Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition

Pei, Soo‐Chang; Huang, Shih-Gu

doi:10.1364/josaa.33.000214

Cited by 16 publications

(10 citation statements)

References 37 publications

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“…The two-dimensional non-separable LCT (2D-NS-LCT) with parameter M [A, B; C, D] of a signal f ∈ L 2 (R 2 ) is defined by [32][33][34][35][36]…”

Section: Preliminariesmentioning

confidence: 99%

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Huo¹,

Xiao²

2021

Preprint

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In this paper, we investigate the multivariate dynamical sampling problem in l 2 (Z 2 ) associated with the two-dimensional discrete time non-separable linear canonical transform (2D-DT-NS-LCT) and shift-invariant spaces associated with the two-dimensional non-separable linear canonical transform (2D-NS-LCT), respectively. Specifically, we derive a sufficient and necessary condition under which a sequence in l 2 (Z 2 ) (or a function in a shift-invariant space) can be stably recovered from its dynamical sampling measurements associated with the 2D-DT-NS-LCT (or the 2D-NS-LCT). We also present a simple example to elucidate our main results.

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“…The two-dimensional non-separable LCT (2D-NS-LCT) with parameter M [A, B; C, D] of a signal f ∈ L 2 (R 2 ) is defined by [32][33][34][35][36]…”

Section: Preliminariesmentioning

confidence: 99%

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Huo¹,

Xiao²

2021

Preprint

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“…eir results show that the original voice cannot be retrieved unless the correct keys and correct domain orders are used. Number of papers published in the linear canonical transform have been studied [38][39][40][41][42][43][44][45][46][47][48][49]. Wang et al [50][51][52][53][54][55][56][57][58][59][60][61] proposed the highdimension Lorenz chaotic system and perceptron model, a chaotic image encryption system.…”

Section: Introductionmentioning

confidence: 99%

A Secure Asymmetric Optical Image Encryption Based on Phase Truncation and Singular Value Decomposition in Linear Canonical Transform Domain

Sangwan

Singh

2021

International Journal of Optics

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A new asymmetric optical double image encryption algorithm is proposed, which combines phase truncation and singular value decomposition. The plain text is encrypted with two-stage phase keys to obtain a uniformly distributed cipher text and two new decryption keys. These keys are generated during the encryption process and are different from encryption keys. It realizes asymmetric encryption and improves the security of the system. The unscrambling keys in the encryption operation are mainly related to plain text. At the same time, the system is more resistant to selective plain text attacks; it also improves the sensitivity of decryption keys. With the application of phase truncation, the key space expanded and the security of the cryptographic system is enhanced. The efficacy of the system is calculated by evaluating the estimated error between the input and retrieved images. The proposed technique provides innumerable security keys and is robust against various potential attacks. Numerical simulations verify the effectiveness and security of the proposed technique.

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“…The linear canonical transform (LCT) 1–9 is a four‐parameter ( a , b , c , d ) class of linear integral transforms, which plays an important role in optics and digital signal processing. Let

A = false(a, b; c, d false), a, b, c, d \in ℝ

, and

a d - b c = 1

, then the LCT of a signal

f false(x false) \in L^{2} false(ℝ false)

associated with parameter A is defined by

L_{f}^{A} false(u false) = {scriptL}_{A} false{f false(x false) false} false(u false) = ({, \begin{matrix} left left \\ array \int_{ℝ} f (x) K_{A} (u, x) d x, & array b \neq 0, \\ array \sqrt{d} e^{j \frac{c d}{2} u^{2}} f (d u), & array b = 0, \end{matrix})

where

K_{A} (u, x) = \sqrt{\frac{1}{j 2 π b}} e^{j \frac{a}{2 b} x^{2} - j \frac{1}{b} u x + j \frac{d}{2 b} u^{2}} .

By choosing specific values for parameter A , several well‐known linear transforms turn out to be special cases of the LCT in (), for example, Fourier transform, fractional Fourier transform (FrFT), and Fresnel transform.…”

Section: Introductionmentioning

confidence: 99%

Truncation error estimates for two‐dimensional sampling series associated with the linear canonical transform

Huo

2021

Math Methods in App Sciences

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The linear canonical transform (LCT) provides a more general framework for many well‐known linear integral transforms, such as Fourier transform, fractional Fourier transform, Fresnel transform, and so forth, in digital signal processing and optics. There has been a great deal of research on sampling expansions of bandlimited signals in the LCT domain. However, results on error estimation and convergence analysis appear to be relatively rare, especially for multi‐dimensional sampling series associated with the LCT. In this paper, we present error estimation and convergence analysis for two‐dimensional (2D) sampling series in the LCT domain. Specifically, we first prove the absolute convergence and uniform convergence of 2D LCT sampling series. Then, we analyze truncation error estimates for uniformly sampling 2D bandlimited signals in the LCT domain, as well as deriving three truncation error bounds. Finally, our theoretical results are demonstrated by numerical examples.

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Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition

Cited by 16 publications

References 37 publications

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

A Secure Asymmetric Optical Image Encryption Based on Phase Truncation and Singular Value Decomposition in Linear Canonical Transform Domain

Truncation error estimates for two‐dimensional sampling series associated with the linear canonical transform

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