In view of characteristics of digital image,such as bulk data capacity,high redundancy and poor security, a new image encryption algorithm was put forward by combining chaotic maps with wavelet transform. Mallat algorithm in wavelet transform firstly was used to decompose the original image, leaving only the lowfrequency information, and then oversampled Chebyshev chaotic maps were used to achi...

This paper presents an improved approach where the wavelet functions are developed for particularly two-dimensional (2D) trusses. In the proposed scheme, a clear-cut formulation in a fluent manner has been derived to numerically solve the second-ordered differential equation of motion governing 2D trusses using two different types of basis functions including, complicated Chebyshev and simple H...

Stochastic fractional differential equations (SFDEs) have many physical applications in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, a new wavelet Galerkin method is proposed for numerical solution of SFDEs. First, fractional and stochastic operational matrices for the Chebyshev wavelets are introduced. Then, these opera...

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the mu...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet tra...

A novel method for solving optimal tracking control of linear quadratic time-varying systems with differentforms time delays in state and input variables constraints is presented this paper. Using the concepts two powerful wavelets, Legendre Chebyshev we convert problem to a static optimization one. The general from by which one can utilize it other wavelets. proposed has ability solve problems...

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...