Imaging and Computing Group

Imaging and Computing Seminar — Fall 2013

• Th 10/03, at 4:00pm, in room E17-136

  Athanasios Polimeridis, EECS, MIT

  Fast Integral Equation Solver for EM Analysis of High-Field MRI

  Abstract: We describe a fast method for estimating the fields in realistic human body models. Such simulations are needed for coil and RF pulse excitation design, specific absorption rate (SAR) prediction, and the design of high-field and parallel-transmission MRI. From an electromagnetic modeling perspective, the human body is a strongly inhomogeneous scatterer and the numerical analysis in this case is by no means trivial. In addition there is a strong drive in MRI technology for higher resolution, which translates to higher frequency. The combination of high dielectric contrast and high frequency suggests a âhostileânumerical solvers, most commonly based on partial differential equations methods, fail to meet the ever increasing requirements for ultra-fast computations. In this talk, we present a new class of volume integral equation methods that offer an ideal platform for customized fast algorithms where maximal use of a specific setting is possible. In the proposed approach the unknown physical quantities can be fairly represented on uniform tessellations, i.e., volumes decomposed into voxels, which is actually the natural setting for MRI data. In this case, the governing integral kernels are translational invariant and the associated matrix-vector products can be accelerated with the help of FFT. Also, the most computational intensive parts of our solver are embarrassingly parallelizable and involve simple operations that can be easily handled by GPU-accelerated libraries. The accuracy and efficiency of the proposed framework is demonstrated in a realistic scenario that considers electromagnetic scattering from a human body model. The remarkable performance of our solver can be attributed mainly to two key-features: the correct Galerkin discretization that leads to fast convergence of the iterative solver without the need of preconditioning, and the reduction of the original volume-volume integrals to purely surface-surface integrals with smoother kernels, which allows fast and accurate computation of the associated matrix element by means of DEMCEM, an open-source software. Our novel volume integral equation solver is currently being incorporated together with other in-house algorithms in a general computational framework for addressing a wide range of challenging applications in MRI device optimization; a project in collaboration with MRI experts from MIT and Harvard/MGH.

  About the speaker: Athanasios G. Polimeridis received the Diploma and the Ph.D. from the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, in 2003 and 2008, respectively. From 2008 to 2012, he was a Post-Doctoral Research Associate at EPFL, Switzerland. Currently he is a Post-Doctoral Research Associate at MIT, where he is a member of the Computational Prototyping Group at the Research Laboratory of Electronics. His research interests revolve around computational methods for problems in physics and engineering (Electromagnetics, Casimir forces, MRI), with emphasis on the development and implementation of integral-equation based algorithms. In 2012, he was awarded a Swiss National Science Foundation Fellowship for Advanced Researchers.

• Th 10/10, at 4:00pm, in room E17-136

  Bart Vandereycken, PACM, Princeton

  Differential geometry for rank-structured tensors from a numerical analysis perspective

  Abstract: Many practical problems lead to high-dimensional equations with an extremely large number of variables that scale exponentially with the dimension; take for example parametric PDEs and the Schroedinger equation. Low-rank tensor techniques are a popular technique to solve such equations since they can circumvent this exponential scaling, known as the curse of dimensionality.

  Certain rank-structured tensors were recently shown to admit smooth structures that turn them into differential manifolds, for example, tensor train (TT) or matrix product states (MPS) in [1,2], and hierarchical Tucker (HT) in [3]. In this talk, I will discuss why treating these tensors as manifolds can be useful from a numerical linear algebra perspective when solving high-dimensional equations.

  In particular, I will explain how the dynamical low-rank algorithm [4] can be used to approximate tensor differential equations in the HT/TT/MPS formats. In this approach, also known as the Dirac-Frenkel variational principle, the time derivative of the tensor to be approximated is projected onto the time-dependent tangent space of the approximation manifold along the solution trajectory. I will discuss the approximation properties of this approach and introduce an explicit but surprisingly stable time-stepping scheme that extends the matrix version of [5].

  Based on joint work with C. Lubich and I. Oseledets.

  • [1] S. Holtz, T. Rohwedder, and R. Schneider. On manifolds of tensors of fixed TT-rank. Num. Math., 2012.
  • [2] J. Haegeman, T. J. Osborne, and F. Verstraete.  Post-matrix product state methods: To tangent space and beyond. Phys. Rev. B, 2013.
  • [3] A. Uschmajew and B. Vandereycken. The geometry of algorithms using hierarchical tensors. Lin. Alg. Appl., 2013.
  • [4] C. Lubich, T. Rohwedder, R. Schneider, B. Vandereycken, Dynamical approximation of hierarchical Tucker and tensor-train tensors. SIAM J. Matrix Anal. Appl., 2013.
  • [5] C. Lubich, I. Oseledets. A projector-splitting integrator for dynamical low-rank approximation. Submitted to BIT, 2013.

• Th 11/07, at 4:00pm, in room E17-136

  Shuchin Aeron, ECE, Tufts

  Methods for Multilinear Data Analytics

  Abstract: In this talk we will focus on statistical signal processing methods for multilinear data (tensors) analytics and consider several problems - (a) Tensor completion from missing entries (b) Unsupervised clustering of tensor data and (c) Collaborative filtering of multilinear data for online learning and prediction. Most approaches for multilinear data analytics are based on tensor factorizations and the performance depends on the particular factorization used. In this context, we exploit a recently proposed tensor factorization, by Kilmer and Martin, referred to as the t-SVD, which is an operator theoretic approach for tensor analysis. We apply the resulting notion of tensor multi-rank and its convex relaxation to derive globally optimal algorithms with provable performance guarantees. We show the performance of these algorithms on 5-D and 4-D pre-stack seismic data completion, video completion/prediction from missing pixels, and tensor robust PCA for separating low rank tensors from sparse corruptions. In addition to t-SVD we exploit the linear algebraic structure arising from this tensor analysis, namely that the set of oriented matrices forms a free module over a commutative ring (of oriented vectors or tubes) with identity, and propose a robust method for clustering images treated as 2-D tensors.

  Bio: Shuchin Aeron is currently an assistant professor in the department of ECE at Tufts University. He received his PhD in ECE from Boston University in 2009. From 2009 to 2011 he was a post-doctoral research fellow at Schlumberger-Doll Research (SDR), Cambridge, MA where he worked on signal processing answer products for borehole acoustics. He has several patents and the proposed workflows are currently implemented in logging while drilling tools. He is the recipient of the best thesis award from both the college of engineering and the department of ECE in 2009. He received the Center of Information and Systems Engineering (CISE) award from Boston University in 2006 and an Schlumberger-Doll Research grant in 2007.

• Th 12/12, at 4:00pm, in room E17-136

  Susan Minkoff, UT Dallas

  TBA

• Seminar
• Fall 2013
• Spring 2013
• Fall 2012
• Spring 2012
• Fall 2011
• Spring 2011
• Fall 2010
• Spring 2010
• Fall 2009