Fast Feature-Preserving Approach to Carpal Bone Surface Denoising.

This paper presents a novel hardware solution for solving sparse matrices using emulation technology. The proposed solution introduces a bio-inspired technique, which is Genetic Algorithm (GA) to solve the sparse system of linear equations (SLEs). The proposed solution can be used with any physical system that can be modeled as SLEs. Computations involved in Finite Element Method (FEM) consume too much time, which affects the final time-to-market value. Profiling shows that the most time-consuming part in the simulation process is the solver part which is responsible for solving the resultant SLEs generated from the FEM. The total number of equations may reach thousands or millions of linear equations. Hardware implementation of GA and making a good use of parallelism in implementing the architecture accelerate the time taken by the solver part. Solving the system by classical numerical methods, such as conjugate gradient (CG) implemented in software is performed sequentially, here the architecture allows the parallelism in performing GA operators, such as selection, crossover, and mutation. The parallelism in the proposed architecture is the superiority point which we rely on. The results show that our proposed method to solve the SLEs outperforms the classical CG software implementation on run time and number of equations.

A projection method for solving nonsymmetric linear systems on multiprocessors

Iterative solvers allow for a trade-off between speed and accuracy. We propose an iterative method for the estimation of the internal states of a given discrete-time linear state-space model from a series of noisy measurements. In particular we identify the MAP estimate of those states as being the solution of a sparse system of linear equations and derive an iterative solver based on the conjugate gradient method. We derive convergence results to quantify the trade-off between speed and accuracy and finally apply the method to channel estimation where it is shown to outperform Kalman smoothing complexity-wise.

Data Flow Analysis of Orthogonal Properties on the Conjugate Gradient and the Lanczos Algorithm

This paper investigates the performance of a class of methods based on the Preconditioned Conjugate Gradient (PCG) method for the solution of large and sparse systems of linear equations which arise from the p‐version of the adaptive finite element method. The hierarchical type of preconditioning used in the past is extended to the SSOR and incomplete factorization type preconditioning and applied with a global handling of the stiffness matrix. The paper also presents some new ideas on Domain Decomposition (DD) matrix‐handling techniques, whereby the explicit formulation of the resulting Schur complement is avoided by utilizing the PCG method with efficient preconditioners and by processing separately on the coarse and the fine mesh. The suitability of the methods to the p‐version of the adaptive finite element method is demonstrated through extensive numerical tests in two dimensions.

Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. This paper presents the results of implementations of several linear algebra algorithms. It shows that very large sparse systems can be solved efficiently by using combinations of structured Gaussian elimination and the conjugate gradient, Lanczos, and Wiedemann methods.

Computer subroutines for solving large sparse systems of linear equations usually involve fairly complicated data structures and storage management. In most cases, the user of such subroutines simply wants top solve his problem and does not have to understand how the storage management is done, or how the matrix components are stored. Thus software for solving sparse systems of linear equations should be designed in such a way that it can insulate the user from these considerations, while still allowing the software to be used in a variety of ways.

During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.

The Graph Signal Processing (GSP) is a mathematical framework that extends the Discrete Signal Processing (DSP) tools such as filtering and signals decomposition to graph data structures. In this paper, we explore the application of the GSP framework to distributed wireless sensor networks to reduce the measured noise and/or estimate the signal of missing sensors. The context is that of distributed monitoring applications, such as the monitoring of large buildings, such as hospitals, public areas and farmlands. Using simulation tools, we analysed the ability of GSP in reducing the noise and in estimating sensor's data in different WSN scenarios. We modelled the sensor networks as Graph structures and apply Graph Shift and Graph Laplacian operations on such graph signals. The analysis of obtained results shows that GSP may represent a valuable tool in the considered scenarios with outstanding performance.

Hyperspectral image (HSI) is often corrupted by various kinds of noises. This letter proposes an innovative HSI denoising approach by leveraging the graph signal processing (GSP) theory and the low-rank (LR) matrix recovery model. With GSP, the piecewise smoothness (PWS) property of the HSI can be efficiently characterized, leading to a new regularization for HSI denoising, termed the adaptive weight graph total variation (AWGTV) regularization. Then, the denoising problem is formulated into a constrained optimization problem that incorporates the AWGTV and the LR property of the HSI. An augmented Lagrange multiplier method is adopted to solve the problem. Numerical experiments conducted on synthetic and real-world datasets and comparisons with existing methods demonstrate the effectiveness of the proposed denoising algorithm.

We compare the relative performances of two iterative schemes based on projection techniques for the solution of large sparse nonsymmetric systems of linear equations, encountered in the numerical solution of partial differential equations. The Block–Symmetric Successive Over‐Relaxation (Block‐SSOR) method and the Symmetric–Kaczmarz method are derived from the simplest of projection methods, that is, the Kaczmarz method. These methods are then accelerated using the conjugate gradient method, in order to improve their convergence. We study their behavior on various test problems and comment on the conditions under which one method would be better than the other. We show that while the conjugate‐gradient‐accelerated Block‐SSOR method is more amenable to implementation on vector and parallel computers, the conjugate‐gradient accelerated Symmetric–Kaczmarz method provides a viable alternative for use on a scalar machine.

There has been much recent interest in the use of incomplete factorizations of matrices, in conjunction with applications of the generalized conjugate gradient method, for approximating solutions of large sparse systems of linear equations. Underlying many of these recent developments is the theory of H-matrices, introduced by A. M. Ostrowski. In this note, further connections of the theory of incomplete factorizations of matrices with the theory of H-matrices are derived.

Generalized sampling of graph signals with the prior information based on graph fractional Fourier transform

The inverse natural convection problem (INCP) in a porous medium is a highly nonlinear problem because of the nonlinear convection and Forchheimer terms. The INCP can be converted into the minimization of a least-squares discrepancy between the observed and the modelled data. It has been solved using different classical optimization strategies that require a monotone descent of the objective function for recovering the unknown profile of the time-varying heat source function. In this investigation, we use this partial differential equation (PDE)-constrained optimization problem as a demanding test bed to compare the performance of several state-of-the-art variants of the conjugate gradients approach. We propose solving the INCP, using the scaled nonlinear conjugate gradient method: a low-cost and low-storage optimization technique. The method presented here uses the gradient direction with a particular spectral step length and the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno updating formula without any matrix evaluations. Two adaptive line search approaches are numerically studied in which there is no need for solving the sensitivity problem to obtain the step length directly, and are compared with an exact line search approach. We combine the proposed optimization scheme for INCP with a consistent-splitting scheme for solving systems of momentum, continuity and energy equations and a mixed finite-element method. We show a number of computational tests that demonstrate that the proposed method performs better than the classical gradient method by improving the number of iterations required and reducing the computational time. We also discuss some practical issues related to the implementation of the different methods.

A new hybrid CG-GAs approach for high sensitive optimization problems: With application for parameters estimation of FG nanobeams