A new denoising method for fMRI based on weighted three-dimensional wavelet transform

This study presents a new three-dimensional discrete wavelet transform (3D-DWT)-based denoising method for functional magnetic resonance images (fMRI). This method is called weighted three-dimensional discrete wavelet transform (w-3D-DWT), and it is based on the principle of weighting the volume subbands which are obtained by 3D-DWT. Briefly, classical DWT denoising consists of wavelet decomposition, thresholding, and image reconstruction steps. In the thresholding algorithm, the thresholding value for each image cannot be chosen exclusively. Namely, a specific thresholding value is chosen and it is used for all images. The proposed algorithm in this study can be considered as a data-driven denoising model for fMRI. It consists of three-dimensional wavelet decomposition, subband weighting, and image reconstruction. The purposes of subband weighting algorithm are to increase the effect of the subband which represents the image better and to decrease the effect of the subband which represents the image in the worst way and thus to reduce the noises of the image adaptively. fMRI is one of the popular methods used to understand brain functions which are often corrupted by noises from various sources. The traditional denoising method used in fMRI is smoothing images with a Gaussian kernel. This study suggests an adaptive approach for fMRI filtering different from Gaussian smoothing and 3D-DWT thresholding. In this study, w-3D-DWT denoising results were evaluated with mean-square error (MSE), peak signal/noise ratio (PSNR), and structural similarity (SSIM) metrics, and the results were compared with Gaussian smoothing and 3D-DWT thresholding methods. According to this comparison, w-3D-DWT gave low-MSE and high-PSNR results for fMRI data.