A new tiling scheme for 2-D continuous wavelet transform with different rotation parameters at different scales resulting in a tighter frame

A desirable property when dealing with frames is that the low and up bounds of frames should be close to each other. This can accelerate the convergence speed in computing the dual-frame and simplify the process of recovering the signal from its frame coefficients. In this letter, a new 2-D continuous wavelet transform tiling scheme, which uses different rotation factor sampling methods for different scales, is proposed. The upper/lower bound of the 2-D wavelet family based on this new tiling scheme is derived. The upper/lower bound of the 2-D Morlet wavelet family is estimated, and the results show that the 2-D wavelet family based on the new tiling scheme can provide a higher lower bound and a lower upper bound compared with the 2-D wavelet family based on the old tiling scheme.