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The generation of magnitude magnetic resonance images comprises a sequence of data encodings or transformations, from detection of an analog electrical signal to a digital phase/frequency k-space to a complex image space via an inverse Fourier transform and finally to a magnitude image space via a magnitude transformation and rescaling. Noise present in the original signal is transformed at each step of this sequence. Denoising MR images from low field strength scanners is important because such images exhibit low signal to noise ratio. Algorithms that perform denoising of magnetic resonance images may be usefully classified according to the data domain on which they operate (i.e. at which step of the sequence of transformations they are applied) and the underlying statistical distribution of the noise they assume. This latter dimension is important because the noise distribution for low SNR images may be decidedly non-Gaussian. Examples of denoising algorithms include 2D wavelet thresholding (operates on the wavelet transform of the magnitude image; assumes Gaussian noise), Nowak's 2D wavelet filter (operates on the squared wavelet transform of the magnitude image; assumes Rician noise), Alexander et. al.'s complex 2D filters (operates on the wavelet transform of the complex image space; assumes Gaussian noise), wavelet packet denoising (wavelet packet transformation of magnitude image; assumes Rician noise) and anisotropic diffusion filtering (operates directly on magnitude image; no assumptions on noise distribution). Effective denoising of MR images must take into account both the availability of the underlying data, and the distribution of the noise to be removed. We classify a number of recently published denoising algorithms and compare their performance on images from a 0.35T permanent magnet MR scanner.
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