Nonsubsampled higher-density discrete wavelet transform for image denoising

Recently, a new set of dyadic wavelet frames based on oversampled filter banks is introduced that provides a higher sampling in both time and frequency, compared to the usual dyadic wavelets. This transform (called HDDWT) is not shift-invariant; a feature which is desirable particularly for signal denoising. In this paper we propose a new transform, referred to as nonsubsampled HDDWT (NS-HDDWT), which is the shift-invariant version of HDDWT. The NS-HDDWT filter bank is built upon iterated nonsubsampled filter banks which are derived from the HDDWT filter bank in a way that is similar to the a trous algorithm. We employ HDDWT and NS-HDDWT for decomposition of images by performing the separable filtering. The performance of both HDDWT and NS-HDDWT is assessed in image denoising. Experimental results show that the performance of NS-HDDWT is superior to that of HDDWT, and in some cases NS-HDDWT outperforms powerful wavelet-based image denoising methods.