Computation of outer inverses of tensors using the QR decomposition

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.

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