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Xu, Yuan

doi:10.1155/imrn.2005.449

Cited by 29 publications

(2 citation statements)

References 13 publications

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“…Later, a novel set of discrete and continuous orthogonal matrices based on orthogonal polynomials was introduced into the field of orthogonal polynomial generation [34]. In [35], several relations linking the differences between bivariate discrete orthogonal polynomials and general polynomials were given.…”

Section: Related Workmentioning

confidence: 99%

A General Method for Generating Discrete Orthogonal Matrices

Chan

2021

IEEE Access

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Discrete orthogonal matrices have applications in information coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize continuous orthogonal functions that have been discovered. The need of such continuous functions is restrictive. Polynomials, as the simplest class of continuous functions, are widely studied for their orthogonalality, to serve the purpose of generating orthogonal matrices. However, beginning with continuous orthogonal polynomials still takes much work. To overcome this complexity while improving the efficiency and flexibility, we present a general method for generating orthogonal matrices directly through the construction of certain even and odd polynomials from a set of distinct positive values, bypassing the need of continuous orthogonal functions. We present a constructive proof by induction that not only asserts the existence of such polynomials, but also tells how to iteratively construct them. Besides the derivation of the method as simple as a few nested loops, we discuss two well-known discrete transforms, the Discrete Cosine Transform and the Discrete Tchebichef Transform, how they can be achieved using our method with the specific values, and show how to embed them into the transform module of video coding. By the same token, we also give the examples for generating new orthogonal matrices from arbitrarily chosen values. The demonstrative experiments indicate that our method is not only simpler to implement, but also more efficient and flexible. It can generate orthogonal matrices of larger sizes, compared with those existing methods.

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Section: Related Workmentioning

confidence: 99%

A General Method for Generating Discrete Orthogonal Matrices

Chan

2021

IEEE Access

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“…For example, a set of fractional order orthogonal Chebyshev moments is used to represent a gray-scale image (Kazem et al, 2013). Discrete fractional order orthogonal Chebyshev moments for Image encryption and watermarking based on FCMs are investigated in Xiao et al (2020;, Fernández et al (2010), and Xu (2005). Shifted Chebyshev polynomials are developed to the new family of basis functions, namely generalized shifted Chebyshev polynomials (Fernández et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Image representation based on fractional order Legendre and Laguerre orthogonal moments

Farouk¹,

Awad²

2021

Int. j. adv. appl. sci.

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In this paper, we have introduced new sets of fractional order orthogonal basis moments based on Fractional order Legendre orthogonal Functions (FLeFs) and Fractional order Laguerre orthogonal Functions (FLaFs) for image representation. We have generated a novel set of Fractional order Legendre orthogonal Moments (FLeMs) from fractional order Legendre orthogonal functions and a new set of Fractional order Laguerre orthogonal Moments (FLaMs) from the fractional order Laguerre orthogonal functions. The new presented sets of (FLeMs) and (FLaMs) are tested with the recently introduced Fractional order Chebyshev orthogonal Moments (FCMs). This edge detection filter can be used successfully in the gray level image and color images. The new sets of fractional moments are used to reconstruct the gray level image. The numerical results show FLeMs and FLaMs are promised techniques for image representation. The computational time of the proposed techniques is compared with the computational time of Chebyshev orthogonal Moments techniques and gives better results. Also, the fractional parameters give the flexibility of studying global features of the image at different positions of moments.

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Knockout of 4.1B triggers malignant transformation in SV40T‐immortalized mouse embryo fibroblast cells

Zhang

Zeng

et al. 2016

Molecular Carcinogenesis

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Protein 4.1B deficiency has been found to promote the tumor development; however, whether 4.1B deficiency participates in malignant transformation is unknown. In this study, we demonstrated that 4.1B gene deletion was sufficient to transform SV40T antigen-immortalized mouse embryonic fibroblasts (iMEFs), as reflected by the ability of 4.1B iMEFs to growth in the environments that were growth restrictive for 4.1B iMEFs and to form tumors in nude mice, whereas 4.1B iMEFs were unable to form tumors in vivo. The histological examination revealed that the tumors generated by 4.1B iMEFs were desmoid tumors with features of local invasion. Moreover, loss of 4.1B significantly accelerated cell cycle progression, accompanied by activation of typical proto-oncogene ERK, AKT, and the G1/S regulatory pathway (p16 -pRb pathway), and up-regulation of many members of the Wnt gene family. In particular, 4.1B iMEFs exhibited nuclear accumulation of β-catenin, which is an indicator for desmoid tumor, with down-regulation of E-cadherin expression and up-regulation of snail, zeb1, and vimentin expression, indicating that EMT potentially occurred in transformed 4.1B iMEFs. Moreover, we showed that 4.1B interacted with E-cadherin in MEF cells. Thus, our study provides previously unidentified roles and mechanisms of 4.1B in cellular transformation. © 2016 Wiley Periodicals, Inc.

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Untitled

Cited by 29 publications

References 13 publications

A General Method for Generating Discrete Orthogonal Matrices

A General Method for Generating Discrete Orthogonal Matrices

Image representation based on fractional order Legendre and Laguerre orthogonal moments

Knockout of 4.1B triggers malignant transformation in SV40T‐immortalized mouse embryo fibroblast cells

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