Contourlet Transform-based Image Denoising

Recently, wavelet theory has been widely used in image denoising. However, since the commonly used two-dimensional tensor product wavelet is isotropic and has the poor direction selectivity, it can only characterize the point singularity, and can hardly characterize the high-dimensional geometrical structures such as edges and textures in images. The contourlet transform, as a new multiscale transform, overcomes these limitations. In the thesis, image denoising algorithms based on the contourlet transform are investigated in detail. The main work can be summarized as follows:1. The theories of the discrete contourlet transform, continue contourlet transformand discrete nonsubsampled contourlet transform are introduced in detail, which are the foundation of denoising algorithms.2. The drawbacks in wavelet denoising and contourlet denoising using hard thresholding are analyzed. A new denoising method based on region segmentation by exploiting the advantages of the two transforms is proposed. The simulation results indicate that the method can get better visual effect and higher PSNR value, and eliminate some denoising artifacts using the contourlet transform.3. Considering the interscale dependencies of nonsubsampled contourlet coefficients, the denoising algorithm based on multiscale product is proposed. After decomposition on white Gaussian noise using the nonsubsampled contourlet transform, the variance of multiscale products of noise contourlet coefficients can be obtained by the linear filter theory. Then non-Gaussian distributed multiscale products of noise contourlet coefficients are transformed into Gaussian functions. Thus the thresholding applying to multiscale products is determined. The simulation results show that the proposed algorithm can get better denoising effect.4. Marginal statistics and joint statistics characteristics of nonsubsampled contourlet coefficients are analyzed. Considering the joint statistics characteristics of neighborhoods of coefficients are characterized by the Gaussian scale mixture model, a denoising algorithm based on this model using Bayes least squares estimator is proposed. The simulation results are satisfactory both in visual quality and PSNR value.