Time-varying lifting structures for single-tree complexwavelet transform

In this paper, we describe a single-tree complex wavelet transform method using time-varying lifting structures. In the dual-tree complex wavelet transform (DT-CWT), two different filterbanks are executed in parallel to analyze a given input signal, which increases the amount of data after analysis. DT-CWT leads to a redundancy factor of 2^d for d-dimensional signals. In the proposed single-tree complex wavelet transform (ST-CWT) structure, filters of the lifting filterbank switch back and forth between the two analysis filters of the DT-CWT. This approach does not increase the amount of output data as it is a critically sampled transform and it has the desirable properties of DT-CWT such as shift-invariance and directional selectivity. The proposed filterbank is capable of constructing a complex wavelet-like transform. Examples are presented.