【摘要】 论文旨在对受模糊和噪声影响的医学图像进行恢复.极小化由保真项构成的能量泛函是图像恢复普遍采用的方法,然而由于该极小化模型的不适定性,对其添加适当的正则化项是必要的.利用医学图像梯度稀疏这一先验条件,对极小化模型添加l_q正则化项.l_q正则化项的添加保证了图像梯度的稀疏性,也使我们不得不求解一个非凸优化问题.利用交替迭代的半二次分裂算法实现对该非凸问题的求解,并给出了该算法的收敛性分析. Shepp-Logan影像模型和MRI图像的数值仿真实验验证了本文的相关理论.基于研究结果,l_1/2正则化方法对梯度分布稀疏的医学图像具有良好的降噪与去模糊效果.更多还原

【Abstract】 The denoising and deblurring of medical images affected by noise and blur can help doctors to obtain the information needed in medical images more accurately. This paper aims to restore medical images affected by blurring and noise. Minimizing the energy functional formed by fidelity term is widely used; however, this minimization problem is ill-posed, it is necessary to add an appropriate regularization term. In this paper, we use the priori information of the medical image, that is the sparsity of the gradient of the image,to add an ■regularization term to the minimization problem. The addition of l_q regularization term guarantees the sparsity of image gradient, but it also forces us to solve a non-convex optimization problem. In this paper, we use the half-quadratic minimization algorithm to solve the non-convex minimization problem and analyze the convergence of the algorithm. Numerical experiments using the Shepp-Logan phantom and MRI images validate the corresponding theories in this paper. Based on the research results, the l_1/2regularization method has a good effect on noise reduction and blur removal for medical images with sparse gradient distribution.更多还原