A Dual-Tree Complex Wavelet with Application in Image Denoising

This paper introduces a recently designed dual-tree complex wavelet and studies its application in image denoising. The primal filter bank is selected to be the Daubechies 9/7 filter bank, and the dual filter bank is designed to have length of 10/8; both filter banks are biorthogonal and symmetric. The wavelets of the dual-tree filter bank form (almost) Hilbert transform pairs, allowing nearly shift-invariance and good directionality of the dual-tree complex wavelet transform. The transform is then used in image denoising. We employ the bivariate shrinkage algorithm for wavelet coefficient modeling and thresholding. Various images are tested. The experimental results compare favorably to some other dual-tree complex wavelets.