利用平衡方法的非凸图像修复

Nonconvex image inpainting via balanced regularization approach

自然图像通常可以看成由两部分构成:卡通部分和纹理部分,这两部分在一些紧框架下,比如曲线波、局部余弦变换、样条小波等都有稀疏表示.该文研究在两个可分离紧框架下的图像修复问题.与大部分算法普遍采用基于分析的或者合成的稀疏先验的不同之处在于:文中采用基于平衡的方法,且对稀疏系数使以非凸限制;最后给出了迭代算法.数值实验表明了建议的非凸图像修复方法比普通的l1凸方法和经典的变分TV方法有更好的修复效果.

Real images usually have two layers,namely,cartoons and textures,both of these layers have sparse approximations under some tight frame systems such as curvelet,local DCTs ,and B-spline wavelet.In this paper, we solve the image inpainting problem by using two separate tight frame systems which can sparsely represent the two parts of the image.Different from existing schemes in the literature which are either analysis-based or synthesis-based sparsity priors,our minimization formulation applies the nonconvex sparsity prior via the balanced approach.We also derive iterative algorithms for finding their solutions.Numerical simulation examples are given to demonstrate that our proposed nonconvex method achieves significant improvements over the classical l1 sparse method and the variation TV method in image inpainting.