Comparative study of Wavelet transform and Fourier domain filtering for medical image denoising

Denoising of images is a crucial preprocessing step in medical imaging, essential for improving diagnostic clarity. While the deep learning methods offer state-of-the-art performance, their computational complexity and data requirements can be prohibitive. This study is twofold. In the first part, we compare the efficiency of various Discrete Wavelet Transform (DWT) filters combined with different thresholding functions for denoising medical images corrupted by Gaussian, Uniform, Poisson, and Salt-and-Pepper noise. In the second part, we compare the denoising results obtained using DWT with those achieved by a block-based Discrete Fourier Cosine Transform (DFCT) approach. The results indicate that DWT-based denoising methods perform best when using Biorthogonal Spline and Daubechies wavelets. However, in contrast to the commonly held assumption that wavelets are superior due to their multi-resolution capabilities, the block-based DFCT method consistently outperforms a global DWT approach across all noise types and performance metrics (SNR, PSNR, IM). We attribute DFCT's outperformed to its localized processing strategy, which better adapts to local image statistics and preserves fine structural details while minimizing global artifacts. Those findings emphasize the importance of algorithmic selection based on processing methodology rather than solely on transform properties. Overall, the study suggests that, block-based DFCT filtering offers an effective and efficient denoising tool for medical imaging applications.