We develop an analytic approach to the Radon transform f̂(ζ) = ∫ τ⊂ζ f(τ), where f(τ) is a function on the affine Grassmann manifold G(n, k) of k-dimensional planes in Rn, and ζ is a k′-dimensional plane in the similar manifold G(n, k′), k′ > k. For f ∈ Lp(G(n, k)), we prove that this transform is finite almost everywhere on G(n, k′) if and only if 1 ≤ p < (n− k)/(k′− k), and obtain explicit inv...

in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

one of the common problems in reflective seismic records is the existence of coherent linear and random noises which cause covering of the most important parts of reflective signals; therefore, it is necessary to attenuate them by processing methods. several processing techniques have been devised for attenuation of coherent linear noises and linear radon or ?-? transform is a powerful techniqu...

In this contribution, the F 1-transform of functions of two variables is introduced. It combines properties of the F-transform of functions of two variables and the F 1-transform of functions of one variable. The aim of this study is to prove approximation properties of the F 1-transform components and of the inverse F 1-transform in this particular case.

We investigate the relationship between the Radon transform and certain phase space localization functions, namely the continuous Gabor and wavelet transforms. We derive inversion formulas for the Radon transform based on the Gabor and wavelet transform. Some of these formulas give a direct reconstruction of f or of 1=2 f from the Radon transform data. Others show how the Gabor and wavelet tran...

the radial trace transform was introduced by the stanford exploration project many years ago (ottolini, 1979 and claerbout, 1983), primarily for use in migration and imaging applications. it has been shown subsequently, because of its particular geometry, to be very useful for wavefield separation (claerbout, 1983) and coherent noise attenuation (henley, 1999). the radial trace transform, unlik...

We use the Battle.Lemarié scaling function in an algorithm for fast computation of the Fourier transform of a piecewise smooth function f. Namely, we compute for —N m, n N (with a given accuracy ) the integrals * ,1 1 • f(m, n) = I I 1(2;,y) dy (0.1) Jo JO in O(ND)+O(N2 log N) operations, where ND is the number of subdomains where the function f is smooth. We consider an application of this alg...