The Curvelet Transform for Image Denoising introduces ridgelet and curvelet transforms as alternatives to wavelet methods for image denoising. These transforms offer exact reconstruction, stability, ease of implementation, and low computational complexity. The ridgelet transform applies a special overcomplete wavelet pyramid to the Radon transform, while the curvelet transform uses ridgelet transforms and filter banks of trous wavelet filters. The philosophy is that transforms should be overcomplete rather than critically sampled. These transforms are applied to denoise images embedded in white noise, with simple thresholding of curvelet coefficients performing competitively with wavelet-based methods. Curvelet reconstructions exhibit higher perceptual quality, offering sharper images and better edge and curvilinear feature recovery. Theoretical results suggest curvelets can outperform wavelets in certain image reconstruction problems. Empirical results support this, showing higher PSNR on standard images like Barbara and Lenna. The paper discusses the theory and digital implementation of ridgelet and curvelet transforms, including their application to image denoising. The digital curvelet transform is based on a multiscale ridgelet pyramid and subband filtering. The algorithm involves subband decomposition, smooth partitioning, renormalization, and ridgelet analysis. The transform is redundant, with a redundancy factor of 16J + 1 for J scales. The transform is invertible, stable, and provides exact reconstruction. Filtering experiments show that curvelet transforms outperform wavelet methods in denoising, with higher PSNR and fewer artifacts. The paper concludes that curvelet transforms offer significant promise for image denoising.The Curvelet Transform for Image Denoising introduces ridgelet and curvelet transforms as alternatives to wavelet methods for image denoising. These transforms offer exact reconstruction, stability, ease of implementation, and low computational complexity. The ridgelet transform applies a special overcomplete wavelet pyramid to the Radon transform, while the curvelet transform uses ridgelet transforms and filter banks of trous wavelet filters. The philosophy is that transforms should be overcomplete rather than critically sampled. These transforms are applied to denoise images embedded in white noise, with simple thresholding of curvelet coefficients performing competitively with wavelet-based methods. Curvelet reconstructions exhibit higher perceptual quality, offering sharper images and better edge and curvilinear feature recovery. Theoretical results suggest curvelets can outperform wavelets in certain image reconstruction problems. Empirical results support this, showing higher PSNR on standard images like Barbara and Lenna. The paper discusses the theory and digital implementation of ridgelet and curvelet transforms, including their application to image denoising. The digital curvelet transform is based on a multiscale ridgelet pyramid and subband filtering. The algorithm involves subband decomposition, smooth partitioning, renormalization, and ridgelet analysis. The transform is redundant, with a redundancy factor of 16J + 1 for J scales. The transform is invertible, stable, and provides exact reconstruction. Filtering experiments show that curvelet transforms outperform wavelet methods in denoising, with higher PSNR and fewer artifacts. The paper concludes that curvelet transforms offer significant promise for image denoising.