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...

Patch-based denoising methods have recently emerged due to its good denoising performance. In this paper, based on analysis of the optimal over-complete patch aggregation, we highlight the importance of a local transform for good image features representation. A finite Radon transform (FRAT) based two-stage over-complete image denoising algorithm is then proposed for obtaining good visual quali...

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...

This paper presents a discrete generalized multi-directional Radon transform (GMDRT) and its exact inversion algorithm. GMDRT is an extension of the classical Radon transform. It aims to project parameterized curves and geometric objects following several directions. For this purpose, we propose an algebraic formalism of the Radon Transform presenting the forward transform as a matrix-vector_ m...

For the automatic detection of retinal blood vessels a preprocessing of the noisy original images is necessary. Retinal blood vessels are assumed to be line-like structures and can therefore be enhanced via convolution with suitable, elongated kernels. Consequently we use the local Radon kernel as a prototype of an elongated kernel for this task. The Radon kernel is rotated at different angles ...

Abstract Vectorial optical field-based spatially polarization modulation has been widely studied for measurement due to its simple system structure. In this system, the information is encoded in irradiance image, and can be realized by image processing. The classical processing methods could not meet increasing demand of practical applications their poor computational efficiency. To address iss...

In this paper, an effective and reliable skew estimation technique for machine printed documents and photos using radon transform is proposed and is compared with other methods used for skew estimation such as Fast Fourier Transform (FFT), Hough Transform (HT), combination of Horizontal Projection Profile (HPP) and Hough Transform, combination of Gabor filter and Radon transform, combination of...

The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite codimension in standard function spaces. Range descriptio...