中文摘要：

该文提出了一种新的多尺度变分图像分解模型。首先在Tadmar的分层多尺度变分模型的基础上,给出了一种新的1（B V,H-）分层多尺度图像分解方法,然后在逆尺度空间上积分＂尺度＂图像并将拉普拉斯算子作用于曲率项就得到了新的积分微分方程。该方程包含一个单调递增的尺度函数,它的值与残差图像的星范数成反比。接着讨论了该方程的重要性质,并给出了数值离散算法。理论分析与数值实验表明新的积分微分方程是一种有效的图像分解模型。

英文摘要：

This paper presents a novel multiscale variational image decomposition model.Based on the hierarchical multiscale variational model of Tadmor,a novel 1（B V,H-）hierarchical multiscale image decomposition method is proposed,then the novel Integro-Differential Equation（IDE） is obtained by integrating in inverse scale space a succession of refined slices of the image and balancing a Laplacian of the curvature term at the finer scale.The IDE includes a monotone increasing scaling function which is shown to dictate the size of the residual image measured in the star-norm.Some theoretical properties of the novel IDE and its numerical implementation methods are given.Theoretical analysis and numerical experiments show the effectiveness of the IDE model.