From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation

We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained from the connection between the Lyapunov equation, solution of systems of linear ODEs and alternating least squares method for low-rank approximation. The numerical experiments confirm the effectiveness of our approach.Comment: 17 pages, 1 figure

A modification of fuzzy arithmetic operators for solving near-zero fully fuzzy matrix equation

Matrix equations have its own important in the field of control system engineering particularly in the stability analysis of linear control systems and the reduction of nonlinear control system models. There are certain conditions where the classical matrix equation are not well equipped to handle the uncertainty problems such as during the process of stability analysis and reduction in control system engineering. In this study, an algorithm is developed for solving fully fuzzy matrix equation particularly for ~ A ~X ~B  ~X = ~ C, where the coefficients of the equation are in near-zero fuzzy numbers. By modifying the existing fuzzy multiplication arithmetic operators, the proposed algorithm exceeds the positive restriction to allow the near-zero fuzzy numbers as the coefficients. Besides that, a new fuzzy subtraction arithmetic operator has also been proposed as the existing operator failed to satisfy the both sides of the nearzero fully fuzzy matrix equation. Subsequently, Kronecker product and V ec-operator are adapted with the modified fuzzy arithmetic operator in order to transform the fully fuzzy matrix equation to a fully fuzzy linear system. On top of that, a new associated linear system is developed to obtain the final solution. A numerical example and the verification of the solution are presented to demonstrate the proposed algorithm

A Medical Image Denoising Method using Subband Adaptive Thresholding Based on a Shearlet Transform

The image denoising process is of great importance when analyzing images and their visualization. A major problem is finding the boundary between clearing the noise and keeping the salient features in the images. This paper proposes adaptive subband threshold image denoising in a shearlet domain based on the Shannon entropy. The method does not suppose a specific type of noise, it does not require data for its spectrum, nor does it lead to highly complex computational algorithms. ACM Computing Classification System (1998): I.5.4, I.4.3, I.4.5

Automated reduction the speckle noise of the panoramic ultrasound images of Muscles and Tendons

Peer reviewedPublisher PD

Analyzing the Performance of Image Denoising Techniques

With the increasing use of digital images, there is a growing demand for finer-tuned images that will improve the quality of what is being captured. Images captured by modern cameras are noisier, which reduces their quality. It is therefore imperative to reduce the amount of noise in these images, as well as the sharpness of the edges, corners, and other details of the image without reducing the image quality. Image noise is one of the main concerns on digital cameras. It has been found that there are a variety of techniques that can be used to reduce noise in images, each of which has different advantages and disadvantages. However, there is still a challenge and concern associated with image denoising since, when noise is removed from an image, the image is likely to appear blurred. The purpose of this paper is to discuss the characteristics of different types of noise in an image, as well as some of the different types of denoising techniques for the right way capture . The objective of this paper is to introduce various denoising techniques that can remove noise from images while maintaining a high level of image quality. Our study also utilized bilateral and nonlocal means filtering techniques, as well as total variability denoising to demonstrate the denoising in a noisy image. The numerical data in pixels in an image is typically changed by digital image filters (convolution kernels). Filters can cause artifacts in an image if they are not used carefully, leading to a misinterpretation of the data. We have ethically applied the filtering techniques in our experiment

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

A Dynamical Systems Approach to Classification of Surgical Gestures in Kinematic and Video Data

In Computer Assisted Intervention (CAI) systems, a surgeon performs the surgery using an interface connected to a computer that remotely controls a set of surgical tools attached to a robot. Such systems are particularly appealing for minimally invasive surgeries since they allow for a larger and more precise set of movements than in traditional laparoscopic interventions, and provide enhanced vision capabilities such as 3D vision and augmented reality. These features directly translate into benefits for the patients such as smaller incisions, less pain and quicker healing. However, the benefits of the technology might be reduced due to the steep learning curve associated with CAI systems. This makes it necessary to account for a fair and objective criterion for the evaluation and assessment of the skills of a novice surgeon. Furthermore, it is desirable to automate the process in order to avoid constant supervision of an expert surgeon, a time consuming, subjective and rather inefficient method. It is therefore necessary to develop algorithmic methods that extract information from kinematic cues provided by the robot and video recordings of the interventions. A common approach is to divide the surgical procedure into smaller actions, forming a vocabulary able to to describe different surgical tasks. Following such an approach requires a method capable of providing temporal segmentation, recognition of the action and final skill assessment. Prior work has usually modeled the interactions between these atomic actions using generative models such as Hidden Markov Models, Factor-Analysis and Switching Linear Dynamical Systems. In this thesis, we focus on the classification problem and assume segmented data. We propose to follow a discriminative approach using Linear Dynamical Systems (LDS) to model and characterize a particular action. We develop new methods for the extraction of meaningful representations by means of averaging in the space of LDSs. These representative points are then used into a discriminative framework for surgical gesture classification. We propose a novel SVM classification method for time series of data that reduces computation at the expense of some degradation in performance. Our contributions are fairly general and can be applied to any temporal signal coming from an LDS