TV-MCP：一种新的脉冲噪音图像恢复方法

对于被脉冲噪音污染的图像恢复问题，广泛使用的TVL1模型会偏离数据获取模型和先验模型，特别是对高水平噪音.针对这个问题，基于MCP函数，提出了一种新的图像恢复模型，称之为TV-MCP模型，并给出了该模型的近似逼近方法，从理论上证明了该算法的全局收敛到TV-MCP模型的稳定点.对于近似逼近子问题的求解，采用交替方向方法求解.通过对多组图像在不同噪音污染水平下的数值仿真实验，验证了本文所提出的模型和方法的有效性．实验结果显示， TV-MCP模型比TVL1模型能够取得更好的恢复效果，尤其是在高噪音污染的图像恢复问题上，TV-MCP恢复图像的SNR值最高可以达到TVL1恢复图像的SNR值的两倍.
For the problem of image restoration of observed images corrupted by impulse noise, the widely used TVL1 model may deviate from both the data acquisition model and prior model, especially for high noise levels. To overcome this problem, based on MCP function, a new model called TV-MCP and its approximation method were proposed. It is proved that the approximation method converges globally to a stationary point of TV-MCP model. Alternating direction method of multipliers was applied to solve the approximation sub-problem. In the numerical experiments, TVL1 and TV-MCP were applied to the problem of image de-noising and de-blurring in the presence of impulse noise, which verifies the effectiveness of the proposed model and method. The results show that TV-MCP outperforms TVL1, especially for the high noise level image de-noising. The maximum SNR value of TV-MCP image restoration can reach 2 times that of TVL1 method.