Denoising Method Based on the Nonsubsampled Shearlet Transform

In this paper, a new bivariate shrinkage denoising method is proposed to model statistics of shearlet coefficients of images. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for shearlet denoising, which generalizes the soft threshold approach. Experimental results show that the proposed method can remove Gaussian white noise while effectively preserving edges and texture information. At the same time, it can achieve a higher PSNR and mean structural similarity than other denoising method. Introduction Nowadays, lots of research work on image processing is concentrated in the multiscale transform. Wavelet threshold has been presented as a true signal estimation technique that exploits the capabilities of wavelet transform (DWT) for signal denoising [1]. After this, a theory for multidimensional data called as MGA has been developed such as curvelet, bandelet, contourlet, Nonsubsampled Contourlet Transform (NSCT) [1] etc.. These new MGA tools provide higher directional sensitivity than wavelets. However, the curvelet, bandelet, contourlet lack of shift-invariance and results in artifacts along the edges to some extend. To represent the edges more efficiently, Labate et al. introduced a new multiscale analysis tool called shearlet that has all properties like other MGA tools as multiscale, localization, anisotropy and directionality [2]. The nonsubsampled shearlet transform (NSST) is realized by nonsubsampled Laplacian pyramid (NSLP) and several shearing filters. The NSST also provides the flexible directional selectivity and shift invariance. Bivariate Shrinkage Let 2 ω be parent shearlet coefficient and 1 ω be child coefficient [3].