In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are an...

Abstract. The reconstruction of Mercury's internal magnetic field enables us to take a look into the inner heart Mercury. In view BepiColombo mission, magnetosphere is simulated using hybrid plasma code, and multipoles are estimated from virtual spacecraft data three distinct methods: truncated singular value decomposition, Tikhonov regularization Capon's minimum variance projection. study show...

BACKGROUND Quantitative assessment of myocardial blood flow (MBF) from cardiovascular magnetic resonance (CMR) perfusion images appears to offer advantages over qualitative assessment. Currently however, clinical translation is lacking, at least in part due to considerable disparity in quantification methodology. The aim of this study was to evaluate the effect of common methodological differen...

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, thi...

We consider Tikhonov regularization of large linear discrete ill-posed problems with a regularization operator of general form and present an iterative scheme based on a generalized Krylov subspace method. This method simultaneously reduces both the matrix of the linear discrete ill-posed problem and the regularization operator. The reduced problem so obtained may be solved, e.g., with the aid ...

A multilinear reference tissue approach has been widely used recently for the assessment of neuroreceptor-ligand interactions with positron emission tomography. The authors analyzed this "multilinear method" with respect to its sensitivity to statistical noise, and propose regularization procedures that reduce the effects of statistical noise. Computer simulations and singular value decompositi...

Truncated singular value decomposition (TSVD) is a popular method for solving linear discrete ill-posed problems with a small to moderately sized matrix A. Regularization is achieved by replacing the matrix A by its best rank-k approximant, which we denote by Ak. The rank may be determined in a variety of ways, e.g., by the discrepancy principle or the L-curve criterion. This paper describes a ...

Straightforward solution of discrete ill-posed linear systems of equations or leastsquares problems with error-contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It ca...

In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using variable projection method. Based on truncated singular value decomposition method and Tikhonov regularization method, propose an improved which neither discards small values, nor treats all corrections. By fitting Mackey–Glass time series in exponential model, compare three methods, ...