Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Conductivity reconstructions using real data from a new planar electrical impedance tomography device
2013
Abstract In this paper, we present results of reconstructions using real data from a new planar electrical impedance tomography device developed at the Institut fur Physik, Johannes Gutenberg Universitat, Mainz, Germany. The prototype consists of a planar sensing head of circular geometry, and it was designed mainly for breast cancer detection. There are 12 large outer electrodes arranged on a ring of radius cm where the external currents are injected, and a set of 54 point-like high-impedance inner electrodes where the induced voltages are measured. Two direct (i.e. non-iterative) reconstruction algorithms are considered: one is based on a discrete resistor model, and the other one is an …
Shape design optimization in 2D aerodynamics using Genetic Algorithms on parallel computers
1996
Publisher Summary This chapter presents two Shape Optimization problems for two dimensional airfoil designs. The first one is a reconstruction problem for an airfoil when the velocity of the flow is known on the surface of airfoil. The second problem is to minimize the shock drag of an airfoil at transonic regime. The flow is modeled by the full potential equations. The discretization of the state equation is done using the finite element method and the resulting non-linear system of equations is solved by using a multi-grid method. The non-linear minimization process corresponding to the shape optimization problems are solved by a parallel implementation of a genetic algorithm (GA). Some n…
Models and solution methods for the uncapacitatedr-allocationp-hub equitable center problem
2017
Hub networks are commonly used in telecommunications and logistics to connect origins to destinations in situations where a direct connection between each origin–destination (o-d) pair is impractical or too costly. Hubs serve as switching points to consolidate and route traffic in order to realize economies of scale. The main decisions associated with hub-network problems include (1) determining the number of hubs (p), (2) selecting the p-nodes in the network that will serve as hubs, (3) allocating non-hub nodes (terminals) to up to r-hubs, and (4) routing the pairwise o-d traffic. Typically, hub location problems include all four decisions while hub allocation problems assume that the valu…
Stochastic description of traffic breakdown
2003
We present a comparison of nucleation in an isothermal-isochoric container with traffic congestion on a one-lane freeway. The analysis is based, in both cases, on the probabilistic description by stochastic master equations. Further we analyze the characteristic features of traffic breakdowns. To describe this phenomenon we apply the stochastic model regarding the jam emergence to the formation of a large car cluster on the highway.
Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution
2012
SUMMARY We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-expone…
Variational multiframe restoration of images degraded by noisy (stochastic) blur kernels
2013
This article introduces and explores a class of degradation models in which an image is blurred by a noisy (stochastic) point spread function (PSF). The aim is to restore a sharper and cleaner image from the degraded one. Due to the highly ill-posed nature of the problem, we propose to recover the image given a sequence of several observed degraded images or multiframes. Thus we adopt the idea of the multiframe approach introduced for image super-resolution, which reduces distortions appearing in the degraded images. Moreover, we formulate variational minimization problems with the robust (local or nonlocal) L^1 edge-preserving regularizing energy functionals, unlike prior works dealing wit…
Iterative Regularization Techniques in Image Reconstruction
2000
In this survey we review recent developments concerning the efficient iterative regularization of image reconstruction problems in atmospheric imaging. We present a number of preconditioners for the minimization of the corresponding Tikhonov functional, and discuss the alternative of terminating the iteration early, rather than adding a stabilizing term in the Tikhonov functional. The methods are examplified for a (synthetic) model problem.
Cell-average multiresolution based on local polynomial regression. Application to image processing
2014
In Harten (1996) [32] presented a general framework about multiresolution representation based on four principal operators: decimation and prediction, discretization and reconstruction. The discretization operator indicates the nature of the data. In this work the pixels of a digital image are obtained as the average of a function in some defined cells. A family of Harten cell-average multiresolution schemes based on local polynomial regression is presented. The stability is ensured by the linearity of the operators obtained and the order is calculated. Some numerical experiments are performed testing the accuracy of the prediction operators in comparison with the classical linear and nonli…
Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images
2016
Abstract Cell-average multiresolution Harten׳s algorithms have been satisfactorily used to compress data. These schemes are based on two operators: decimation and prediction. The accuracy of the method depends on the prediction operator. In order to design a precise function, local polynomial regression has been used in the last years. This paper is devoted to construct a family of non-separable two-dimensional linear prediction operators approximating the real values with this procedure. Some properties are proved as the order of the scheme and the stability. Some numerical experiments are performed comparing the new methods with the classical linear method.
Non-linear Local Polynomial Regression Multiresolution Methods Using $$\ell ^1$$-norm Minimization with Application to Signal Processing
2015
Harten’s Multiresolution has been developed and used for different applications such as fast algorithms for solving linear equations or compression, denoising and inpainting signals. These schemes are based on two principal operators: decimation and prediction. The goal of this paper is to construct an accurate prediction operator that approximates the real values of the signal by a polynomial and estimates the error using \(\ell ^1\)-norm in each point. The result is a non-linear multiresolution method. The order of the operator is calculated. The stability of the schemes is ensured by using a special error control technique. Some numerical tests are performed comparing the new method with…