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

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high tem poral resolution imaging, there is a growing need to remove these noise art ifacts. The noise in magnitude MR images is signal-dependent (Rician), wher eas most de-noising algorithms assume additive Gaussian (white) noise. Howe ver, the Rician distribution only looks Gaussian at high SNR. Some recent w ork by Nowak employs a wavelet-based method for de-noising the square magni tude images, and explicitly takes into account the Rician nature of the noi se distribution. In this article, we apply a wavelet de-noising algorithm d irectly to the complex image obtained as the Fourier transform of the raw k -space two-channel (real and imaginary) data. By retaining the complex imag e, 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 a lgorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested o n 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 mi cro-images acquired using gradient echo and spin echo sequences. For the si mulated data, the original image could be well recovered even for high valu es of noise (SNR approximate to 0 dB), suggesting that the present algorith m may provide better recovery of the contrast than Nowak's method. The mean -square error, bias, and variance are computed for the simulated images. Ov er a range of amounts of added noise, the present method is shown to give s maller bias than when using a soft threshold, and smaller variance than a h ard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast im provements of up to 8% (for SNR = 33 dB) were found. In general, the improv ement in contrast was greater the lower the original SNR, for example, up t o 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applica tions of the algorithm to the segmentation of medical images, to micro-imag ing 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. (C) 2000 Elsevier Science Inc. All rig hts reserved.