Chen Greif

Bio: Chen Greif is an academic researcher from University of British Columbia. The author has contributed to research in topics: Linear system & Matrix (mathematics). The author has an hindex of 22, co-authored 67 publications receiving 1695 citations. Previous affiliations of Chen Greif include Tel Aviv University & PTC.

ℓ1-Sparse reconstruction of sharp point set surfaces

Abstract: We introduce an e1-sparse method for the reconstruction of a piecewise smooth point set surface. The technique is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that common objects, even geometrically complex ones, can typically be characterized by a rather small number of features. This, in turn, naturally lends itself to incorporating the powerful notion of sparsity into the model. The sparse reconstruction principle gives rise to a reconstructed point set surface that consists mainly of smooth modes, with the residual of the objective function strongly concentrated near sharp features. Our technique is capable of recovering orientation and positions of highly noisy point sets. The global nature of the optimization yields a sparse solution and avoids local minima. Using an interior-point log-barrier solver with a customized preconditioning scheme, the solver for the corresponding convex optimization problem is competitive and the results are of high quality.

On solving block-structured indefinite linear systems

Abstract: We consider 2 × 2 block indefinite linear systems whose (2, 2) block is zero. Such systems arise in many applications. We discuss two techniques that are based on modifying the (1, 1) block in a way that makes the system easier to solve. The main part of the paper focuses on an augmented Lagrangian approach: a technique that modifies the (1,1) block without changing the system size. The choice of the parameter involved, the spectrum of the linear system, and its condition number are discussed, and some analytical observations are provided. A technique of deflating the (1,1) block is then introduced. Finally, numerical experiments that validate the analysis are presented.

An Arnoldi-type algorithm for computing page rank

Abstract: We consider the problem of computing PageRank. The matrix involved is large and cannot be factored, and hence techniques based on matrix-vector products must be applied. A variant of the restarted refined Arnoldi method is proposed, which does not involve Ritz value computations. Numerical examples illustrate the performance and convergence behavior of the algorithm.

Preconditioners for the discretized time‐harmonic Maxwell equations in mixed form

Abstract: SUMMARY We introduce a new preconditioning technique for iteratively solving linear systems arising from flnite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators, but are augmentation-free and Schur complement-free. We provide a complete spectral analysis, and show that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations are accompanied by numerical results that demonstrate the scalability of the proposed approach. Copyright c ∞ 2006 John Wiley & Sons, Ltd.

Numerical solution of saddle point problems

Abstract: Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

Robot vision

Abstract: A scheme is developed for classifying the types of motion perceived by a humanlike robot. It is assumed that the robot receives visual images of the scene using a perspective system model. Equations, theorems, concepts, clues, etc., relating the objects, their positions, and their motion to their images on the focal plane are presented. >

Probability and Random Processes

Abstract: tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.