基于非冗余平移不变小波变换的磁共振图像降噪

MR image denoising based on nearly shift-insensitive and nonredundancy discrete wavelet transform

背景:MRI成像机制决定了其时间/空间分辨率和信噪比之间存在矛盾,因此图像降噪变得十分必要。目前基于离散小波变换的降噪方法广泛应用,然而存在平移敏感性的缺陷。目前已出现了克服平移敏感性的离散小波变换,但其冗余性导致计算复杂度的快速增加。目的:针对图像降噪设计小波滤波器,减小降采样过程的影响,保持离散小波变换的非冗余性,并针对MRI图像Rician噪声的降噪进行分析。方法:由于平移敏感性主要是由于离散小波变换分解时降采样产生的混叠项带来的,在保证非冗余的前提下,提出了通过减小混叠项的影响来减小平移敏感性。在此基础上,设计了一个双正交小波。最后,将其以常见的阈值降噪方法应用到磁共振图像Rician噪声的降噪中。结果与结论:文章提出了设计小波滤波器的新方法,即满足严格重构条件外满足一些附加要求,最后将设计过程简化为一个有约束条件的最优化过程。将设计的双正交小波应用于MR图像,仿真结果表明降噪效果较通常小波有所改善,间接表明了设计思路和方法的有效性。

BACKGROUND：The imaging mechanism of MRI means there is a contradiction between the time/space resolution and signal noise ratio （SNR）. Thus,the image denoising becomes very necessary. The image denoising method using discrete wavelet transform （DWT） has been applied widely. However,DWT has some drawbacks. The drawbacks of DWT have led to the development of shift insensitive wavelet transforms,e.g. Kingsbury＇s double-tree complex wavelet transform （DTCWT）,which necessarily leads to considerably redundant wavelet representation and a huge increase in computational complexity. OBJECTIVE：To design wavelet filter to reduce influence in sampling and maintain non-redundancy of DTCWT and analyze denoising of Rician noise of MRI images. METHODS：The shift sensitivity was mainly caused by the aliasing terms in the downsampling of wavelet decomposition. A new scheme was proposed to approximately eliminate the aliasing terms while remains the wavelet representation free from redundancy. The framework of the proposed DWT was similar to that of the general DWT except that the wavelet filters satisfy some additional requirements beyond the requirements on wavelet filters. A biorthogonal wavelet was designed. The proposed wavelet was applied to denoise the magnetic resonance image with Rician noise using general the thresholding method. RESULTS AND CONCLUSION：A new method for designing wavelet filter,which simplifies the design procedures into an optimal procedure with constraint conditions. The designed biorthogonal wavelet was used in MR images. The simulation results show the superiority of the proposed wavelet in the term of SNR.