Sliced Ridgelet Transform for Image Denoising

Image denoising based on curvelet transforms gives better results than image denoising based on the standard ridgelet transforms. This paper introduces an approach for image denoising that is based on ridgelets computed in a localized manner and that is computationally less intensive than curvelets, but with similar denoising performance. In this localized ridgelet transform, denoted sliced ridgelet transform, the ridge function is divided into several slices of constant length. The projection of each slice at a certain angle is computed and followed by a one-dimensional wavelet transform, to produce the ridgelet coefficients for each slice. The denoising operation corresponds to a simple thresholding of these ridgelet coefficients. Finally, inverse wavelet transform and inverse Radon transform are applied to the denoised ridgelet coefficients, to reconstruct a denoised version of the input image.