Ridgelet Decomposition: Discrete Implementation and Color Denoising

Philippe Carré (1) , David Helbert (1)

1 SIC - SIGNAL-IMAGE-COMMUNICATION

In this paper, we review an implementation of the Ridgelet transform: The Discrete Analytical Ridgelet Transform (DART). This transform uses the Fourier strategy for the computation of the associated 2-D and 3-D discrete Radon transforms. The innovative step is the definition of a discrete 3-D transform and 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 without any iterative method. We had proved in different publications that the 2D and 3D DART are performant for the level of greys images restorations. Therefore we have interesting to 2D/3D color image restorations. We have compared the restoration results in function of different color space definition and importance of the white Gaussian noise. We criticize our results with two different measures : the Signal Noise Ratio calculation and perceptual measures to evaluate the perceptual colour difference between original and denoised images. These experimental results show that the simple thresholding of the DART coefficients is competitive than classical denoising techniques.

Domaines: Traitement des images [eess.IV]

Philippe Carré, David Helbert. Ridgelet Decomposition: Discrete Implementation and Color Denoising. Wavelet Applications in Industrial Processing III, Oct 2005, Boston, MA, United States. ⟨10.1117/12.629569⟩. ⟨hal-00331496⟩