Translation invariant complex discrete wavelet transforms

The CDWT was first proposed by Kingsbury as a tool for motion estimation in 1998. It was effective at solving the problem of poor translation invariance in the traditional DWT and has been applied in various fields. Thus, its practical use occurred early on, and its rationality was not theoretically interpreted. We have constructed an important base theory of the CDWT, and established a novel design methodology of the complex wavelet based on an arbitrary orthogonal wavelet and a new computation method based on the coherent parallel-tree algorithm of the CDWT. Based on these works, this paper shows new research results and future work.