运用总变分最小化和振荡函数的图像分解方法

为有效地提取纹理和去噪而不损坏图像的边缘及其他重要细节,Meyer(2001)提出了分别用BV空间和G空间刻画图像的主体和细节部分,笔者在Meyer的图像分解模型基础上,建立能量最小化PDE方程,将模型离散化后,利用投影算法和ROF模型的求解方法,将图像分解为有界变差部分u和包含纹理和噪声的部分v.数值实验表明,此方法仅用共40次迭代就能达到很好的分解效果,且去噪的信噪比比ROF模型提高了29.95%,而且除能有效地提取纹理和去噪外本方法对图像的边缘及其他重要细节损坏较小.

Image Decomposition with Total Variation Minimization and Oscillatory Functions

In order to effectively Abstract the texture and denoise but not damage the edge and other important details of image,Meyer(2001) proposed using elements of BV space and G space to characterize cartoon and details of image respectively.The authors present PDE of minimizing energy on the basis of Meyer's work.After the model is discretizated,projection algorithm and the method for ROF model are applied.Thus an image is decomposed into two parts,bounded variation component u and texture with noise v.The numerical experiments show that the method can obtain good results only by total 40 iterations.Using this algorithm,ratio of signal to noise is improved 29.95% compared with ROF model.This algorithm effectively Abstracts texture and denoises,but rarely damages the edges and other important details.