Discrete analytical Ridgelet transform

Abstract

In this paper, we present a new implementation of the Ridgelet transform based on discrete analytical 2-D lines: the discrete analytical Ridgelet transform (DART). This transform uses the Fourier strategy for the computation of the associated discrete Radon transform. The innovative step of the DART is the construction of discrete analytical lines in the Fourier domain. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a DART adapted to a specific application. Indeed, the DART representation is not orthogonal it is associated with a flexible redundancy factor. The DART has a very simple forward/inverse algorithm that provides an exact reconstruction. We apply the DART and its extension to a local-DART (with smooth windowing) to the denoising of some images. These experimental results show that the simple thresholding of the DART coefficients is competitive or more effective than the classical denoising techniques.