Curvelet Transform for Image Denoising

The Curvelet transform represents an advanced multi-scale transformation evolved from wavelet transform principles. Unlike wavelet transforms that primarily utilize scale and position parameters, Curvelet transforms integrate additional orientation parameters, granting them enhanced directional sensitivity. Our implementation presents a robust image denoising methodology leveraging Curvelet transform capabilities. The algorithm operates through multi-scale decomposition using Fast Discrete Curvelet Transform (FDCT) via wrapping, where image data undergoes frequency domain partitioning into multiple scales and angles. Key implementation steps include thresholding Curvelet coefficients through soft/hard thresholding functions, with noise variance estimation using median absolute deviation on finest scale coefficients. This approach effectively preserves edge information while eliminating noise artifacts through directional filtering across multiple orientations, significantly improving image quality and clarity through optimized coefficient manipulation and inverse transformation processes.