  In this article, specific definitions of the Moore-Penrose inverse, Drazin
inverse of the quaternion tensor and the inverse along two quaternion tensors
are introduced under the T-product. Some characterizations, representations and
properties of the defined inverses are investigated. Moreover, algorithms are
established for computing the Moore-Penrose inverse, Drazin inverse of the
quaternion tensor and the inverse along two quaternion tensors, respectively.
