1,721,012 research outputs found
Fast simulation of solid tumors thermal ablation treatments with a 3D reaction diffusion model☆
No full textAn efficient computational method for near real-time simulation of thermal ablation of tumors via radio frequencies is proposed. Model
simulations of the temperature field in a 3D portion of tissue containing the tumoral mass for different patterns of source heating can be used
to design the ablation procedure. The availability of a very efficient computational scheme makes it possible to update the predicted outcome of
the procedure in real time. In the algorithms proposed here a discretization in space of the governing equations is followed by an adaptive time
integration based on implicit multistep formulas. A modification of the ode15s MATLAB function which uses Krylov space iterative methods
for the solution of the linear systems arising at each integration step makes it possible to perform the simulations on standard desktop for much
finer grids than using the built-in ode15s. The proposed algorithm can be applied to a wide class of nonlinear parabolic differential equations
Sparsity promoting hybrid solvers for hierarchical bayesian inverse problems
Full text linkThe recovery of sparse generative models from few noisy measurements is an important and challenging problem. Many deterministic algorithms rely on some form of l1-l2 minimization to combine the computational convenience of the l2 penalty and the sparsity promotion of the l1. It was recently shown within the Bayesian framework that sparsity promotion and computational efficiency can be attained with hierarchical models with conditionally Gaussian priors and gamma hyperpriors. The related Gibbs energy function is a convex functional, and its minimizer, which is the maximum a posteriori (MAP) estimate of the posterior, can be computed efficiently with the globally convergent Iterated Alternating Sequential (IAS) algorithm [D. Calvetti, E. Somersalo, and A. Strang, Inverse Problems, 35 (2019), 035003]. Generalization of the hyperpriors for these sparsity promoting hierarchical models to a generalized gamma family either yield globally convex Gibbs energy functionals or can exhibit local convexity for some choices for the hyperparameters [D. Calvetti et al., Inverse Problems, 36 (2020), 025010]. The main problem in computing the MAP solution for greedy hyperpriors that strongly promote sparsity is the presence of local minima. To overcome the premature stopping at a spurious local minimizer, we propose two hybrid algorithms that first exploit the global convergence associated with gamma hyperpriors to arrive in a neighborhood of the unique minimizer and then adopt a generalized gamma hyperprior that promotes sparsity more strongly. The performance of the two algorithms is illustrated with computed examples
Tikhonov regularization and the L-curve for large discrete ill-posed problems
No full textAbstractDiscretization of linear inverse problems generally gives rise to very ill-conditioned linear systems of algebraic equations. Typically, the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible. Tikhonov regularization is one of the most popular regularization methods. A regularization parameter specifies the amount of regularization and, in general, an appropriate value of this parameter is not known a priori. We review available iterative methods, and present new ones, for the determination of a suitable value of the regularization parameter by the L-curve criterion and the solution of regularized systems of algebraic equations
Computable error bounds and estimates for the conjugate gradient method
No full textThe conjugate gradient method is one of the most popular iterative methods for computing approximate solutions of linear systems of equations with a symmetric positive definite matrix A. It is generally desirable to terminate the iterations as soon as a sufficiently accurate approximate solution has been computed. This paper discusses known and new methods for computing bounds or estimates of the A-norm of the error in the approximate solutions generated by the conjugate gradient method
The IAS-MEEG Package: A Flexible Inverse Source Reconstruction Platform for Reconstruction and Visualization of Brain Activity from M/EEG Data
Full text linkWe present a standalone Matlab software platform complete with visualization for the reconstruction of the neural activity in the brain from MEG or EEG data. The underlying inversion combines hierarchical Bayesian models and Krylov subspace iterative least squares solvers. The Bayesian framework of the underlying inversion algorithm allows to account for anatomical information and possible a priori belief about the focality of the reconstruction. The computational efficiency makes the software suitable for the reconstruction of lengthy time series on standard computing equipment. The algorithm requires minimal user provided input parameters, although the user can express the desired focality and accuracy of the solution. The code has been designed so as to favor the parallelization performed automatically by Matlab, according to the resources of the host computer. We demonstrate the flexibility of the platform by reconstructing activity patterns with supports of different sizes from MEG and EEG data. Moreover, we show that the software reconstructs well activity patches located either in the subcortical brain structures or on the cortex. The inverse solver and visualization modules can be used either individually or in combination. We also provide a version of the inverse solver that can be used within Brainstorm toolbox. All the software is available online by Github, including the Brainstorm plugin, with accompanying documentation and test data
An L-ribbon for large underdetermined linear discrete ill-posed problems
No full textThe L-curve is a popular aid for determining a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side vector, which is contaminated by errors of unknown size. However, for large problems, the computation of the L-curve can be quite expensive, because the determination of a point on the L-curve requires that both the norm of the regularized approximate solution and the norm of the corresponding residual vector be available. Recently, an approximation of the L-curve, referred to as the L-ribbon, was introduced to address this difficulty. The present paper discusses how to organize the computation of the L-ribbon when the matrix of the linear system of equations has many more columns than rows. Numerical examples include an application to computerized tomography
A regularizing Lanczos iteration method for underdetermined linear systems
No full textThis paper is concerned with the solution of underdetermined linear systems of equations with a very ill-conditioned matrix A, whose dimensions are so large to make solution by direct methods impractical or infeasible. Image reconstruction from projections often gives rise to such systems. In order to facilitate the computation of a meaningful approximate solution, we regularize the linear system, i.e., we replace it by a nearby system that is better conditioned. The amount of regularization is determined by a regularization parameter. Its optimal value is, in most applications, not known a priori. We present a new iterative method based on the Lanczos algorithm for determining a suitable value of the regularization parameter by the discrepancy principle and an approximate solution of the regularized system of equations. © 2000 Elsevier Science B.V
AN ITERATIVE METHOD FOR IMAGE RECONSTRUCTION FROM PROJECTIONS
No full textImage reconstruction from projections gives rise to large ill-conditioned linear systems of equations. The large size of the systems often makes solution by an iterative method attractive. The sensitivity of the solution to perturbations in the system of equations generally makes it necessary to regularize the system before solution. We describe how Tikhonov regularization and Richardson iteration can be combined to yield an efficient adaptive method that determines both a suitable regularization parameter and a solution of the associated regularized system of equations
A hierarchical Krylov–Bayes iterative inverse solver for MEG with physiological preconditioning
No full textThe inverse problem of MEG aims at estimating electromagnetic cerebral activity from measurements of the magnetic fields outside the head. After formulating the problem within the Bayesian framework, a hierarchical conditionally Gaussian prior model is introduced, including a physiologically inspired prior model that takes into account the preferred directions of the source currents. The hyperparameter vector consists of prior variances of the dipole moments, assumed to follow a non-conjugate gamma distribution with variable scaling and shape parameters. A point estimate of both dipole moments and their variances can be computed using an iterative alternating sequential updating algorithm, which is shown to be globally convergent. The numerical solution is based on computing an approximation of the dipole moments using a Krylov subspace iterative linear solver equipped with statistically inspired preconditioning and a suitable termination rule. The shape parameters of the model are shown to control the focality, and furthermore, using an empirical Bayes argument, it is shown that the scaling parameters can be naturally adjusted to provide a statistically well justified depth sensitivity scaling. The validity of this interpretation is verified through computed numerical examples. Also, a computed example showing the applicability of the algorithm to analyze realistic time series data is presented
Computational tools for calculating alternative muscle force patterns during motion: A comparison of possible solutions
No full textComparing the available electromyography (EMG) and the related uncertainties with the space of muscle forces potentially driving the same motion can provide insights into understanding human motion in healthy and pathological neuromotor conditions. However, it is not clear how effective the available computational tools are in completely sample the possible muscle forces. In this study, we compared the effectiveness of Metabolica and the Null-Space algorithm at generating a comprehensive spectrum of possible muscle forces for a representative motion frame. The hip force peak during a selected walking trial was identified using a lower-limb musculoskeletal model. The joint moments, the muscle lever arms, and the muscle force constraints extracted from the model constituted the indeterminate equilibrium equation at the joints. Two spectra, each containing 200,000 muscle force samples, were calculated using Metabolica and the Null-Space algorithm. The full hip force range was calculated using optimization and compared with the hip force ranges derived from the Metabolica and the Null-Space spectra. The Metabolica spectrum spanned a much larger force range than the NS spectrum, reaching 811N difference for the gluteus maximus intermediate bundle. The Metabolica hip force range exhibited a 0.3-0.4 BW error on the upper and lower boundaries of the full hip force range (3.4-11.3 BW), whereas the full range was imposed in the NS spectrum. The results suggest that Metabolica is well suited for exhaustively sample the spectrum of possible muscle recruitment strategy. Future studies will investigate the muscle force range in healthy and pathological neuromotor conditions
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