【作者】 徐启飞；

【导师】 陈武凡；

【作者基本信息】 南方医科大学 ， 生物医学工程， 2008， 硕士

【摘要】 目前超分辨率重建在军事、天文、遥感等领域都有重要的应用,在医学领域的应用范围也很广泛,例如正电子发射成像(Positron Emission Tomography,PET)、磁共振成像(Magnetic Resonance Imaging,MRI)等。PET能够在分子水平上利用影像技术反映人体心脑代谢和功能,以及新医药开发研究等领域中显示出他卓越的性能。可是在实际中由于受到低计数率和一些物理噪声的影响,PET图像的分辨率低。传统的重建方法虽然具有成像速度快的优点,但其重建图像质量较差,分辨率依旧较低。为此本文将采用超分辨率算法,提高PET图像的分辨率。超分辨率图像重建是图像降采样过程的逆过程,即从多幅低分辨率图像中抽取有用信息来获取一幅高分辨率图像。由于模糊、扭曲、偏移等降采样因素导致图像很多高频信息损失,因此超分辨率图像重建问题是一个病态问题。通常采用正则化方法先引入先验信息对病态问题进行矫正。在正则化算法中,正则化参数的选择是尤为重要,不仅决定着算法的收敛速度是否便于实际应用,而且决定着重建图像是否具有现实意义。二十多年来,国际上出现了很多解决该问题的方法;近十年来成就突出,尤其是M.G.Kang等提出的线性正则化参数思想,进而产生了一系列线性相关的算法。而病态问题实际上为非线性正则化问题,因此本文提出了一系列非线性正则化函数,具体如下:非线性自适应正则化函数Ⅰ:2006年WF.Chen与M.Chen提出了自适应地正则化函数,在改进图像质量的同时减少了计算量。根据WF.Chen和M.Chen以及H.He与L.P.Kondi的相关理论基础,提出了一种自适应非线性正则化函数的重建算法,进而利用实验方法分析代价函数的凸性。通过数学理论,根据代价函数凸性我们得到自适应步长因子,从而改进了图像的空间分辨率,加快了算法的收敛速度。为验证该算法的有效性,采用光学图像进行实验。实验结果表明,自适应非线性正则化函数的重建算法是有效的。非线性自适应正则化函数Ⅱ:根据H.He和L.P.Kondi与R.C.Hardie,K.J.Barnard和E.E.Armstrong 1997年文献,提出了一种基于正则化参数的自适应线性斜率超分辨率算法。该算法通过对正则化线性斜率的自适应,更新动态优化代价函数,以降低对PET图像高频成份的抑制。为验证该算法的有效性,采用模拟PET序列图像进行实验。实验结果表明,新算法在改善图像空间分辨率上取得良好的效果。非线性自适应正则化函数Ⅲ:为获得高分辨率的MR图像,需要提高磁场梯度;同时由于传统扫描方式会减小像素体尺寸,从而降低了信噪比。结合E.S.Lee和M.G.Kang的算法,提出了包含先验信息的自适应正则化超分辨率MR图像重建算法。通常,采用非线性正则化参数对病态问题进行校正时,代价函数的凸性问题只有通过实验手段进行证明,很难从理论角度对进行论证。本算法中的非线性正则化参数的提出,使得的代价函数的凸性可以采用理论方法进行论证,确保代价函数具有全局最小值。根据体模图像重建结果可知,超分辨率重建技术可以提高MR图像分辨率。同时通过实验对比分析发现新算法要优于其他算法。更多还原

【Abstract】 At present super-resolution reconstruction in the military, astronomy, remote sensing, it is also extensive scope of application in the medical field, such as positron emission imaging (Positron Emission Tomography, PET), magnetic resonance imaging (Magnetic Resonance Imaging, MRI), etc. PET is able to represent heart and brain metabolism and functions on molecule level by imaging techniques, and has shown great performance in oncology, cardiopathy, neurology and new medicine studies. But positron emission tomography is an ill-posed inverse problem because the observed projection data are contaminated by noise due to low count rate and physical effects. Traditional method often reconstructs noisy images of low quality, super-resolution methods can be used to improve PET image quality.Image super resolution is the inverse process of image degradation, which is referred to as generating a high-resolution image from one or several low-resolution images. A low-resolution image can be considered as the degraded version of the high-resolution image and the degradations include warping, blurring and down-sampling. Obviously image super-resolution is an ill-conditioned problem. The ill-posed problem could be normally solved by regulation parameter which contains the priori information of the images. The choice of the regulation parameter is very important, which does not only decide the rate of the convergence but also impact the quality of the reconstruction image. Many methods have been proposed to overcome the ill-posed problem in the past twenty years. Many outstanding theories have been proposed in the past 10 years, especially the MG Kang etc propose the parameters of linear regularization method, and then a series of linear regularization algorithms come out. However, the ill-posed problem is nonlinear regularization problems. Consequently a series of nonlinear regularization are proposed in the paper.The nonlinear adaptive regularizationⅠ: The regularization of the adaptive function is proposed by WF.Chen and M. Chen in 2006, which improves the image quality while reduces the amount of computation. According to WF.Chen and M. Chen, H. He and LP Kondi the relevant theoretical foundation, a novel nonlinear adaptive regularization function is proposed. The convexity of the cost function is analyzed experimentally. Based on the convex of the cost function, we get the adaptive step size by the mathematical theory. Consequently, the spatial resolution of the image and the rate of convergence are significantly improved. Optical images are used to test the proposed method. The results show that our algorithm is very effective.The nonlinear adaptive regularizationⅡ: according to H. He and LP Kondi in 2006 reference and RC Hardie, K.J Barnard, and EE Armstrong in 1997 reference. An adaptive linear slope algorithm based on the regularization parameter (RP) is proposed. This algorithm can adaptively optimize the cost function and reduce the suppression of high frequency component of PET image by adaptively updating linear slope of the RP. The proposed method is performed on simulated PET image sequence. The results of the experiment indicate that the proposed algorithm outperforms conventional approaches in the spatial resolution.The nonlinear adaptive regularizationⅢ: In order to obtain high resolution MR images, gradient magnetic field is required and the signal-to-noise will be reduced due to the decrease in voxel size with traditional scan. Based E.S. Lee and M.G Kang algorithm, the adaptive of super resolution MR Image reconstruction, which includes the images prior information is proposed. Usually, it is difficult to prove the convexity of the cost function, when a nonlinear regularization is adopted. Most of time, experimental means is the only way to prove the convexity of the cost function. It is can be proved in the proposed algorithm and ensures that the cost function has a global minimum. As shown from the results obtained in the phantom imaging, the proposed super resolution technique can improve the resolution of MR image. The new algorithm is superior to other algorithms by experimental comparative analysis.更多还原