Image Restoration Using Gaussian Scale Mixtures in Complex Curvelet Transform Domain

In this paper, a complex Curvelet transform is presented at first. The key innovation can be generalized as follows:2D and 1D complex wavelet transform instead a¿ trous algorithm sub-band decomposition and 1D wavelet transform respectively, and increase the sampling rate during the 1D IFFT. So the new complex Curvelet transform has non-aliasing performance, and can avoid "scratch" and "embedded stain" phenomenon in reconstruction image. On this basis, a new image restoration method using Gaussian scale mixtures in complex Curvelet transform domain is presented. The GSM model can effectively capture the amplitude and phase information of complex Curvelet coefficients. So the degraded complex coefficients modeled can be estimated effectively by using Bayesian least squares(BLS) estimator in order to recover the signal coefficients. Experimental results show that the proposed method can efficiently avoid the problem of noise amplification during the iteration restoration processing. The proposed method has better visual effects, bigger PSNR values than both Wiener restoration method and Lucy-Richardson restoration method.