A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Fast Discrete Approximation Algorithm for the Radon Transform
SIAM Journal on Computing
Discrete analytical hyperplanes
Graphical Models and Image Processing
Signal Processing - Image and Video Coding beyond Standards
Image Representation Via a Finite Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
The curvelet transform for image denoising
IEEE Transactions on Image Processing
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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.