In this paper, we introduce new representations and characterizations of the outer inverse of tensors through QR decomposition. Derived representations are usable in generating corresponding representations of main tensor generalized inverses. Some results on reshape operation of a tensor are added to the existing theory. An effective algorithm for computing outer inverses of tensors is proposed and applied. The power of the proposed method is demonstrated by its application in 3D color image deblurring.

中文翻译：

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使用QR分解计算张量的外部逆

在本文中，我们通过QR分解介绍了张量的外部逆的新表示和表征。派生表示可用于生成主张量广义逆的相应表示。关于张量整形操作的一些结果被添加到现有理论中。提出并应用了一种有效的张量外逆计算算法。该方法在3D彩色图像去模糊中的应用证明了该方法的强大功能。