Denoising of complex MRI data by wavelet-domain filtering: Application to high-b-value diffusion-weighted imaging

The Rician distribution of noise in magnitude magnetic resonance (MR) images is particularly problematic in low signal-to-noise ratio (SNR) regions. The Rician noise distribution causes a nonzero minimum signal in the image, which is often referred to as the rectified noise floor. True low signal is likely to be concealed in the noise, and quantification is severely hampered in low-SNR regions. To address this problem we performed noise reduction (or denoising) by Wiener-like filtering in the wavelet domain. The filtering was applied to complex MRI data before construction of the magnitude image. The noise-reduction algorithm was applied to simulated and experimental diffusion-weighted (DW) images. Denoising considerably reduced the signal standard deviation (SD, by up to 87% in simulated images) and decreased the background noise floor (by approximately a factor of 6 in simulated and experimental images).