Complex denoising of MR data via wavelet analysis: application for functional MRI

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.