Computation of outer inverses of tensors using the QR decomposition

Sahoo, Jajati Keshari; Behera, Ratikanta; Stanimirović, Predrag S.; Katsikis, Vasilios N.

doi:10.1007/s40314-020-01225-4

Cited by 16 publications

(3 citation statements)

References 37 publications

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“…First, the measurement matrix is decomposed by standard QR decomposition to obtain matrix Q and R. As for R, its principal diagonal elements are much larger than the nondiagonal elements [40], and then, one sets all non-diagonal elements to 0 to get matrix R; thus, the new measurement matrix Q R is obtained. The detailed steps are as follows.…”

Section: Qr Decompositionmentioning

confidence: 99%

Content-adaptive image compression and encryption via optimized compressive sensing with double random phase encoding driven by chaos

Gan

Chai

et al. 2022

Complex Intell. Syst.

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With the advancement of multimedia technology and coming of big data era, the size of image data is significantly increased. However, the traditional image encryption methods cannot solve the emerging problems of efficient compression. To settle with this challenge, an effective content-adaptive image compression and encryption method based on compressive sensing and double random phase encoding (DRPE) is proposed in this paper. The original image is converted to one low-frequency part and three high-frequency parts by DWT and then permutated by sorting-based chaotic sequences. Afterward, a novel measurement matrix optimization algorithm based on adaptive step size is presented to measure the high-frequency components. To enhance the security of the scheme, the DRPE, quantization, and diffusion are successively performed on the complex matrix composed of the shuffled low-frequency component and three measurement value matrices to obtain the cipher image. Logistic-Sine chaotic system is utilized to produce the chaotic keystreams for the encryption process, and its system parameter and initial value are determined by the information entropy of the plain image and external key parameters, so that the proposed cipher can withstand known-plaintext and chosen-plaintext attacks effectively. Numerical experiments demonstrate the effectiveness of the proposed image compression and encryption algorithm.

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Section: Qr Decompositionmentioning

confidence: 99%

Content-adaptive image compression and encryption via optimized compressive sensing with double random phase encoding driven by chaos

Gan

Chai

et al. 2022

Complex Intell. Syst.

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“…With the rapid development of engineering [1][2][3], physics and astronomy [4][5][6], energy [7], and other disciplines [8,9], the key problem of QR factorization (QRF) has become a major research topic. In [10], a new representation and characterization of the outer inverse of the tensor is solved by QRF, and an innovative algorithm is presented to apply the tensor inverse to the deblurring of 3D color images. Furthermore, Mehraa et al [11] apply QRF to optical system protection, and an encryption scheme based on gyrator wavelet transform is designed, which resists the attack of iterative algorithms.…”

Section: Introductionmentioning

confidence: 99%

Bounded Adaptive Function Activated Recurrent Neural Network for Solving the Dynamic QR Factorization

Yang

Xie

et al. 2023

Mathematics

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The orthogonal triangular factorization (QRF) method is a widespread tool to calculate eigenvalues and has been used for many practical applications. However, as an emerging topic, only a few works have been devoted to handling dynamic QR factorization (DQRF). Moreover, the traditional methods for dynamic problems suffer from lagging errors and are susceptible to noise, thereby being unable to satisfy the requirements of the real-time solution. In this paper, a bounded adaptive function activated recurrent neural network (BAFARNN) is proposed to solve the DQRF with a faster convergence speed and enhance existing solution methods’ robustness. Theoretical analysis shows that the model can achieve global convergence in different environments. The results of the systematic experiment show that the BAFARNN model outperforms both the original ZNN (OZNN) model and the noise-tolerant zeroing neural network (NTZNN) model in terms of accuracy and convergence speed. This is true for both single constants and time-varying noise disturbances.

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“…3,4 This leads to the study of different types of tensor products, 2,5 which have recently attracted a great deal of interest (see References 3,[5][6][7][8][9]. In this connection, the inverses and generalized inverses over different product of tensors [10][11][12][13] have generated a tremendous amount of interest in mathematics, physics, computer science, and engineering.…”

Section: Introductionmentioning

confidence: 99%

Computation of generalized inverses of tensors via t‐product

Behera

Sahoo

Mohapatra

et al. 2021

Numerical Linear Algebra App

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Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a noncommutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore–Penrose inverse, and weighted Moore–Penrose inverse of tensors over a noncommutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem.

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Computation of outer inverses of tensors using the QR decomposition

Cited by 16 publications

References 37 publications

Content-adaptive image compression and encryption via optimized compressive sensing with double random phase encoding driven by chaos

Content-adaptive image compression and encryption via optimized compressive sensing with double random phase encoding driven by chaos

Bounded Adaptive Function Activated Recurrent Neural Network for Solving the Dynamic QR Factorization

Computation of generalized inverses of tensors via t‐product

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