  The quaternion offset linear canonical transform(QOLCT) has gained much
popularity in recent years because of its applications in many areas, including
color image and signal processing. At the same time the applications of
Wigner-Ville distribution (WVD) in signal analysis and image processing can not
be excluded. In this paper we investigate the Winger-Ville Distribution
associated with quaternion offset linear canonical transform (WVD-QOLCT).
Firstly, we propose the definition of the WVD-QOLCT, and then several important
properties of newly defined WVD-QOLCT, such as nonlinearity, bounded,
reconstruction formula, orthogonality relation and Plancherel formula are
derived. Secondly a novel canonical convolution operator and a related
correlation operator for WVD-QOLCT are proposed. Moreover, based on the
proposed operators, the corresponding generalized convolution, correlation
theorems are studied.We also show that the convolution and correlation theorems
of the QWVD and WVD-QLCT can be looked as a special case of our achieved
results.
