The problem of recovering an image from noisy data arises in many different areas of scientific investigation and medical imaging. The traditional methods behave poorly when the object to recover has edges.

A new system of representation, namely, the curvelets, was developed over several years in an attempt to break an inherent limit plaguing wavelet denoising of images. The author(1) and standard images were denoised using both wavelet and curvelet transforms and results are presented in this paper. It has been found that 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. Existing theory for curvelet transform suggests that this new approach can outperform wavelet methods in certain image reconstruction problems, such as image denoising and compression.