A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR approximately 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak's method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.