In the meantime, the watermark image is decomposed only via QR factorization. Then, we add a coefficient of matrix R from the watermark image to the matrix R from the host image. This process embeds a proportion of the watermark image inside the host image. According to the experiments, our scheme is susceptible to the weakest attacks, so it is a fragile watermarking technique. So it helps to understand whether an image is manipulated or not. The validation dataset is composed of some images from the USC-SIPI image database.

Journal ArticleDOI
TL;DR: In this article, an accurate and effective low-rank approximation to accelerate non-self-consistent GW (G0W0) calculations under the static Coulomb hole plus screened exchange (COHSEX) approximation for periodic systems is presented.
Abstract: The GW approximation is an effective way to accurately describe the single-electron excitations of molecules and the quasiparticle energies of solids. However, a perceived drawback of the GW calculations is their high computational cost and large memory usage, which limit their applications to large systems. Herein, we demonstrate an accurate and effective low-rank approximation to accelerate non-self-consistent GW (G0W0) calculations under the static Coulomb hole plus screened exchange (COHSEX) approximation for periodic systems. Our approach is to adopt the interpolative separable density fitting (ISDF) decomposition and Cauchy's integral to construct low-rank representations of the dielectric matrix ϵ and self-energy matrix Σ. This approach reduces the number of floating point operations from O(Ne4) to O(Ne3) and requires a much smaller memory footprint. Two methods are used to select the interpolation points in ISDF, including the standard QR factorization with column pivoting (QRCP) procedure and the machine learning K-means clustering (K-means) algorithm. We demonstrate that these two methods can yield similar accuracy for both molecules and solids at much lower computational cost. In particular, K-means clustering can significantly reduce the computational cost of selecting the interpolation points by an order of magnitude compared to QRCP, resulting in an overall speedup factor of about ten times ISDF accelerated the static COHSEX calculations compared with conventional COHSEX approximation.

Journal ArticleDOI
TL;DR: In this paper, a constitutive model for elastic-plastic materials is developed using scalar, conjugate, stress-strain, base pairs in a finite deformation setting.
Abstract: A constitutive model for elastic–plastic materials is developed using scalar, conjugate, stress–strain, base pairs in a finite deformation setting. These conjugate base pairs arise from an alternative QR decomposition of the deformation gradient that decomposes its matrix into an orthogonal rotation and an upper-triangular matrix, called the Laplace stretch. This decomposition is particularly useful from an experimental standpoint, as it enables one to directly measure the components of Laplace stretch and its plastic contributions in a specific coordinate system. Moreover, from an experimental standpoint, it is difficult to parameterize current material models due to a covariance between their tensor invariants, traditionally used in their constructions. The use of scalar, conjugate, base pairs are also helpful from that point of view. Interestingly, the multiplicative elastic–plastic decomposition of Laplace stretch leads to an additive decomposition of the total strain attributes into their corresponding elastic and plastic components. Although an additive strain decomposition is commonly used in small-strain theory, here such a decomposition is possible even for finite deformations. An additive decomposition of the strain attributes has a deeper consequence in the construction of our constitutive model. A maximum rate of dissipation criterion has been used in deriving our constitutive equations, as this criterion is valid for a wider class of materials. Two constitutive assumptions – one for a Helmholtz potential, and one for the rate of dissipation function – are required for our constitutive construction. This model does not presuppose the existence of a yield surface. In fact, it is shown that whether a material exhibits a yielding or a creep-like behavior depends upon the differentiability of the rate of dissipation function. Two cases of plastic deformation – volume-preserving and dilatant-pressure dependent deformations – have been considered. To illustrate the proposed model, finite strain versions of classical J 2 plasticity and a Drucker–Prager model are derived.

Posted Content
TL;DR: In this article, a fast hierarchical algorithm for solving large, sparse least squares problems is proposed, which is built on top of a Nested Dissection based multifrontal QR approach.
Abstract: In this work, we develop a fast hierarchical solver for solving large, sparse least squares problems. We build upon the algorithm, spaQR (sparsified QR), that was developed by the authors to solve large sparse linear systems. Our algorithm is built on top of a Nested Dissection based multifrontal QR approach. We use low-rank approximations on the frontal matrices to sparsify the vertex separators at every level in the elimination tree. Using a two-step sparsification scheme, we reduce the number of columns and maintain the ratio of rows to columns in each front without introducing any additional fill-in. With this improvised scheme, we show that the runtime of the algorithm scales as $\mathcal{O}(M \log N)$ and uses $\mathcal{O}(M)$ memory to store the factorization. This is achieved at the expense of a small and controllable approximation error. The end result is an approximate factorization of the matrix stored as a sequence of sparse orthogonal and upper-triangular factors and hence easy to apply/solve with a vector. Finally, we compare the performance of the spaQR algorithm in solving sparse least squares problems with direct multifrontal QR and CGLS iterative method with a standard diagonal preconditioner.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a subsampling strategy for the offline stage of the RBM, which exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples.
Abstract: We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples. It consists of two stages. In the first stage, we construct a low-fidelity approximation to the solution manifold over a fine training set. Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain. These points reveal the structure of the parametric dependence of the output variable. The second stage proceeds with a subsampled training set containing a by far smaller number of parameters than the initial training set. Different subsampling strategies inspired from recent variants of the empirical interpolation method are also considered. Tests on benchmark examples justify the new approach and show its potential to substantially speed up the offline stage of the Reduced Basis Method, while generating reliable reduced-order models.

Journal ArticleDOI
Fabien Treyssède1
TL;DR: In this paper, a model reduction strategy for fast finite element analysis of continuously symmetric elastic waveguides is presented, where the initial three-dimensional problem is first reduced to a two-dimensional quadratic eigenvalue problem based on a semi-analytical finite element method.

Proceedings ArticleDOI
24 Mar 2021
TL;DR: In this article, two optimized computational procedures of the Recursive Least Squares (RLS) adaptive filtering algorithm based on the Matrix Inversion Lemma (MIL) are presented.
Abstract: This paper presents two optimized computational procedures of the Recursive Least Squares (RLS) adaptive filtering algorithm based on the Matrix Inversion Lemma (MIL). The traditional MIL RLS algorithm might be unstable due to the accumulation of the errors of the computations. These errors are the reasons of the loss of the Hermitian structure of the adaptive filter input signal correlation matrix. As a result, the matrix becomes noninvertible and this leads to the wrong calculation of the weighs and the unstable behavior of the adaptive filter. In this paper it is suggested to compute the main diagonal and only the upper or the lower diagonal part of the correlation matrix. The rest of the computations, required at each iteration, are executed assuming the Hermitian structure of the whole matrix. In this case, no loss of the matrix symmetry appears. This ensures the optimized MIL RLS algorithm stability that is demonstrated via the simulation of an adaptive antenna array. The optimization also decreases the MIL RLS algorithm complexity. This is demonstrated via the estimates of the number of the arithmetical operations per iteration of the traditional MIL RLS algorithm, its optimized versions and RLS algorithms based on the QR decomposition and Householder transform.

Journal ArticleDOI
TL;DR: A dual security robust watermarking (DSRW) method based on a hybrid optimization algorithm for image protection in the DWT domain used in the IoT perceptive layer and the advanced cat swarm optimization (ICSO) algorithm to find the best module for watermark inclusion is proposed.
Abstract: Digital watermarking is a technology that allows users to add copyright notifications or other confirmation messages to digital media. Image recognition is one of the applications of digital watermarking, which is used to identify digital images. The goal is not to prevent theft or theft of content but to provide a means of identifying the images and ensuring the integrity of the image. This paper proposes a dual security robust watermarking (DSRW) method based on a hybrid optimization algorithm for image protection in the DWT domain used in the IoT perceptive layer. First, we introduce the redistributed differential wavelet transform (RI-DWT) to induce the LH and HL subbands. Second, we proposed the advanced cat swarm optimization (ICSO) algorithm to find the best module for watermark inclusion. After the best batch selection, the inclusion procedure adds the binary score to the selected first-level approximate subband of the RI-DWT for each selected module. Optimal QR decomposition is used to estimate a single value in the image matrix. The main objective of the proposed watermarking plan is to ensure high robustness and security. The simulation results examine the significance of the proposed scheme and the validity of the proposed methods. The experiments are conducted to check various common image processing attacks, and the watermark extraction process generates high-quality image after different attacks.

Journal ArticleDOI
TL;DR: In this article, a new scheme using devil's toroidal lens masks (DTLMs) and QR decomposition in gyrator transform (GT) domain is proposed to enhance the security in optical image encryption scheme.
Abstract: To enhance the security in optical image encryption scheme and to safeguard it from the invaders, this paper proposes a new scheme using devil’s toroidal lens masks (DTLMs) and QR decomposition in gyrator transform (GT) domain. The proposed cryptosystem utilizes DTLMs which are the complex phase masks designed using the combination of a phases of devil’s mask ( $${\rm DM})$$ and toroidal mask $$\left({\rm TM}\right)$$ . QR is an operation used to decompose the matrix and is utilized to supersede the phase-truncation (PT) task in the traditional phase-truncated Fourier transform (PTFT). Hence, the proposed method is immune to the attacks to which the PTFT-based cryptosystems are vulnerable. The cryptosystem is asymmetric as both the encryption and decryption processes are different along with different encryption and decryption keys. The private keys produced during the encryption method are utilized in the decryption process to retrieve the original image. The decryption process can be realized with both the digital and the modified optical architecture. Recommended scheme strengthens the safety of DRPE by growing the key capacity and the number of parameters for safety and vigorous against diverse protection.

Proceedings ArticleDOI
10 Jan 2021
TL;DR: In this article, the authors proposed the CR-QRM-MLD for the SD-SM-MIMO with the null modulation which reduces the transmission power and keeps the maximum transmission rate.
Abstract: For the transmission technique by a multiple-input multiple-output (MIMO), space division (SD) multiplexing and spatial modulation (SM) have been proposed. However, since they have a trade-off problem between the system performance and the maximum transmission rate, we have proposed the SD-SM-MIMO. SD-SM-MIMO achieves a little computational complexity and a high system performance by the channel ranking and the QR decomposition with M-algorithm maximum likelihood detection (CR-QRM-MLD). By using this system, in this paper, we propose the CR-QRM-MLD for the SD-SM-MIMO with the null modulation which reduces the transmission power and keeps the maximum transmission rate.

Proceedings ArticleDOI
31 Jul 2021
TL;DR: In this article, a fast sparse approximate QR factorization, spaQR, is proposed to solve the sparse least squares problem in near-linear time, which shows up to 57% improvement over solving the normal equations using Cholesky and 63 percent improvement over a standard preconditioner with Conjugate Gradient Least Squares.
Abstract: A wide range of problems in computer graphics and vision can be formulated as sparse least squares problems. For example, Laplacian mesh deformation, Least Squares Conformal Maps, Poisson image editing, and as-rigid-as-possible (ARAP) image warping involve solving a linear or non-linear sparse least squares problem. High performance is crucial in many of these applications for interactive user feedback. For these applications, we show that the matrices produced by factorization methods such as QR have a special structure: the off-diagonal blocks are low-rank. We leverage this property to produce a fast sparse approximate QR factorization, spaQR, for these matrices in near-linear time. In our benchmarks, spaQR shows up to 57% improvement over solving the normal equations using Cholesky and 63% improvement over a standard preconditioner with Conjugate Gradient Least Squares (CGLS).