Abstract In fusion devices, the X-ray plasma emissivity contains essential information on magnetohydrodynamic activity, magnetic equilibrium and transport of impurities, in particular for tokamaks soft (SXR) energy range 0.1–20 keV. this context, tomography diagnostics are a key method to estimate local from given set line-integrated measurements. Unfortunately, reconstruction problem is mathem...

Methods: This study relies solely on simulations of a transmit-array head coil at 7T. The coil consisted of 8 stripline dipoles distributed every 40degrees on a cylindrical surface of 27.6-cm diameter, leaving an open space in front of the patient’s eyes. An eight-anatomical structure human head model (provided by Aarkid, East Lothian, Scotland) was placed at the centre of the coil. The same he...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

INTRODUCTION GRAPPA [1] reconstructs the missing k-space data by a linear combination of the acquired data using a set of weights obtained through calibrations. Several methods have been proposed in recent years to improve GRAPPA using localized coil calibration and variable density sampling [2], multicolumn multiline interpolation [3], regularization [4,5], reweighted least square [6], high-pa...

We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of g...

Abstract Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, results on convergence theory are based technical proofs and sometimes difficult to interpret. It is also often not clear how those translate into discrete, numerical setting. In this paper we present a new strategy study properties of method example re...

This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularization. Given a priori estimates on the covariance structure of errors in the measurement data b, and a suitable statistically-chosen σ, the Tikhonov regularized least squares functional J(σ) = ‖Ax − b‖2Wb + 1/σ 2‖D(x − x0)‖2, evaluated at its minimizer x(σ), approximat...

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

Tikhonov regularization approach and block motion model are used to solve super-resolution problem for face video data. Video is preprocessed by 2-D empirical mode decomposition method to suppress illumination artifacts for super-resolution.