The cycle spinning-based sharp frequency localized contourlet transform for image denoising

Contourlet transform provides flexible number of directions and captures the intrinsic geometrical structure of images. The efficient directional filter banks with low redundancy of contourlet are very attractive for image processing. However, non-ideal filters are used in the original contourlet transform, especially when combined with laplacian pyramid, which results in pseudo-Gibbs phenomena around singularities for image denoising. Sharp frequency localized contourlet transform (SFLCT) is a new construction contourlet to overcome this drawback by replacing the laplacian pyramid with a new multiscale decomposition which significantly improve the denoising performance than the original form. Unfortunately, the downsampling of SFLCT makes it lack translation invariance. Thus, we employ a cycle spinning (CS) method to improve the denoising performance of SFLCT, named as cycle spinning based SFLCT (CS-SFLCT), by averaging out the translation dependence. Experimental results demonstrate that the proposed CS-SFLCT outperforms SFLCT, contourlet and cycle spinning-based contourlet for denoising in terms of PSNR and in visual effects.