Quaternionic curvelet transform

In this paper, we extend the continuous curvelet transform to the space of quaternion valued functions using convolution. We prove that the quaternionic curvelet transform is consistent with the continuous curvelet transform of complex valued functions. Also it satisfies the inversion formula, Parseval's formula and linearity property. Finally, we derive a convolution theorem for quaternionic curvelet transform and extend it to a suitable Boehmian space.