Image Denoising using Shiftable Directional Pyramid and Scale Mixtures of Complex Gaussians

In this paper, a modified version of the complex directional pyramid (PDTDFB) is proposed. Unlike the previous approach, the new FB provides approximately tight-frame decomposition. We introduced the complex Gaussian scale mixture (CGSM) for modeling the distribution of complex directional wavelet coefficients. The statistical model is then used to obtain the denoised coefficients from the noisy image decomposition by Bayes least squares estimator. Performance of the denoised images using the PDTDFB is compared to the conventional transforms including the orthogonal wavelet, the contourlet and the steerable pyramid. The experiments show that the PDTDFB could achieve higher quality image denoising than the wavelet and the contourlet with the hard thresholding method, and is comparable to the steerable pyramid in terms of mean squared error (MSE) and perceptual image quality (SSIM) with the Bayes least squares estimator.