Multi-linear Generalised Radon Transforms 2

Multi - linear Generalised Radon Transforms 1 Jonathan

Shot interpolation for radon multiple suppression

Decreased CMP fold, such as that found in multi-source, multi-streamer acquisition geometries, can hinder processing steps which benefit from well sampled CMP gathers, such as radon transforms. In two steps of linear least squares, multiscale prediction-error filters (PEF)s can estimate local dips from the recorded data and then use the dip information to fill in unrecorded shot or receiver gat...

Discrete Analogues in Harmonic Analysis , I : ` 2 Estimates for Singular Radon Transforms

This paper studies the discrete analogues of singular Radon transforms. We prove the `2 boundedness for those operators that are “quasi-translation-invariant.” The approach used is related to the “circle-method” of Hardy and Littlewood, and requires multi-dimensional extensions of Weyl sums and Gauss sums, as well as variants that replace scalar sums by operator sums.

Combining the Radon, Markov, and Stieltjes Transforms for Object Reconstruction

In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. By virtue of the relation between the Radon transform, the Fourier transform and the 2-dimensional inverse Fourier transform, the shape of an object can be reconstructed from the knowledge of the object’s Radon transform. Unfortunately, a discrete implementation requires the use of interpolation techniques, s...

Radon Transforms and the Finite General Linear Groups

Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approach is analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used...