Images are often corrupted by noise in the procedures of image acquisition and transmission. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can represent images with very few coefficients. In this paper, we propose a new image denoising approach in extended DST domain, which combines hidden Markov tree (HMT) model and Bessel K Form (BKF) distribution. Firstly, the marginal statistics of extended DST coefficients are studied, and their distribution is analytically calculated by modeling extended DST coefficients with BKF probability density function. Then, an extended Shearlet HMT model is established for capturing the intra-scale, inter-scale, and cross-orientation coefficients dependencies. Finally, an image denoising approach based on the extended Shearlet HMT model is presented. Extensive experimental results demonstrate that our extended Shearlet HMT denoising approach can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed approach can preserve edges very well while removing noise.

It is a challenging work to design an edge-preserving image denoising scheme. Nonlocal means methods have been widely adopted as simple algorithms for image denoising, but they tend to overblur the image and sharpen the boundary with many texture details lost. In this paper, we propose a new nonlocal means image denoising approach in shiftable complex directional pyramid (PDTDFB) domain, in which the robust radial harmonic Fourier moments (RHFMs) are utilized. The novelty of the proposed approach includes: (1) PDTDFB based multi-scale structural similarity is explored, which has good robustness to noise interference, (2) Geometric invariant radial harmonic Fourier moments (RHFMs) are introduced into similarity measure function, which can improve the denoising ability. Experimental results demonstrate that our image denoising method can obtain better performances in terms of both subjective and objective evaluations than some other state-of-the-art denoising techniques. Especially, it can preserve edges very well while removing noise.

Based on nonsubsampled shearlet transform (NSST) and fuzzy support vector machines (FSVMs), we present a new denoising approach that can effectively suppress noise from an image while keeping its features intact. The noisy image is firstly decomposed into different subbands of frequency and orientation responses using NSST. The NSST detail coefficients are then divided into edge/texture-related coefficients and noise-related ones by FSVMs classifier. And finally the detail subbands of NSST coefficients are denoised by using the adaptive Bayesian threshold. Extensive experimental results demonstrate that our approach is competitive relative to many state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.