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首页> 外文会议>Image Processing pt.3; Progress in Biomedical Optics and Imaging; vol.7 no.30 >Noise Reduction from Magnetic Resonance Images using Nonseperable Transforms
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Noise Reduction from Magnetic Resonance Images using Nonseperable Transforms

机译：使用不可分变换从磁共振图像中减少噪声

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摘要

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 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.
机译：近年来，多尺度变换在图像处理中得到了很多应用。小波变换是一种强大的多尺度变换，用于对嘈杂的信号和图像进行降噪，但通常的二维可分离小波次优。这些可分离的小波变换可以成功地识别图像中的零维奇异点，但是可以弱化识别诸如边缘，曲线和直线之类的一维奇异点。从这个意义上说，Candes和Donoho提出了不可分离的变换，例如Ridgelet和Curvelet变换。这些不可分离的变换所产生的系数已显示出比小波系数稀疏。这个事实导致比小波变换更好的去噪能力。这些新的不可分离的变换由于其基本元素的特殊结构，因此可以识别直线和曲线上的方向。基本上，磁共振图像很可能会产生Rician噪声。在某些特殊情况下，这种噪声可以被认为是高斯白噪声。本文提出了一种新的MR图像去噪方法。该方法基于Monoscale Ridgelet变换。结果表明，该变换可以成功地对高斯白噪声中嵌入的MR图像进行去噪。与基于视觉感知和信噪比的常规小波去噪方法相比，该结果更好。

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