Image Denoising Using Curvelet Transform

In the field of image processing, the Curvelet transform has emerged as an efficient denoising tool due to its excellent multiscale analysis and directional sensitivity characteristics. Compared to traditional wavelet transforms, Curvelet can better capture curved features and edge information in images, making it particularly outstanding when processing images with complex textures.

The core concept of Curvelet transform involves decomposing images into different scales and directions, forming a sparse representation. This sparsity means that the main energy of the image concentrates on a few coefficients, while noise typically distributes more broadly. Based on this characteristic, the denoising process usually employs thresholding methods - preserving larger transform coefficients (corresponding to genuine image structures) while suppressing smaller coefficients (likely corresponding to noise).

Implementing Curvelet denoising in MATLAB typically requires using Curvelet transform toolboxes (such as CurveLab). The implementation approach generally includes the following steps: First, perform Curvelet decomposition on the noisy image to obtain coefficients at different scales and directions; then select appropriate thresholding rules (like soft thresholding or hard thresholding) based on noise statistical characteristics (such as Gaussian noise variance); finally reconstruct the image through inverse transformation. Key functions in implementation include fdct_usfft() for forward transform and ifdct_usfft() for inverse transform, with thresholding operations applied to coefficient matrices between these transformations.

Compared to traditional methods, Curvelet-based denoising techniques can more effectively preserve edge and detail information, making them particularly suitable for applications requiring high detail fidelity such as medical imaging and remote sensing images. However, their computational complexity is relatively high, requiring careful consideration of performance versus effectiveness trade-offs in real-time applications.