In this paper we formulate the Radon transform as a wnvolution integral over the Euclidean motion group (SE(2)) and provideaminimummean square error(MMSE) stochastic deconvolution method for the Radon transform inversion. Proposed approach provides a fundamentally new formulation that can model nonstationary signal and noise fields. Key components of our development are the Fourier transform ov...

In [14], P.Schapira obtained a formula for RS in the general situation. This formula gives an inversion formula for the Radon transform of constructible functions from a real projective space to its dual in the case when the whole dimension is odd. We can, that is, reconstruct a constructible function φ on the projective space from its Radon transform RS(φ). This topological meaning is that we ...

The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension 3 we prove that the Radon transform is one-to-one on the space of continuous functions K on the boundary which are invariant with respect to the corresponding group of symmetries. We prove also that the frequency map associated with a class of Liouville ...

In this paper, Gait Energy Image (GEI) has constructed to apply Principal Component Analysis (PCA) with and without Radon Transform (RT). The Radon Transform is used to detect features within an image and PCA is used to reduce dimension of the images without much loss of information. The side view of slow walk; fast walk and carrying a ball walk have been selected from the CMU MoBo database for...

New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GRmethod consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GRmethod pr...

It is widely recognised that the most popular manner of image representation is obtained by using an energy-preserving transform, like the Fourier transform. However, since the advent of computerised tomography in the 70s, another manner of image representation has also entered the center of interest. This new type is the projection space representation, obtained via the Radon transform. Method...