Design of extrafine complex directional wavelet transform and application to image denoising

In this paper, we propose decimated and undecimated designs of extrafine complex directional wavelet transform (EFiCDWT) having 12 highpass directional subbands at each scale. EFiCDWT is obtained using a new mapping-based complex wavelet transform (CWT) followed by a complex-valued filter bank (FB) stage. The FB stage having 2-D prototype complex FIR filters designed using complex transformations, finely decompose the 6 complex directional subbands of CWT to have extra directionality. Our design on decimated EFiCDWT is near shift-invariant with redundancy factor of 2 (due to complex coefficients) while undecimated design is completely shift-invariant and hence useful for image denoising. Main advantage of the proposed designs is their directional extensibility with possible generalized separable implementations. The proposed designs are tested for image denoising application using simple hard-thresholding scheme and they show better denoising performance.