Discontinuity Preserving Noise Removal Method based on Anisotropic Diffusion for Band Pass Signals

nonlinear discontinuity-preserving method for noise removal for band pass signals such as signals modulated with Binary Phase-Shift Keying (BPSK) modulation is proposed in this paper. This method is inspired by the anisotropic diffusion algorithm to remove noise and preserve discontinuities in band pass signals modulated with a single frequency. It is demonstrated here that nonlinear noise removal method for a real valued band pass signal requires a solution for a nonlinear partial differential equation which is of fourth order in space and second order in time. The results presented in this work show better performance in nonlinear noise removal for real valued band pass signals in comparison with the previous work in the literature

Behavioral analysis of anisotropic diffusion in image processing

©1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/83.541424In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator

Adaptive pre-filtering techniques for colour image analysis

One important step in the process of colour image segmentation is to reduce the errors caused by image noise and local colour inhomogeneities. This can be achieved by filtering the data with a smoothing operator that eliminates the noise and the weak textures. In this regard, the aim of this paper is to evaluate the performance of two image smoothing techniques designed for colour images, namely bilateral filtering for edge preserving smoothing and coupled forward and backward anisotropic diffusion scheme (FAB). Both techniques are non-linear and have the purpose of eliminating the image noise, reduce weak textures and artefacts and improve the coherence of colour information. A quantitative comparison between them will be evaluated and also the ability of such techniques to preserve the edge information will be investigated

Optimized Anisotropic Rotational Invariant Diffusion Scheme on Cone-Beam CT

Cone-beam computed tomography (CBCT) is an important image modality for dental surgery planning, with high resolution images at a relative low radiation dose. In these scans the mandibular canal is hardly visible, this is a problem for implant surgery planning. We use anisotropic diffusion filtering to remove noise and enhance the mandibular canal in CBCT scans. For the diffusion tensor we use hybrid diffusion with a continuous switch (HDCS), suitable for filtering both tubular as planar image structures. We focus in this paper on the diffusion discretization schemes. The standard scheme shows good isotropic filtering behavior but is not rotational invariant, the diffusion scheme of Weickert is rotational invariant but suffers from checkerboard artifacts. We introduce a new scheme, in which we numerically optimize the image derivatives. This scheme is rotational invariant and shows good isotropic filtering properties on both synthetic as real CBCT data

An adaptive noise removal approach for restoration of digital images corrupted by multimodal noise

Data smoothing algorithms are commonly applied to reduce the level of noise and eliminate the weak textures contained in digital images. Anisotropic diffusion algorithms form a distinct category of noise removal approaches that implement the smoothing process locally in agreement with image features such as edges that are typically determined by applying diverse partial differential equation (PDE) models. While this approach is opportune since it allows the implementation of feature-preserving data smoothing strategies, the inclusion of the PDE models in the formulation of the data smoothing process compromises the performance of the anisotropic diffusion schemes when applied to data corrupted by non-Gaussian and multimodal image noise. In this paper we first evaluate the positive aspects related to the inclusion of a multi-scale edge detector based on the generalisation of the Di Zenzo operator into the formulation of the anisotropic diffusion process. Then, we introduce a new approach that embeds the vector median filtering into the discrete implementation of the anisotropic diffusion in order to improve the performance of the noise removal algorithm when applied to multimodal noise suppression. To evaluate the performance of the proposed data smoothing strategy, a large number of experiments on various types of digital images corrupted by multimodal noise were conducted.Keywords — Anisotropic diffusion, vector median filtering, feature preservation, multimodal noise, noise removal