We consider denoising and deblurring problems for tensors. While images can be discretized as matrices, the analogous procedure for color images or videos leads to a tensor formulation. We extend the classical ROF functional for variational denoising and deblurring to the tensor case by employing multi-dimensional total variation regularization. Furthermore, the resulting minimization problem is calculated by the FISTA method generalized to the tensor case. We provide some numerical experiments by applying the scheme to the denoising, the deblurring, and the recoloring of color images as well as to the deblurring of videos.

翻译：图像可以分解为矩阵,而类似的彩色图像或视频程序则可以产生抗拉配方。我们通过采用多维全变异规范,将传统ROF功能的变异分解和分解功能扩大到抗拉情况。此外,由此产生的最小化问题由FISTA方法(该方法一般适用于抗拉情况)计算。我们通过对彩色图像的分解、分解和重新涂色以及视频的分解应用该方法,提供了一些数字实验。