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

Abstract: Denoising of images is a crucial preprocessing step in medical imaging, essential for improving diagnostic clarity. While deep learning methods offer state-of-the-art performance, their computational complexity and data requirements can be prohibitive. In this study we present a comprehensive comparative analysis of two classical, computationally efficient transform-domain techniques: Discrete Wavelet Transform (DWT) and Discrete Fourier Cosine Transform (DFCT) filtering. We evaluated their efficacy in denoising medical images which corrupted by Gaussian, Uniform, Poisson, and Salt-and-Pepper noise. Contrary to the common hypothesis favoring wavelets for their multi-resolution capabilities, our results demonstrate that a block-based DFCT approach consistently and significantly outperforms a global DWT approach across all noise types and performance metrics (SNR, PSNR, IM). We attribute DFCT's superior performance to its localized processing strategy, which better preserves fine details by operating on small image blocks, effectively adapting to local statistics without introducing global artifacts. This finding underscores the importance of algorithmic selection based on processing methodology, not just transform properties, and positions DFCT as a highly effective and efficient denoising tool for practical medical imaging applications.