一种变分自适应中值滤波算法

针对自适应中值和变分滤波方法脉冲噪声去除能力的不足，提出了一种新的变分自适应中值滤波方法。首先采用自适应中值滤波器对脉冲噪点进行标识，然后对标识的噪点构建由逼近条件和边缘保持正则化条件构成的代价函数，通过变分方法对代价函数寻优求解，对噪点进行恢复。最后进行了仿真试验，并与标准中值滤波，开关中值滤波，自适应中值滤波，和变分滤波方法进行了比较。试验结果表明，在信噪比和细节保留方面明显优于上述滤波方法，可以有效去除高达90%的脉冲噪声。

Impulse noise reduction by variational method based on adaptive median filter

To improve the performance of impulse noise reduction, a new variational method based on adaptive median filter was proposed. First, adaptive median filter was used to identify the impulse noise. Second, a cost function of the identified noisy pixels was designed, which was composed of data-fidelity term and edge-preserving regtdarization term. Third, variational method was used to get the optimal solution which minimize the cost function and restore the noisy pixels. Simulation results demonstrate that our proposed method is obviously better than standard median filter, switching median filter, variational method and adaptive median filter, and can erase as much as 90% impulse noise.