基于曲线波变换的图像分解

将图像分解为卡通部分(有界变差部分)和震荡部分(文本部分)是近年来图像处理的一个重要问题.图像的卡通部分是由一个有界变差(BV)函数来刻画,相应的将BV罚项合并到变分泛函中需要解偏微分方程.Daubechies用B¹₁(L₁)项代替BV罚项并且用小波解变分问题.按照她的方法,我们通过设计一种数字曲线波算法和一种依赖于尺度的阈值规则,从而得到了一种有效的基于数字曲线波变换的图像分解算法.我们可以看出该算法对噪声具有很强的鲁棒性并且能使图像边缘保持稳定.

Image Decomposition by Curvelet Transform

Recent years,decomposing an image into cartoon component(bounded variation component) and oscillating component(texture component) is an important problem in the field of image processing.The cartoon component of an image is modeled by a bounded variation(BV) function;the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.Daubechies replaced the BV penalty term by a Besov term and wrote the problem in a wavelet framework.Following her ideas,we propose a new image decomposition algorithm based on the digital curvelet transform.By designing a digital curvelet transform algorithm and a scale-dependent thresholding rule,elegant and numerically efficient schemes are obtained.We can see that this approach is very robust to additive noise and can keep the image edges stable.