With the rapid development of computer science and technology in modern society, image science is widely used in various fields, especially in medicine field. Image processing plays an important role in medical images. Medical images are often corrupted by noise due to various sources of interference and other phenomena during their acquisition and transmission that affects the measurement processes in imaging reduced image detail due to the introduction of noise. Keeping useful diagnostic information to suppress noise is a challenging task. Salt and pepper noise as a kind of ordinary noise is one of the impulse noises. In this work, we will use a logarithmic image prior constraint the objective function for the removal of the impulse noise. Also, we used the split Bregman iterative method to solve the objective function. Theoretically, under reasonable assumptions, we give partial convergence analysis of the algorithm. Computationally, we use the split Bregman iterative method under the guarantee of convergence analysis and the weight of SVD decomposition; a complex problem is transformed into several simple subproblems to solving, wherein u-subproblem can be solved by fast Fourier transform; h, d-subproblems can be solved use shrinkage operator, respectively. In the experimental aspects, we have done a lot of experiments and compared with other state-of-the-art methods. The experimental results show that the method is superior to other methods in terms of effectiveness impulse noise (salt and pepper noise) for medical images (CT or MRI).

随着现代社会中计算机科学技术的飞速发展，图像科学被广泛应用于各个领域，特别是在医学领域。图像处理在医学图像中起着重要作用。医学图像在采集和传输过程中通常会由于各种干扰源和其他现象而被噪声破坏，这些噪声会影响成像过程中的测量过程，这是由于引入了噪声导致图像细节减少。保持有用的诊断信息以抑制噪声是一项艰巨的任务。椒盐噪声作为一种普通噪声是脉冲噪声之一。在这项工作中，我们将使用对数图像先验约束的目标函数来去除脉冲噪声。此外，我们使用了分裂的Bregman迭代方法来求解目标函数。从理论上讲 在合理的假设下，我们对该算法进行了部分收敛性分析。计算上，在收敛分析和SVD分解权重的保证下，采用分裂Bregman迭代法。一个复杂的问题被转化为几个简单的子问题来解决，其中u-子问题可以通过快速傅立叶变换来解决；h，  d-子问题可以分别使用收缩算子解决。在实验方面，我们进行了大量实验，并与其他最新方法进行了比较。实验结果表明，该方法在医学图像（CT或MRI）的有效脉冲噪声（盐和胡椒噪声）方面优于其他方法。