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

TL;DR

This study systematically compares two transform-domain denoising strategies for medical images: a global Discrete Wavelet Transform (DWT) method and a block-based Discrete Fourier Cosine Transform (DFCT) approach. Using a 512×512 CT image contaminated with Gaussian, Uniform, Poisson, and Salt-and-Pepper noise, the authors evaluate performance with $SNR$, $PSNR$, and $IM$ across multiple wavelet families and thresholding rules, alongside a blockwise DFCT filter with local processing. The central finding is that the block-based DFCT consistently outperforms the global DWT across all noise types, attributing gains to local adaptation and suppression of global artifacts. The work underscores that processing framework can dominate transform properties in practical denoising and positions block-based DFCT as an effective, efficient option for clinical imaging tasks, with future work focusing on adaptive local-wavelet strategies to bridge any remaining gaps.

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.

Figures (11)

• Figure 1: Three-level decomposition of an image into sub-bands using a 2D Discrete Wavelet Transform.
• Figure 2: Test image used for denoising evaluation: (a) original clean CT scan; and its noisy versions corrupted with (b) Gaussian noise ($\sigma=25$); (c) uniform noise; (d) Poisson noise ($\sigma=42.85$); (e) salt-and-pepper noise (density $=0.02$).
• Figure 3: Denoising performance (PSNR in dB) for Gaussian noise: comparison of the top four thresholding functions for each wavelet filter.
• Figure 4: Denoising performance (PSNR in dB) for uniform noise: comparison of the top four thresholding functions for each wavelet filter.
• Figure 5: Denoising performance (PSNR in dB) for Poisson noise: comparison of the top four thresholding functions for each wavelet filter.