20 March 2006 Noise reduction from magnetic resonance images using nonseperable transforms
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Multi-scale transforms have got a lot of applications in image processing, in recent years. Wavelet transform is a powerful multiscale transform for denoising noisy signals and images, but the usual two-dimensional separable wavelets are sub-optimal. These separable wavelet transforms can successfully identify zero dimensional singularities in images, but can weakly identify one dimensional singularities such as edges, curves and lines. In this sense, non-separable transforms such as Ridgelet and Curvelet transforms are proposed by Candes and Donoho. The coefficients produced by these non-separable transforms have shown to be sparser than wavelet coefficients. This fact results in better denoising capabilities than wavelet transform. These new non-separable transforms can identify direction in lines and curves, because of special structure of their basis elements. Basically, Magnetic Resonance images are probable to have Rician noise. In some special cases, this kind of noise can be supposed to be white Gaussian noise. In this paper, a new method for denoising MR images is proposed. This method is based on Monoscale Ridgelet transform. It is shown that this two transform can successfully denoise MR images embedded in white Gaussian noise. The results are better in comparison with usual wavelet denoising methods, based on both visual perception and signal-to-noise ratio.
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Ehsan Nezhadarya, Ehsan Nezhadarya, Mohammad Bagher Shamsollahi, Mohammad Bagher Shamsollahi, "Noise reduction from magnetic resonance images using nonseperable transforms", Proc. SPIE 6144, Medical Imaging 2006: Image Processing, 61446F (20 March 2006); doi: 10.1117/12.653159; https://doi.org/10.1117/12.653159

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