A new digital implementation of ridgelet transform for images of dyadic length

Abstract

Ridgelet transform is a new directional multi-resolution transform and it is more suitable for describing the signals with high dimensional singularities. Finite ridgelet transform is a discrete version of ridgelet transform, which is as numerical precision as the continuous ridgelet transform and has low computational complexity. However, finite ridgelet transform is only suitable for images of prime-pixels length, which is a limitation of its applications in image processing. In this paper, a new digital implementation of ridgelet transform that is suitable for images of dyadic length is proposed. This method not only expands the applications of finite ridgelet transform, but also simplifies the algorithm. First, we introduce the concept of ridgelet transform in the continuous domain. Then, we illustrate finite ridgelet transform and the new method. Finally, we compare the new method with finite ridgelet transform by applying both digital ridgelet transforms to the denoising of images embedded in additive white Gaussian noise and the new method gets a better performance in image denoising. The new algorithm can also be used as the important building block in curvelet transform and get surprising visual performances in denoising for natural image.