An efficient algorithm for denoising MR and CT images using digital curvelet transform

This chapter presents a curvelet-based approach for the denoising of magnetic resonance (MR) and computed tomography (CT) images. Curvelet transform is a new multiscale representation suited for objects which are smooth away from discontinuities across curves, which was developed by Candies and Donoho (Proceedings of Curves and Surfaces IV, France:105-121, 1999). We apply these digital transforms to the denoising of some standard MR and CT images embedded in white noise, random noise, and poisson noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state-of-the-art" techniques based on wavelet transform methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Since medical images have several objects and curved shapes, it is expected that curvelet transform would be better in their denoising. The simulation results show the outperforms than wavelet transform in the denoising of both MR and CT images from both visual quality and the peak signal-to-noise (PSNR) ratio points of view.