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Keywords
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Iterative method, Global least squares, Constrained equation, Einstein product, Image restoration
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Abstract
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In this paper, we present an iterative method for solving tensor equations, specifically
multilinear systems of the form A ∗N X ∗M B + C ∗N X ∗M D = E with one of the constraints X = X^T
, X = P ∗N X ∗M Q, X = −P ∗N X ∗M Q and X = P ∗N X ∗N P, where P and Q are reflexive tensors. The proposed method is grounded in the generalized least squares method with the Einstein product. To address the constrained tensor
equation using the global least squares method, we introduce a multilinear operator and
its adjoint. For a more detailed survey, we compare the proposed method for solving the
constrained tensor equation with one of the matrix format methods for the associated
matrix equation. We also use the new method to solve the image restoration problem
with a symmetrical structure, as a special case of constrained tensor equation. Finally,
we give some examples to illustrate the effectiveness of the proposed method.
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