In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast tensor-tensor product computations. In particular, we will focus on the tensor discrete cosine versions of GMRES, Golub-Kahan bidiagonalisation and LSQR methods. The presented numerical tests show that the methods are very fast and give good accuracies when solving some linear tensor ill-posed problems.

翻译：在目前的工作中,我们针对诸如彩色或视频图像恢复等不妥的线性抗拉问题提出了新的高光克克隆亚空间方法。这些方法基于高光度离散的余弦变异,可快速计算高光度减速产品。特别是,我们将侧重于GMRES、Golub-Kahan 焦光度成像法和 LSQR 方法的高光度离散的余弦体版本。所提供的数字测试显示,这些方法非常快速,在解决一些线性抗拉错误问题时提供了良好的理解性。