In this work, we study and analyze the contourlet transform for low bit-rate image coding. This image-based geometrical transform has been recently introduced to efficiently represent images with a spars set of coefficients. In order to explore the potentiality of this new transform as a tool for image coding, we developed a direct coding scheme that is based on using non-linear approximation o...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

The purpose of this document is to summarize main points of the paper, “Numerical Inversion of Laplace Transforms of Probability Distributions”, and provide R code for the Euler method that is described in the paper. The code is used to invert the Laplace transform of some popular functions. Context Laplace transform is a useful mathematical tool that one must be familiar with, while doing appl...

We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf (a, b, θ) of functions f(x1, x2) on R , into a transform domain with continuous scale a > 0, location b ∈ R, and orientation θ ∈ [0, 2π). The transform is defined by Γf (a, b, θ) = 〈f, γabθ〉 where the inner products project f onto analyzing elements called curvelets γabθ which are smooth and of rapid decay away from an a by √ ...

The symmetric spaces the title refers to are the spaces X = G=K where G is a connected semisimple Lie group with nite center and K is a maximal compact subgroup. The Fourier transform on X is deened by means of the Iwasawa decomposition G = NAK of G where N is nilpotent and A abelian. Let g; n; a; k denote the corresponding Lie algebras. We also need the group M = K A ; the centralizer of A in ...

The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y) 7→ H(f)(x) = ∫∞ 0 J0(2 √ xy)f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dede...

Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...

In this paper we devise a method for recovering band limited signals which have been subjected to a distorting procedure called companding. A band limited signal is a function in L2 whose Fourier transform vanishes outside of a bounded interval. In practice most real signals are in this class since they have no indefinitely high frequency components. The operation of companding a signal f(t) co...

We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective support obeying the parabolic scaling principle length ≈ width. Our comparisons allow to extend Theorems known for one decomposition to others. We start from a Continuous Curvelet Transform f → Γf ...