CAJ | 학술논문

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(,)BV 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1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.
해문제출료일충신적다척도변분도상분해모형.수선재Tadmar적분층다척도변분모형적기출상,급출료일충신적(,)BV H-분층다척도도상분해방법,연후재역척도공간상적분“척도”도상병장랍보랍사산자작용우곡1솔항취득도료신적적분미분방정.해방정포함일개단조체증적척도함수,타적치여잔차도상적성범수성반비.접착토론료해방정적중요성질,병급출료수치리산산법.이론분석여수치실험표명신적적분미분방정시일충유효적도상분해모형.
@@@@This paper presents a novel multiscale variational image decomposition model. Based on the hierarchical multiscale variational model of Tadmor, a novel ( , )BV H- hierarchical multiscale image decomposition method 1 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.