The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform [3] and the curvelet transform [7, 6]. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of `a trous wavelet filters. Our philosophy ...

• Type: Conference
• Year: 2001
• Where: ICIP
• Authors: Emmanuel J. Candès
• Keywords: Digital Radon Transform, ICIP 2001, Image Processing, Ridgelet Transform, Undecimated Wavelet Transforms