Image Analysis Using a Dual-Tree $M$-Band Wavelet Transform
This work addresses image denoising for applications like natural, texture, and seismic image analysis, but it is incremental as it builds on existing dual-tree wavelet methods.
The paper tackled the problem of image denoising by proposing a 2D generalization of the dual-tree M-band wavelet transform, focusing on constructing a dual basis and directional analysis, and introducing an optimal reconstruction technique. The result demonstrated significant improvements in noise reduction and direction preservation across various image types, wavelets, and thresholding strategies.
We propose a 2D generalization to the $M$-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 $M$-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 $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.