2-D Stationary Wavelet Transform and 2-D Dual-Tree DWT for MRI Denoising

The noise emergence in the digital image can occur throughout image acquisition, transmission, and processing steps. Consequently, eliminating the noise from the digital image is required before further processing. This study aims to denoise noisy images (including Magnetic Resonance Images (MRIs)) by employing our proposed image denoising approach.

This proposed approach is based on the Stationary Wavelet Transform (SWT 2-D) and the 2 - D Dual-Tree Discrete Wavelet Transform (DWT). The first step of this approach consists of applying the 2 - D Dual-Tree DWT to the noisy image to obtain noisy wavelet coefficients. The second step of this approach consists of denoising each of these coefficients by applying an SWT 2-D based denoising technique. The denoised image is finally obtained by applying the inverse of the 2-D Dual-Tree DWT to the denoised coefficients obtained in the second step. The proposed image denoising approach is evaluated by comparing it to four denoising techniques existing in literature. The latters are the image denoising technique based on thresholding in the SWT-2D domain, the image denoising technique based on deep neural network, the image denoising technique based on soft thresholding in the domain of 2-D Dual-Tree DWT, and Non-local Means Filter.

The proposed denoising approach, and the other four techniques previously mentioned, are applied to a number of noisy grey scale images and noisy Magnetic Resonance Images (MRIs) and the obtained results are in terms of PSNR (Peak Signal to Noise Ratio), SSIM (Structural Similarity), NMSE (Normalized Mean Square Error) and Feature Similarity (FSIM). These results show that the proposed image denoising approach outperforms the other denoising techniques applied for our evaluation.

In comparison with the four denoising techniques applied for our evaluation, the proposed approach permits to obtain highest values of PSNR, SSIM and FSIM and the lowest values of NMSE. Moreover, in cases where the noise level σ = 10 or σ = 20, this approach permits the elimination of the noise from the noisy images and introduces slight distortions on the details of the original images. However, in case where σ = 30 or σ = 40, this approach eliminates a great part of the noise and introduces some distortions on the original images.

The performance of this approach is proven by comparing it to four image denoising techniques existing in literature. These techniques are the denoising technique based on thresholding in the SWT-2D domain, the image denoising technique based on a deep neural network, the image denoising technique based on soft thresholding in the domain of 2 - D Dual-Tree DWT and the Non-local Means Filter. All these denoising techniques, including our approach, are applied to a number of noisy grey scale images and noisy MRIs, and the obtained results are in terms of PSNR (Peak Signal to Noise Ratio), SSIM(Structural Similarity), NMSE (Normalized Mean Square Error) and FSIM (Feature Similarity). These results show that this proposed approach outperforms the four denoising techniques applied for our evaluation.