Fractional cycle spinning via modulated lapped transform for overcomplete image representation

This paper aims to introduce an overcomplete transform based on fractional cycle spinning (FCS). Conventionally, the CS approach of wavelet transforms has been proposed, in order to achieve translation invariance with redundancy, unlike the classical critically sampled wavelet transform. This advantage contributes to efficient image processing, such as image denoising. The proposed FCS generalizes CS and show that richer overcompleteness can be provided by fractional shifts of input signals. For realizing fractional delay, we present the approach based on modulated lapped transforms (MLTs). It is shown that their filter kernels can express arbitrary fractional delay by carefully selecting their window function. In addition, this paper extend the conventional MLT to the dual-tree MLT to improve its poor directional selectivity. Then, an efficient lattice structure for the FCS is described for lower computational complexity. Finally experimental results show FCS can be applied better than the conventional CS in image denoising.