Image Denoising Using Curvelet Transform

The Curvelet transform is a widely used method for image denoising that effectively reduces noise by extracting curvilinear features and edge information from images. In this implementation, we utilize a MATLAB 7.0 program to execute the Curvelet transform algorithm. The program employs a multi-scale geometric analysis approach where the image is decomposed into different frequency bands and orientations using ridgelet transforms in frequency domains. Key functions include implementing the discrete Curvelet transform via frequency wrapping or unequally spaced fast Fourier transforms (USFFT), followed by thresholding techniques to suppress noise components while preserving significant curve-based features. This denoising process enhances image clarity by selectively removing noise coefficients in the transform domain while maintaining important structural elements. The Curvelet transform serves as a powerful tool with broad applications in image processing, particularly effective for preserving edges and curved singularities that traditional wavelet transforms might模糊. The MATLAB implementation typically involves steps like curvelet coefficient computation, threshold selection (hard or soft thresholding), and inverse transform operations to reconstruct the denoised image.