一种基于积分微分方程的泊松噪声去除算法
doi: 10.3724/SP.J.1146.2012.01087
An Integro-differential Equation Approach to Reconstructing Images Corrupted by Poisson Noise
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摘要: 该文提出一种新的基于积分微分方程的泊松噪声去除算法。首先讨论了经典的总变差(TV)最小模型，在此基础上提出一种新的变分多尺度分层图像表示方法，然后在逆尺度空间上积分尺度图像从而得到了新的积分微分方程。这种新的积分微分方程含有一个单调增加的尺度函数。通过选取适当的尺度函数，该方程可以有效地去除泊松型噪声。数值实验证明了该算法比经典的TV和四阶偏微分方程算法具有更好的去噪效果。Abstract: This paper presents a novel integro-differential equation approach for removing Poisson noise. The classical Total Variational (TV) minimization model is discussed, and then the novel hierarchical multiscale variational image representation model is given. To arrive at the novel integro-differential equation, one integrates in inverse scale space a succession of refined slices of the image. The novel integro-differential equation includes a monotone increasing scaling function. According to choose an adaptive scaling function, this equation can remove Poisson noise efficiently. Finally, the experiment results demonstrate the proposed model obtains better effects compare with the classical TV and fourth-order partial differential equation models.
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