A non-subsampled non-aliasing contourlet transform and the denoising algorithm with adaptive thresholding

Focused on the frequency aliasing and shift-variance of contourlet transform, a shift-invariant (non-subsampled) non-aliasing contourlet transform(NS-NACT) is proposed based on non-subsampled non-aliasing pyramidal filter banks(NS-NPFB) and undecimated directional filter banks(UDFB). Based on the NS-NACT, an adaptive-threshold denoising algorithm is designed. Experimental results show that this algorithm can raise the PSNR about 0.65 dB and 3.47 dB (when noise variance is 30), respectively, and effectively eliminate the Gibbs phenomena and maintain more detail of image compared with contourlet transform and undecimated wavelet transform.