Ariela Sofer - Academia.edu (original) (raw)

Papers by Ariela Sofer

SIAM Journal on Matrix Analysis and Applications, 1996

We study preconditioning strategies for linear systems with positive-de nite matrices of the form... more We study preconditioning strategies for linear systems with positive-de nite matrices of the form Z T GZ, where Z is rectangular and G is symmetric but not necessarily positive de nite. The preconditioning strategies are designed to be used in the context of a conjugate-gradient iteration, and are suitable within algorithms for constrained optimization problems. The techniques have other uses, however, and are applied here to a class of problems in the calculus of variations. Numerical tests are also included.

IEEE Transactions on Medical Imaging, Apr 1, 2000

Interior-point methods have been successfully applied to a wide variety of linear and nonlinear p... more Interior-point methods have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on path-following interior-point methodology, for performing regularized maximum-likelihood (ML) reconstructions on three-dimensional (3-D) emission tomography data. The algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant). We propose two methods, a primal method which updates only the primal image variables and a primal-dual method which simultaneously updates the primal variables and the Lagrange multipliers. A parallel implementation permits the interior-point methods to scale to very large reconstruction problems. Termination is based on well-defined convergence measures, namely, the Karush-Kuhn-Tucker first-order necessary conditions for optimality. We demonstrate the rapid convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed methods can readily be applied to solve the regularized, weighted least squares reconstruction problem.

IEEE Transactions on Nuclear Science, Jun 1, 1997

The use of paired, opposing position-sensitive phototube scintillation cameras (SCs) operating in... more The use of paired, opposing position-sensitive phototube scintillation cameras (SCs) operating in coincidence for small animal imaging with positron emitters is currently under study. Because of the low sensitivity of the system even in 3D mode and the need to produce images with high resolution, it was postulated that a 3D expectation maximization (EM) reconstruction algorithm might be well suited for this application. We investigated six reconstruction algorithms for the 3D SC PET camera: 2D filtered back-projection (FBP), 3D reprojection (3DRP), 2D EM, 3D EM, 2D ordered subset EM (OSEM), and 3D OSEM. Noise was assessed for all slices by the coefficient of variation in a simulated uniform cylinder. Resolution was assessed from a simulation of 15 point sources in the warm background of the uniform cylinder. At comparable noise levels, the resolution achieved with EM and OSEM (0.9-mm to 1.2-mm) is significantly better than that obtained with FBP or 3DRP (1.5-mm to 2.0-mm.) Images of a rat skull labeled with 18 F-fluoride suggest that 3D EM and 3D OSEM can improve image quality of a small animal PET camera.

ACM Transactions on Mathematical Software, Dec 1, 1992

Siam Journal on Optimization, Aug 1, 1998

The theory of self-concordance has been used to analyze the complexity of interiorpoint methods b... more The theory of self-concordance has been used to analyze the complexity of interiorpoint methods based on Newton's method. For large problems, it may be impractical to use Newton's method; here we analyze a truncated-Newton method, in which an approximation to the Newton search direction is used. In addition, practical interior-point methods often include enhancements such as extrapolation that are absent from the theoretical algorithms analyzed previously. We derive theoretical results that apply to such an algorithm, an algorithm similar to a sophisticated computer implementation of a barrier method. The results for a single barrier subproblem are a satisfying extension of the results for Newton's method. When extrapolation is used in the overall barrier method, however, our results are more limited. We indicate (by both theoretical arguments and examples) why more elaborate results may be di cult to obtain.

In the tomographic imaging problem, images are reconstructed from a set of measured projections. ... more In the tomographic imaging problem, images are reconstructed from a set of measured projections. Iterative reconstruction methods are computationally intensive alternatives to the more traditional Fourier-based methods. Despite their high cost, the popularity of these methods is increasing because of the advantages they pose. Although numerous iterative methods have been proposed over the years, all of these methods can be shown to have a similar computational structure. This paper presents a parallel algorithm that we originally developed for performing the expectation maximization algorithm in emission tomography. This algorithm is capable of exploiting the sparsity and symmetries of the model in a computationally efficient manner. Our parallelization scheme is based upon decomposition of the measurement-space vectors. We demonstrate that such a parallelization scheme is applicable to the vast majority of iterative reconstruction algorithms proposed to date.

Springer eBooks, 2001

This paper presents a new image-guided prostate biopsy system under development. The system featu... more This paper presents a new image-guided prostate biopsy system under development. The system features a 3-D prostate cancer distribution atlas and new biopsy protocols optimized based on the cancer atlas using a nonlinear integer programming approach. Both the cancer atlas and the optimal protocols are being dynamically registered and superimposed onto the trans-rectal ultrasound images during live-patient biopsy procedures. Clear visual guidance will be provided to the physicians by color-coded spots on top of the ultrasound images, which represent best possible targets for biopsy. Clinical test will be performed to evaluate the system.

ORSA journal on computing, Feb 1, 1993

A logarithmic barrier method is applied to the solution of a nonlinear programming problem with i... more A logarithmic barrier method is applied to the solution of a nonlinear programming problem with inequality constraints. An approximation to the Newton direction is derived that avoids the ill conditioning normally associated with barrier methods. This approximation can be used within a truncated-Newton method, and hence is suitable for large-scale problems; the approximation can also be used in the context of a parallel algorithm. Enhancements to the basic barrier method are described that improve its efficiency and reliability. The resulting method can be shown to be a primal-dual method when the objective function is convex and all of the constraints are linear. Computational experiments are presented where the method is applied to 1000-variable problems with bound constraints. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Springer eBooks, Nov 21, 2005

Page 1. Mathematical Programming 45 (1989) 529-546 529 North-Holland BLOCK TRUNCATED-NEWTON METHO... more Page 1. Mathematical Programming 45 (1989) 529-546 529 North-Holland BLOCK TRUNCATED-NEWTON METHODS FOR PARALLEL OPTIMIZATION Stephen G. NASH* and Ariela SOFER** Operations Research and Applied ...

Journal of the Operational Research Society, Oct 1, 1996

Appendices A, B, C, and D cover the approximation of point processes, phase-type distributions of... more Appendices A, B, C, and D cover the approximation of point processes, phase-type distributions of DFR/IFR, majorization, and computational issues. The Reference section, consisting of 84 items, covers up-to-date related research. Overall, I found the book an interesting work. Certainly, it will be a useful source book for specialists in this area, and a very good starting book for new researchers who would like to conduct research in the area.

Lecture notes in statistics, 1986

The isotone regression problem of finding a least squares isotone sequence is extended by imposin... more The isotone regression problem of finding a least squares isotone sequence is extended by imposing order restrictions also on higher order differences of the sequence. This new problem has a number of applications, and one example in the area of software reliability is presented.

Siam Journal on Optimization, 2001

In emission tomography, images can be reconstructed from a set of measured projectionsusing a max... more In emission tomography, images can be reconstructed from a set of measured projectionsusing a maximum likelihood (ML) criterion. In this paper, we present a primal-dual algorithmfor large-scale three-dimensional image reconstruction. The primal-dual method is specialized to theML reconstruction problem. The reconstruction problem is extremely large; in several of our datasets the Hessian of the objective function is the product of

Mathematical Programming, May 1, 1991

Most nonlinear programming problems consist of functions which are sums of unary functions of lin... more Most nonlinear programming problems consist of functions which are sums of unary functions of linear functions. Advantage can be taken of this form to calculate second and higher order derivatives easily and at little cost. Using these, high order optimization techniques such as Halley's method can be utilized to accelerate the rate of convergence to the solution. These higher order derivatives can also be used to compute second order sensitivity information. These techniques are applied to the solution of the classical chemical equilibrium problem.

A good preconditioner can accelerate the convergence of an optimization algorithm. We have develo... more A good preconditioner can accelerate the convergence of an optimization algorithm. We have developed some nasty-looking formulas for preconditioners that can be used for constrained optimization. But appearances can be deceiving. The formulas work well, and they are easy to use (at least for the computer). Although these preconditioners were developed with constrained optimization in mind, they have other uses. In particular we have applied them to a class of problems that arise in the calculus of variations.

Volume 47, Number 4, August 2020, 2020

The 2020 INFORMS Annual Meeting in itself will be a paradigm shift For the first time ever, the m... more The 2020 INFORMS Annual Meeting in itself will be a paradigm shift For the first time ever, the meeting will be entirely virtual With the impact of the COVID-19 pandemic continuing to be felt across the globe, this new format ensures that the global INFORMS community stays safe, healthy and well-connected during these challenging times From Nov 8-11, 2020, the inaugural Virtual INFORMS Annual Meeting will feature more than 3,500 synchronous and asynchronous presentations from O R and analytics professionals across the globe

Encyclopedia of Operations Research and Management Science

Electronic Systems Effectiveness and Life Cycle Costing, 1983

We suggest that users are interested solely in the quality of predictions which can be obtained f... more We suggest that users are interested solely in the quality of predictions which can be obtained from software reliability models. Some ways of analysing the quality of predictions are proposed and several models and inference procedures are compared on real software failure data sets. We conclude that some predictions are extremely poor: notably those arising from ML analysis of the Jelinski-Moranda model. Others seem quite good. We suggest promising areas for future work.