Research On Image Denoising Based Wavelet Transform

There is much noise in image. In order to further image analysis and communication, the noise needs to be reduced in image pre-processing. Recently, with the improvement of wavelet theory, wavelet analysis has penetrated into many fields. Meanwhile, wavelet applied to image denoising successfully, and many new image denoising algorithms based on wavelet have been proposed.The research content of this dissertation consists of four aspects: first aspect is the researching on wavelet shrinkage threshold and proposing a new shrinkage threshold; second aspect is the researching on relationship between wavelet coefficients and the image denoising algorithm based on it; third aspect is using bivariate distribution model the interscale dependency and the image denoising based on intra-and interscale dependency using bivariate model; the other is the preliminary study on the Contourlet transform and the image denoising algorithm based on it.Donoho has proposed the wavelet shrinkage threshold, which is not optimal threshold but the maximum of the optimal shrinkage threshold. And it is irrelevant with the image itself. We proposed a new wavelet shrinkage threshold which is relevant with the singularity of the image. The denoising results show it is more optimal.There exists great relationship between wavelet coefficients; that are inter-scale and intra-scale dependencies. Considering the inter-scale dependency of the wavelet coefficients, an inter-scale dependency based wavelet shrinkage denoising algorithm is presented. Shrinkage thresholds of each subband are selected according to the energy of each subband in each scale and relationship of coefficients between scales. The experiment results show the new algorithm is more effective than classical algorithms.The denoising algorithm based on wavelet coefficients statistical model is one of the new methods of wavelet denoising. The key of that method is the wavelet coefficients statistical model. According to the inter-scale dependency, a bivariate model is proposed. And combining with the intra-scale dependency, we proposed a new bivariate shrinkage wavelet denoising based on inter-and intra-scale dependency. The new method can greatly remove noise and preserve image edges.The key for wavelet shrinkage to obtain better effect lies in that wavelet transformcan provide sparse representation for images. However, when wavelet transform represents the edge of images, wavelet coefficients is not enough sparse, because wavelet transform does not possess much directionality. Based on that, a new image representation method, Contourlet transform, is proposed. The Contourlet transform possess not only spatial and frequency locality and multi-resolution but also directionality and anisotropy. So it can provide sparse representation for edges of images. And we apply it to image denoising. The results show the denoising method based on Contourlet transform is better than wavelet transform, especially to the images which consist of abundant edge.