基于全变差正则化的图像修复研究

Image inpainting based on total variation regularization

图像修复是一种插值问题,用待修复区域边界已知图像内容填充修复受损区域。这种插值问题的一个经典的解法就是解拉普拉斯方程。但是它过于平滑,对于图像插值效果通常不能令人满意,不能修复跳变边缘。全变差正则化是一个有效地恢复锋锐边缘图像的修复方法。重点研究了全变差正则化图像修复方法,并设计了改进的修复模型。实验结果表明,改进模型的全变差图像修复方法是有效的,复原图像在客观评价标准和主观视觉效果方面均有更好的表现。

Image inpainting is an interpolation problem, filling the corrupted region with a condition to agree with the known image on the boundary. A classical solution for such problem is to solve Laplace＇ s equation. However, Laplace＇ s equation is unsatisfactory for images, because it is overly smooth. It cannot restore a step edge passing through the corrupted region. Total variation（TV） regularization is an effective image inpainting technique which is able to recover sharp edges. This paper focuses on the total variation inpainting algorithm, furthermore, proposes an improved image inpainting model. The numerical results show that the total variation inpainting based on the improved model is effective, the PSNR, MSSIM and subjective visual effect of the inpainted image have better performance.