Performance of the Restarted Homotopy Perturbation Method and Split Bregman Method for Multiplicative Noise Removal

In this paper, we first propose restarted homotopy perturbation methods (RHPM) for multiplicative noise removal of the RLO and AA2 models. The main difficulty in applying the RHPM to the nonlinear denoising problem is settled by using binomial series techniques. We next propose the split Bregman methods for multiplicative noise removal of the RLO and AA2 models. The difficulty in applying the split Bregman method to the nonlinear denoising problem can be handled by transforming ill-conditioned linear systems into well-conditioned linear systems using splitting techniques of singular matrices. Lastly, numerical experiments for several test problems are provided to demonstrate the efficiency and reliability of the RHPM and split Bregman methods.

Evolution of Modular Networks Under Selection for Non-Linearly Denoising

Many biological and artifact networks often represent modular structures in which the network can be decomposed into several subnetworks. Here, we propose a simple model for the modular network evolution based on the nonlinear denoising in node activities. This model suggests that modular networks can evolve under certain conditions — if the stipulated goals for the networks or the input and target output pairs involve modular features, or if the signal transfer in a node is carried out in a nonlinear manner with respect to the saturation at the upper and lower bounds. Our model highlights the positive role played by noise in modular network evolution.

Performance of Restarted Homotopy Perturbation Method for TV-Based Image Denoising Problem

We first propose a restarted homotopy perturbation method (RHPM) for solving a nonlinear PDE problem which repeats HPM process by computing only the first few terms instead of computing infinite terms, and then we present an application of RHPM to TV- (Total Variation-) based image denoising problem. The main difficulty in applying RHPM to the nonlinear denoising problem is settled by using binomial series techniques. We also provide finite difference schemes for numerical implementation of RHPM. Lastly, numerical experiments for several test images are carried out to demonstrate the feasibility, efficiency, and reliability of RHPM by comparing the performance of RHPM with that of existing TM and recently proposed RHAM methods.

An Algorithm Based on Compound Anisotropic Diffusion for Image Denoising

In this paper we present a compound anisotropic diffusion filter algorithm to apply edge sensitive ICOV operator in NCD model. According to the correlation coefficient of the ICOV operator, we obtain effective nonlinear denoising. The experiment have validated that our algorithm have better effect in smoothing and better ability in edge preservation.

A Novel Adaptive Probabilistic Nonlinear Denoising Approach for Enhancing PET Data Sinogram

We propose filtering the PET sinograms with a constraint curvature motion diffusion. The edge-stopping function is computed in terms of edge probability under the assumption of contamination by Poisson noise. We show that the Chi-square is the appropriate prior for finding the edge probability in the sinogram noise-free gradient. Since the sinogram noise is uncorrelated and follows a Poisson distribution, we then propose an adaptive probabilistic diffusivity function where the edge probability is computed at each pixel. The filter is applied on the 2D sinogram prereconstruction. The PET images are reconstructed using the Ordered Subset Expectation Maximization (OSEM). We demonstrate through simulations with images contaminated by Poisson noise that the performance of the proposed method substantially surpasses that of recently published methods, both visually and in terms of statistical measures.