Image Analysis Using a Dual-Tree -Band Wavelet Transform
arXiv:1702.08534 · doi:10.1109/TIP.2006.875178
Abstract
We propose a 2D generalization to the -band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (\textit{i}) the construction of the dual basis and (\textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the -band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed -band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various -band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.