schur decomposition
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2022 ◽  
Author(s):  
Aimad Er-Raiy ◽  
Radouan Boukharfane ◽  
Francisco E. Hernandez Perez ◽  
Hong G. Im ◽  
Matteo Parsani
Keyword(s):  

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Deyang Wu ◽  
Miaomiao Wang ◽  
Jing Zhao ◽  
Jiayan Wang ◽  
Meiyu Zhong ◽  
...  

With the widespread use of medical images in telemedicine, personal information may be leaked. The traditional zero-watermarking technology has poor robustness under large-scale attacks. At the same time, most of the zero-watermarking information generated is a binary sequence with a single information structure. In order to effectively solve the poor robustness problem of traditional zero-watermarking under large-scale attacks, a color zero-watermarking algorithm for medical images based on bidimensional empirical mode decomposition (BEMD)-Schur decomposition and color visual cryptography is proposed. Firstly, the color carrier image and the color copyright logo are decomposed into R, G, and B three color components, respectively, and the feature value of each sub-block are extracted by wavelet transform, BEMD decomposition, block operation, and Schur decomposition. Then, the R, G, and B components of the copyright logo are scrambled by Arnold scramble and converted into binary watermark information. Finally, a color visual cryptography scheme is proposed to generate two color shared images based on the carrier characteristics and copyright information. One shared image is used to generate a color zero-watermark, and the other is used for copyright authentication phase. Experimental results show that this algorithm has strong robustness and stability in resisting large-scale noise attacks, filtering attacks, JPEG compression, cropping attacks, and translation attacks at different positions. Compared with similar zero-watermarking algorithms, the robust performance is improved by about 10%, and it can adapt to more complex network environments.


Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 211
Author(s):  
Asuka Ohashi ◽  
Tomohiro Sogabe

We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.


Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2018
Author(s):  
Javier Ibáñez ◽  
Jorge Sastre ◽  
Pedro Ruiz ◽  
José M. Alonso ◽  
Emilio Defez

The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. In this work, we present a Taylor series algorithm, based on the free-transformation approach of the inverse scaling and squaring technique, that uses recent matrix polynomial formulas for evaluating the Taylor approximation of the matrix logarithm more efficiently than the Paterson–Stockmeyer method. Two MATLAB implementations of this algorithm, related to relative forward or backward error analysis, were developed and compared with different state-of-the art MATLAB functions. Numerical tests showed that the new implementations are generally more accurate than the previously available codes, with an intermediate execution time among all the codes in comparison.


2021 ◽  
Vol 72 (4) ◽  
pp. 229-239
Author(s):  
Jawad F. Al-Asad ◽  
Hiren K. Mewada ◽  
Adil H. Khan ◽  
Nidal Abu-Libdeh ◽  
Jamal F. Nayfeh

Abstract This work proposes a novel frequency domain despeckling technique pertaining to the enhancement of the quality of medical ultrasound images. The results of the proposed method have been validated in comparison to both the time-domain and the frequency-domain projections of the schur decomposition as well as with several other benchmark schemes such as frost, lee, probabilistic non-local means (PNLM) and total variation filtering (TVF). The proposed algorithm has shown significant improvements in edge detection and signal to noise ratio (SNR) levels when compared with the performance of the other techniques. Both real and simulated medical ultrasound images have been used to evaluate the numerical and visual effects of each algorithm used in this work.


2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Youxia Dong ◽  
Xiaoling Huang ◽  
Guodong Ye

A visually meaningful image encryption scheme with an asymmetric structure based on the discrete wavelet transform (DWT) and Schur decomposition is proposed in this study. First, the RSA algorithm is used to generate the initial values for the chaotic system to produce the random sequence. Then, both scrambling and diffusion operations are performed on the plain image to obtain the preencrypted image. Moreover, the Schur decomposition is applied on the preencrypted plain image to obtain the upper triangular and orthogonal matrices. Second, the cover image is scrambled followed by a DWT operation. Four subbands are then formed, namely, LL, HL, LH, and HH. Finally, the former upper triangular matrix and orthogonal matrix are embedded into subbands LH and HH produced by the cover image. After the application of the inverse DWT and inverse scrambling operation, the final visually meaningful cover image embedded with a secret plain image can be obtained. No one can identify any useful information about the plain image from the final embedded cover image, nor can anybody know that there is any hidden secret image. Experimental simulations show that the normalized correlation values between the original cover image and the final visually meaningful cover image are approximately 0.9997. Therefore, the proposed encryption scheme is imperceptible for secret image communications.


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