The paper introduces and discusses the implementation of two new mathematical transforms, the ridgelet transform and the curvelet transform, for image denoising. These transforms are designed to offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. The ridgelet transform is based on wavelet analysis in the Radon domain, while the curvelet transform uses ridgelets as a component step and implements curvelet subbands using a filter bank of \( \alpha \)- trous wavelet filters. The authors apply these transforms to denoise standard images embedded in white noise and find that simple thresholding of the curvelet coefficients is competitive with state-of-the-art techniques based on wavelets. The curvelet reconstructions exhibit higher perceptual quality, particularly in edge and linear feature recovery. The theoretical foundations of the curvelet and ridgelet transforms suggest that these methods can outperform wavelet-based approaches in certain image reconstruction problems, and empirical results support this claim.The paper introduces and discusses the implementation of two new mathematical transforms, the ridgelet transform and the curvelet transform, for image denoising. These transforms are designed to offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. The ridgelet transform is based on wavelet analysis in the Radon domain, while the curvelet transform uses ridgelets as a component step and implements curvelet subbands using a filter bank of \( \alpha \)- trous wavelet filters. The authors apply these transforms to denoise standard images embedded in white noise and find that simple thresholding of the curvelet coefficients is competitive with state-of-the-art techniques based on wavelets. The curvelet reconstructions exhibit higher perceptual quality, particularly in edge and linear feature recovery. The theoretical foundations of the curvelet and ridgelet transforms suggest that these methods can outperform wavelet-based approaches in certain image reconstruction problems, and empirical results support this claim.