Image restoration with significant Curvelet coefficients index set constrains

Image denoising is an important step in image processing. In this paper, a new image restoration approach based on the index set of significant Curvelet coefficients constrains is proposed. Firstly, the noisy image is processed by Curvelet thresholding method, at the same time, the index set is preserved by the curvelet coefficients whose absolute magnitude is more than the thresholding value. Secondly, a complementary image is obtained by applying the index set to the difference image between the original noisy image and the reconstructed image by thresholding method. Then the complementary image is added to reconstructed image to obtain the final results. In order to reduce the pseudo-Gibbs phenomena and the curvelet-like artifacts, the nonlinear diffusion scheme is used to processing the reconstructed image. Experimental results show that the proposed method can well remove noise better, preserve more details of original image, and achieve higher Peak Signal to Noise Ratio (PSNR).