Paper Info
Title
On locality of Radon to Riesz transform
Abstract
In this paper we present a novel approach to locally compute the Riesz transform from the knowledge of the Radon transform. Previous implementations of the Riesz transform are based on the Fourier or the Radon transforms and their inversion formulae, and therefore needs for the knowledge of the function or its Radon data on the whole domain. More recent attempts on rectangular domains involves convolutions with the Poisson kernel and local derivatives. On the other hand, starting from the links between the Riesz and the Radon transforms, we address in this paper a new local Radon based Riesz formula in the general n-dimensional case, for even n. The advantage of this formula, local in the Radon space, is pointed out in the bidimensional case, where we provide a new local Radon based Riesz algorithm, and conduct numerical tests for the estimation of the Riesz transform on convex sets, from truncated Radon data. Finally we study the robustness to noise of the current approach. HighlightsWe propose a new Radon based Riesz transform formula, local in Radon space, in even dimension.The formula is based on derivatives of the Radon data followed by weighted backprojections.The Riesz transform can thus be computed on images regions from truncated Radon data.Numerical experiments show that the Riesz transform can be exactly computed from truncated Radon data (i.e. with no error).Local orientations can be computed from the local Radon based Riesz transform.
Year
DOI
Venue
2016
10.1016/j.sigpro.2015.07.024
Signal Processing
Keywords
Field
DocType
Riesz transform,Hilbert transform,Radon transform,Local reconstruction
Mathematical analysis,Radon space,Convolution,Radon,Fourier transform,Hilbert transform,Radon transform,Riesz transform,Mathematics,Riesz potential
Journal
Volume
Issue
ISSN
120
C
0165-1684
Citations 
PageRank 
References 
1
0.36
7
Authors
2
Name
Order
Citations
PageRank
Laurent Desbat1336.39
ValÉrie Perrier2999.27