Image Denoising using Tight-Frame Dual-Tree Complex Wavelet Transform

In this paper, we propose a new approach to design the 1D biorthogonal filters of dual-tree complex wavelet transform (DTCWT) in order to have almost tight-frame characteristics. The proposed approach involves use of triplet halfband filter bank (THFB) and optimization of free variables obtained using factorization of generalized halfband polynomial (GHBP) to design the filters of two trees of DTCWT. The wavelet functions associated with these trees exhibit better analyticity in terms of qualitative and quantitative measures. Transform-based image denoising using the proposed filters shows comparable performance to the best performing orthogonal wavelet filters.