in this paper‎, ‎based on cas wavelets we present quadrature rules for numerical solution‎ ‎of double and triple integrals with variable limits of integration‎. ‎to construct new method‎, ‎first‎, ‎we approximate the unknown function by cas wavelets‎. ‎then by using suitable collocation points‎, ‎we obtain the cas wavelet coefficients that these coefficients are applied in approximating the unk...

Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on 1 the Galerking method, 2 the Shannon wavelet representation, 3 the decorrelation of the generalized Shannon sampling theorem, and 4 the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing function...

Hilbert transform of wavelets has been used to approximate functions in L2(R) . It is proved that Hilbert transform of wavelets with many vanishing moments does a good job in approximating smooth functions in L2(R) . We also prove that Hölder continuity of a function helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we give a result that relates the Hilb...

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. In fact, we demonstrate that only a few coefficients of the approximation ...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

The problem of estimating the power spectra of non-stationary stochastic processes by using the harmonic wavelet transform is addressed in this paper. Conventional spectral analysis provides spectral coefficients that are averaged over time and thus, does not represent the evolutionary behavior of power spectra of non-stationary processes. In this study, evolutionary power spectrum of a non-sta...

The de-noising is a challenging task in the field of signal and image processing. Any natural image corrupted by gussian noise can be de-noised using wavelet method. Wavelet-based image denoising is an important technique in the area of image noise reduction. Wavelets have their natural ability to represent images in a very sparse form which is the foundation of wavelet-based denoising through ...

We introduce a sparse image representation that takes advantage of the geometrical regularity of edges in images. A new class of one-dimensional wavelet orthonormal bases, called foveal wavelets, are introduced to detect and reconstruct singularities. Foveal wavelets are extended in two dimensions, to follow the geometry of arbitrary curves. The resulting two dimensional “bandelets” define orth...