A novel approach to image denoising using the Pareto optimal curvelet thresholds

The denoising of a noisy image using wavelet methods is very representative, however, the wavelet methods may smooth the edges while denoising and the optimal thresholds are hardly acquired. In this paper, an efficient algorithm of image denoising based on multi-objective optimization in the discrete curvelet transform (DCT) domain is proposed, which can achieve the Pareto optimal denoised image with the optimal curvelet thresholds. First, the second generation discrete curvelet transform (Fast DCT) is introduced, and the thresholding functions are analyzed; then the multiple criteria for image denoising are presented, and the relation between these criteria and the curvelet thresholds is analyzed; finally the algorithm of multi-objective constriction particle swarm optimization (MOCPSO) is designed to optimize the curvelet thresholds. In MOCPSO, a new crowding operator is used to maintain the population diversity; the adaptive mutation operator is introduced to avoid the earlier convergence; the uniform design is used to obtain the optimal combination of the algorithm parameters. Experiments indicate that the denoising method based on Pareto optimal curvelet thresholds is more effective than other methods, and can attain the Pareto optimal denoising results.