Related papers: The ridgelet transform of distributions
We introduce and study the directional Stockwell transform as a hybrid of the directional short-time Fourier transform and the ridgelet transform. We prove an extended Parseval identity and a reconstruction formula for this transform, as…
We define and study the (minimal) Radon transform on a real symmetric variety.
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…
We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional…
Let $\mathscr Q$ be the quaternion Heisenberg group, and let $\mathbf P$ be the affine automorphism group of $\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary…
We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation…
We revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its…
In this article, we explore convolutions of distributions with distributions given by (weighted) line integration. We also explore the scattering of singularities of such convolutions.
The wavefront set provides a precise description of the singularities of a distribution. Because of its ability to control the product of distributions, the wavefront set was a key element of recent progress in renormalized quantum field…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
Singularities of the Radon transform of a piecewise smooth function $f(x)$, $x\in R^n$, $n\geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $f(x)$ are…
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of…
We show that the use of Brylinski's Radon transform elucidates some points of the Green-Griffiths approach to the Hodge conjecture.
Diffusion processes associated with semi-Dirichlet forms are studied in the paper. The main results are Fukushima's decomposition for the diffusions and a transformation formula for the corresponding martingale part of the decomposition.…